Organic quantum materials: A review

Interests in organic quantum materials (OQMs) have been explosively growing in the field of condensed physics of matter due to their rich chemistry and unique quantum properties. They are strongly correlated systems and show novel electromagnetic performance such as high‐temperature superconducting, quantum sensing, spin electronics, quantum dots, topological insulating, quantum Hall effects, spin liquids, qubits, and so forth, which exhibit promising prospects in information communication and thus facilitate the construction of a modern intelligent society. This article reviews recent developments in the research on the electromagnetic characteristics of OQMs. We mainly give an overview on the progress of superconductors and quantum spin liquids based on organic materials and describe their possible mechanisms. Numerous experimental findings exhibit new exciton interactions and provide insights into exotic electronic properties. Finally, their association and strategies for realizing multiple quantum states in one system are discussed.


| INTRODUCTION
Over the past decades, studies on quantum materials (QMs) have been dramatically growing due to their exotic properties showing great potential in quantum computation. [1][2][3] Scientists argue that their nontrivial properties may provide a new way for highly efficient and low-cost data communication, thus starting a huge revolution in the fields of information, energy, and artificial intelligence (AI). [4][5][6] The future smart community requires an AI that can perform harsh and numerous calculations like human brains. 7,8 As the building blocks of an artificial brain network, artificial synapses should mimic the data processing behaviors of biological ones, which exhibit dynamic responses towards signals. 9,10 QMs are extensively attractive in this field because of their highly controllable electronic structures and nonlinear performance. 11 Through proper phase control in QMs, exotic and unprecedented electromagnetic properties like superconductivity may be obtained, advancing the realization of brain-inspired functions. 12,13 Hence, QMs play a vital role in developing an intelligent society.
QMs are those whose properties cannot be fully described by classical behaviors of particles and originate from novel quantum effects. [14][15][16] In classical materials, physical performance is explainable by particle interactions, even additional low-level quantum treatment toward electrons is necessary to describe their behaviors comprehensively. 17 For example, ion motion is considered the consequence of electrostatic interactions, but the complete explanation of the motion asks for a quantum mechanical description of electronic states. 18 Differently, classical theories do not explain the effects observed in QMs (like quantum fluctuation and spin entanglements). Interactions of degrees of freedom (lattice, charge, orbital, and spin) give rise to complicated electronic states. 19 Thereby, exotic phenomena, such as quantum hall effects, 20,21 topological insulators, 22 spin liquids, 23 and superconductivity, 24 are observed. While QMs were synthesized long ago, relevant investigations about their quantum effects are challenging and sometimes very confusing because of their complicated states. Different groups obtained opposite results in the same material system, making the exploration much more difficult and challenging.
Organic QMs (OQMs) provide an excellent platform for studying underlying mechanisms for exotic effects due to easy modification of their structures, thus offering opportunities to understand the contribution of various atom groups to properties. The electromagnetic performance of OQMs is the key research point for their promising prospects in industry fields. In this article, we review the previous works on the electromagnetic characteristics of OQMs, which mainly consist of organic superconductors and quantum spin liquids, and introduce possible mechanisms responsible for these quantum properties. In Section 2, we describe critical experimental findings in organic superconductors and possible explanations for the superconductivity nature. Section 3 summarizes possible spin liquid candidates and reveals their physical essence. In Section 4, we present the connection between superconducting and quantum disorder states.

| ORGANIC SUPERCONDUCTORS
Superconductors (SCs) refer to materials that show zero resistivity and Meissner effects. 25 Organic SCs (OSCs) have been extensively attractive as they provide flexible and modifiable systems for the investigation of superconductivity and many-body effects. 26,27 Observation of unusual results gives a general recognition that OSCs are unconventional SCs [28][29][30] because their behaviors are not well explainable by classical Bardeen-Cooper-Schrieffer (BCS) theory, where electron-phonon coupling should be responsible. 31 Instead, in OSCs, electrons interact with each other, and such electron correlation is believed as the origin of unconventional superconductivity. 32 The main types of OSCs are as follows: charge transfer salts, aromatic hydrogens intercalated with metals, alkali-doped fulleride, and magic-angle graphene. The following section introduces their state properties and discusses proposed mechanisms for superconductivity. Relevant phase diagrams are presented as well.

| Charge transfer salts
There are two main types of superconducting charge transfer (CT) salts: (TM) 2 X salts (also called Bechgaard salts) and (ET) 2 X salts, where TM is TMTSF (tetramethyl-tetraselenafulvalene) or TMTTF (tetramethyl-tetraselenafulvalene), ET is Bis(ethylenedithio)tetrathiafulvalene, and X is a counterpart anion. Since few new SCs based on CT salts have been reported in the past decade, in this part, we will briefly describe their characteristics. More details can be seen in other reviews. 33 39 a series of SCs were discovered, among which (TMTSF) 2 ClO 4 was the only ambientpressure OSC. 40 Besides, superconductivity was observed in (TMTTF) 2 X salts as well. 41,42 Commonly, T c of (TM) 2 X salts is around several kelvins, and pressure is needed to trigger superconductivity except (TMTSF) 2 ClO 4 . 43 Figure 1 illustrates the structures of typical donors used in CT salt-based OSCs. In (TM) 2 X salts, planar TM molecules form infinite stacks along a axis. 44 Their short intermolecular distances produce strong π orbital overlap and make the crystals highly conductive along a axis. In comparison, the conductivity along other directions is significantly smaller due to the reduced degrees of overlap. 45 Therefore, all these salts crystallize in triclinic structures, and their quasi-one-dimensional (1D) electronic structures permit superconducting transitions at high pressures. 46 (TM) 2 X salts can present various ground states by controlling their chemical or external pressures. 47 Figure 2 shows a general pressure-temperature phase diagram of (TM) 2 X salts. 48 Compared with (TMTSF) 2 X salts, the electronic structure dimensionality of (TMTTF) 2 X salts is smaller, leading to stronger electron correlation. With the same anion, (TMTTF) 2 PF 6 becomes insulating at 230 K at ambient pressure due to electron localization, 49 while (TMTSF) 2 PF 6 is still metallic. 50 As temperature decreases, (TMTTF) 2 PF 6 enters the spin-Peierls state with condensed spin chains. 51 Increasing pressure would lead to more intense intermolecular orbital overlap and reduced system dimensionality. As a result, applying pressure allows (TMTTF) 2 PF 6 to access various states and eventually become superconducting at 50 kbar, 52,53 higher than that of (TMTSF) 2 PF 6 .
Extensive studies have attempted to reveal the pairing mechanism; however, it is still a puzzle. In the early stage, the salts were considered as conventional SCs. Specific heat results of (TMTSF) 2 ClO 4 were interpreted as the presence of spin fluctuations. 54 Defects by irradiation were proposed to destroy cooper pairs and reduce T c . 55 However, the appearance of uncommon results made the superconductivity nature doubtful. For example, (TMTSF) 2 ClO 4 showed the positive T 3 dependence of spin-lattice relaxation rate T 1 −1 under T c , 56 while BCS SCs suggest that the rate should be enhanced in the superconducting state. The rate decrement indicated a superconducting gap function with linear nodes. In contrast, a nodeless gap function was also obtained in this salt, suggested by the lack of low-energy electronic excitations. 57 Abrikosov et al. 58 pointed out that T c suppression by impurities in (TMTSF) 2 PF 6 indicated the triplet pairing, which was supported by larger upper critical field Hc 2 in (TMTSF) 2 64 Subsequently, fieldangle-resolved specific heat data of the same compound indicated the spin-singlet superconductivity, 65 which was also confirmed by the emergence of Knight shift in its low-field phase. 66 Furthermore, no evident gap nodes were discovered. In summary, one should note that there is no definite decision on the superconductivity nature of (TM) 2 X SCs for obtained controversial results. More efforts should be paid to understand the discrepancy. Conductive ET layers are separated by insulating anion layers, resulting in anisotropic physical properties. 70 In κ-phases, pairs of ET molecules are dimerized and orthogonal, 71,72 while ETs and anions commonly adopt segregated-stacking modes in others. 73 Strong ET dimerization produces hall-filling bands of κ-(ET) 2 X salts, leading to the Mott transition due to the competition between Coulomb interactions and the kinetic energy. 74 Noted that superconductivity would be enhanced near the transition, OSCs based on κ-(ET) 2 X salts are widely studied. Figure 3 illustrates the phase diagram of κ-(ET) 2 X salts where U stands for on-site repulsion and t is the transfer integral. 75 The values of U/t suggest the strength of Coulomb interaction. Anion difference induces changes in chemical pressure inside the salts and then controls U/t values. For X = CuN(CN) 2 Cl, the salt with large U/t is insulating at ambient conditions for localized charge, 76 while the resistivity for X = CuN (CN) 2 Br is smaller due to reduced U/t value. 77 Applying external pressure can bring these salts to pass the phase boundary and eventually become superconductive. Besides, antiferromagnetic and superconducting states are very close, and sometimes they can coexist, indicating that antiferromagnetic fluctuations may play a role in the superconducting transition. 78,79 As seen in Figure 1, twisted ethylene-terminal groups of ET molecules allow more intense molecular orbital overlap than TM molecules, giving rise to 2D electronic structures and higher T c of (ET) 2 X salts. 80,81 The recorded highest T c reaches 11.6 K for κ-(ET) 2 CuN(CN) 2 Br at ambient pressure, 82 and 14.2 K for β′-(ET) 2 ICl 2 upon 82 kbar. 83 Besides temperature and pressure, magnetic field was found to trigger superconductivity in λ-(BETS) 2 FeCl 4 , which became superconducting when the in-plane magnetic field was in the range from 18 to 41 T. 84,85 The superconductivity was induced by a small internal magnetic field from Jaccarino-Peter field compensation effect. 86 Although NMR experiment results clarify the singlet pairing in ET salts, [87][88][89] 92 pointed out the existence of an unconventional coupling way in κ-(ET) 2 CuN(CN) 2 Br instead of electronphonon coupling. On the other hand, isotope effects predicted by BCS theory work well in (ET) 2 X salts, 93 except that T c was enhanced by the substitution of hydrogen atoms by deuterium, explained by the result of the change in the internal lattice pressure. 94 By replacing central atoms to avoid this pressure effect, T c reduced as expected, indicating strong electron-photon coupling. 95 Enhanced thermal conductivity of ET salts in the superconducting state was considered as the result of an increased phonon mean free path. 96,97 Inelastic neutron scattering results 98,99 and Raman spectra of salts 100,101 also suggested the coupling between electrons and phonons. Results about order parameter symmetry are also questionable. The absence of the Hebel-Slichter peak commonly appearing in conventional SCs, 102 and temperature dependence of 1/T 1 T in β″-(ET) 2 SF 5 CH 2 CF 2 SO 3 were interpreted as the signature of line nodes and against s-wave pairing. 103 The constant value of 1/T 1 T in the normal state implied charge fluctuations-mediated pairing instead of magnetic fluctuations, which would enhance it. Studies in scanning tunneling spectroscopy [104][105][106] and penetration depth 107 for ET salts also revealed line nodes of gap functions. However, specific-heat measurements suggested nodeless gaps due to the exponential disappearance of electronic specific heat under T c , 81 while surface impedance tests indicated superconducting gaps without nodes as well. 108 To conclude, the inconclusive phenomena cannot decide which coupling mechanism mediates the singlet pairing in OSCs based on ET salts, and the pairing symmetry is unclear. Data like specific heat are isotropic, which cannot detect gap differences in various directions, and applying a magnetic field may change gap symmetry. 109 To explain these controversies, we should develop more test tools sensitive to directions and phases.

| Metal intercalated aromatic hydrogens
Organic compounds upon metal doping are potential SCs, as firstly demonstrated in K-doped graphite KC 8 F I G U R E 3 Phase diagram of κ-(ET) 2 X salts. Reproduced with permission: Copyright 2009, American Physical Society. 75 with T c of 0.14 K. 110 Subsequently, other superconductive graphite intercalated compounds (GICs) were developed, such as LiC 2 , 111 NaC 2 , 112 CaC 6 , and YbC 6 , 113 where T c was 1.9, 5, 11.5, and 6.5 K respectively. Metal atoms are intercalated between adjacent or multiple graphitic planes, resulting in CT. 114 It is proposed that the superconductivity originates from CT and short interplanar distance. 115 Thus, metal doping is a significantly efficient strategy to modify the electronic structures of materials, leading to fantastic properties like superconductivity.
Aromatic hydrocarbons (AHs) consist of benzene rings and possess (4n + 2) π electrons, resulting in a high degree of electron delocalization. 116,117 Their unique structures can be considered as one part of a graphene sheet. Inspired by GIC-based SCs, Mitsuhashi et al. developed superconducting K 3.3 picene and found two phases with T c of 7 K and 18 K, respectively, 118 revitalizing great interests in aromatic SCs. In the next few years, several SCs based on metal-doped AHs were discovered: K or Rb-doped phenanthrene (T c was around 5 K) 119 ; K 3 coronene (multiple superconducting phases with T c of 3.5, 7, 11, and 15 K, respectively), 120 and K 3 1,2:8, 9-dibenzopentacene (T c of 33 K), 121 which has the highest T c under ambient pressure among reported aromatic SCs so far. The T c increase from phenanthrene, picene to 1,2:8,9-dibenzopentacene with benzene rings from 3, 5 to 7 indicates that a higher T c may be realized if an AH with longer chains is employed. Here we summarize all reported superconducting AHs in Figure 4. Most AHs are polycyclic compounds, where their benzene rings are fused linearly or in zig-zag conformation. Also, these benzene rings can be connected through C-C single bonds, as appearing in p-terphenyl, biphenyl, and 1,3,5-triphenylbenzene.
In Figure 5, we compare the T c difference of aromatic SCs listed above except for doped p-terphenyl for its doubtful results. Noted that one metal-doped AH system may have different superconductive phases. Here, we list their highest T c to analyze. As the number of benzene rings (n) increases, T c tends to be enhanced. With the same n, doped chrysene and 1,3,5-triphenylbenzene show relatively low T c compared with triphenylene, which should be ascribed to the differences in dopants and AH structures. Despite that, the hypothesis seems to work well for the collective data of reported works and suggests that with a large enough n, aromatic SCs may overcome the BCS limit and realize T c of more than 40 K.
Usually, alkali metals doped aromatic SCs have low shielding fractions, 122 the highest value of which is 16% F I G U R E 4 Aromatic hydrocarbons (AHs) used in aromatic superconductors.
F I G U R E 5 T c of typical aromatic superconductors is plotted as a function of (n). for pressed K 3 picene, 118 preventing researchers from determining their structures. In 2011, Wang et al. 123 found that Sr 1.5 phenanthrene and Ba 1.5 phenanthrene showed a superconducting transition at 5.6 K and 5.4 K, respectively. The shielding fraction for Ca 1.5 phenanthrene was only 1.25% at 2 K, but that of Ba 1.5 phenanthrene was huge, over 65%. However, the follow-up reports were retracted because the samples were actually doped with La instead of Ba due to mislabeling. 124,125 Later, another group discovered La or Sm-doped phenanthrene (T c~6 K) had shield fractions close to 50%. 126 But the T c -pressure behavior of La-phenanthrene was almost the same as that of pure La, thus giving a common recognition that its superconductivity should originate from La, which also has a high shielding fraction. 127 Furthermore, the results of these groups could not be reproduced by others, making these findings questionable. In 2014, Artioli and coworkers 128 systematically studied three Sm-doped AHs with n from 3 to 5 (phenanthrene, chrysene, and picene), which all exhibited superconducting states. T c of Sm-phenanthrene agreed well with the precious work, but a tiny shielding fraction was obtained. Small fractions were also observed in Sm-chrysene and Sm-picene. Therefore, previous observation of high shielding fractions was considered as a misunderstanding of experimental data. The small fractions in aromatic SCs are still the main obstacle for structure investigation.
Before superconducting pentacene (a linear oligoacene), all aromatic SCs adopted AHs with zig-zag-fused benzene rings. K-pentacene exhibited CT and antiferromagnetic-like behaviors, 129-131 which suggested a strong electron correlation and the possibility of being an SC. For the first time, Nakagawa and coworkers realized a superconducting K 3 pentacene where benzene rings were linearly fused. 132 They found that the compound became more symmetric from triclinic to monoclinic with T c of 4.5 K. Contrast to K 3 picene with the same n, unit cell volume of K 3 pentacene was increased by metal intercalation. Accomplished higher symmetry led to orbital degeneracy, allowing orbitals to accept electrons from metals. Thereby, carrier density was enough for superconductivity. Besides linear oligoacenes, superconductivity was observed in single C-C bond-linked AHs. Wang et al. [133][134][135] reported impressive improvement in T c of doped p-terphenyl from 7.2 K, 43 K to 123 K in preprint literature. Liu et al. 136 also discovered a step-like magnetization transition at 125 K. However, the compound exhibited a weak ferromagnetic background and a low diamagnetic volume, which made its superconductivity questionable. Differently, solid evidence for the superconducting transition in biphenyl was obtained. Meissner effect was observed in K-biphenyl at 7.2 K, while a relatively small shielding fraction of 0.004% was obtained, which may be due to impurities and its small size. 136 Theoretical calculations revealed that the superconductive phase might correspond to K 2 biphenyl instead of K 3 biphenyl, because its lowest formation energy was different from other aromatic SCs with a molar ratio of approximately 3:1. With more linked benzene rings, Sm 3 1,3,5-triphenylbenzene showed a clear superconducting transition at 4.3 K by magnetic susceptibility tests. 137 The authors also tried to realize superconducting Smdoped 1,3,5-Tris(bromomethyl)benzene and triphenylene but failed. Because only two reliable SCs based on C-C bond linked AHs were obtained, and their dopants and n were different, it is hard to give a conclusion about their T c dependence towards components, more detailed investigation is necessary for the dissuasion.
Modern simulation tech is a solid stool to advance the development of SCs. Yoon et al. 138 innovatively applied a computational method to pick AH candidates for the SC preparation, and successfully obtained a superconductive phase of Na 3 triphenylene. A small split may be necessary between the lowest unoccupied molecular orbital (LUMO) and LUMO + 1 for the emergence of superconductivity. The energy difference Δ between these energy levels of 200 AHs was calculated (see Figure 6). Considering that previously reported AHs: phenanthrene, picene, and coronene all have small Δ up to 0.2 ev (except for 1,2:8,9-dibenzopentacene but it has a small gap), and stacking type of AH molecules shall be similar, 10 candidates were selected. Afterward, they experimentally confirmed the superconductivity of Na 3triphenylene with T c of 15 K, indicating the feasibility of the calculation. Other candidates' potential in superconductivity still needs to be explored. Nerveless, it is worth employing this method to narrow the range of possible AH molecules for SCs to save unnecessary cost and time.
Although numbers of AH-based SCs are reported, their existence was once questioned. For example, the ground states of K-picene and K-coronene films were non-metallic, 139 and K x picene films on Ag (111) substrates were insulated. 140 Heguri et al. 141,142 proposed that the reaction of metal and phenanthrene would produce molecular decomposition other than combination, thus leading to the appearance of metal hydrides or unknown products. Observation of the superconducting performance of these compounds should originate from ferromagnetic impurities. Instead, Kambe and coworkers 143 developed a solution process to selectively prepare and confirm the 18-K superconducting phase of K 3 picene, where the softened Raman scattering peaks suggested the transfer of three electrons from potassium to picene. Teranishi et al. 144 observed zero resistivity of two K-picene phases below 7 K and 11 K, respectively. Though the amounts of the superconducting phases were tiny, resistivity drops were evident due to the closely connected phases, resulting in the formation of a current pathway. In contrast to K 3 picene films on Au, SiO 2 , and Ag (111), the films on graphite showed a Fermi edge suggesting its metallic state, which indicated that substrate orientations would affect the ground states of K x picene films. 145 The reported manufacturing methods of these aromatic SCs are usually simple, but the reaction process is complex and hard to control, sometimes inducing different results in the same system. 146 Besides dopants and their concentrations, other factors must be concerned. Further work is needed to study their functions in superconductivity. Nerveless, a larger number of experimental and theoretical reports on aromatic SCs from different groups provide strong evidence for the presence of superconducting phases in metal-intercalated AH compounds.
Hitherto, the superconductivity mechanism in aromatic SCs remains unclear for complex structural resolution and reaction processes. T c increment with pressure and local magnetic moment manifests the unconventional nature of their superconductivity. As Figure 7 shows, in the superconducting 18-K phase of K-picene, the application of pressure led to a linear increase of T c with dT c onset /dP = 12.5 K GPa −1 . 143 In contrast, an opposite result was obtained in another 7-K phase, where behaviors could be well described by strong electron-photon coupling within the BCS framework. Band broadening triggered by pressure decreased the density of states on the Fermi level (N(ε F )). According to the equation: Electron-phonon coupling strength λ V = × N(εF), 147 where V is the interaction matrix element, λ should be reduced with a decrease in N(ε F ), explaining its T c changes toward pressure. However, K or Rb doped-phenanthrene exhibited a positive T c trend toward pressure, 119 against the BCS model, where T c suppression was expected. The presence of local spins also illustrated the unconventional nature of superconductivity. Besides, enhancement of T c with n in three SCs (K-phenanthrene, 119 K-picene, 118 and K-1,2:8,9dibenzopentacene 121 ) provided clear evidence against electron-photon coupling model where λ should reduce as more carbon atoms decreased V, while N(ε F ) was fixed. In contrast, the T c variance of Sm-[n]phenacenes showed an apparent reduction from 5.5 to 4 K as n increased. 128 Apparently, BCS theory cannot explain these opposite results. There may exist multiple mechanisms in these SCs. Casula et al. 148 suggested that three phonons (intramolecular, intermolecular, and intercalant phonons) contributed to λ. In K 3 picene, 20% of λ came from F I G U R E 6 (A) Energy difference Δ of 200 AH molecules from the database, (B) Stacking type of filtered molecules with Δ lower than 0.2 eV, (C) Molecular structure of final 10 candidates. Reproduced with permission: Copyright 2020, American Chemical Society. 138 local contributions of pure molecules, and the remaining was from nonlocal couplings. 149 Mott transition in the solid with a sizeable U/W ratio indicated strong electron correlation, explained by the formation of 5% volume expansion by local magnetic moment. 150 The inclusion of correlation effects also stabilized the antiferromagnetic state in the compound. Hence, magnetic instability and electron correlation are important factors in aromatic SCs. Electron donation from dopants to AH molecules allows the generation of sufficient carriers in the transport pathway, facilitating the appearance of superconducting phases.
In summary, metal-intercalated AH compounds are promising materials in high-temperature SCs. Although magnetic properties and electronic structures are extensively investigated, several unsolved problems exist. Small shielding fractions of the SCs make it challenging to study structures, and all of their structures are based on theoretical prediction, exact stoichiometry is hard to determine due to lousy samples, and some results are not reliable due to the terrible sample reproductivity, raising an urgent command for reliable manufacturing methods. Multiple superconducting phases with different T c were discovered in one system, possibly because of different metal insertion ways, but the exact reason is still ambiguous. The underlying mechanism for opposite changes of T c towards pressure also needs to explore. Therefore, the most important direction is to determine the exact SC structures and understand the interactions between metals and AH molecules. A new strategy shall be developed to improve the nucleation of reactants and avoid their decomposition. Adjustment of metal size and charge states, benzene ring number, and their conformation will give access to high-quality samples for further study. Note that the energy gap would decrease with more benzene rings in linear oligoacenes, and only a few of them show superconducting transitions after metal intercalation. Thus, more attention should be paid to study how T c varies as more benzene rings are added.

| Alkali-doped fullerides
Fulleride molecule C 60 is a promising material for intercalation due to its high electron affinity and weak intermolecular forces. 151 Following GIC-based SCs, Hebard et al. 152 developed a fulleride SC (FSC), potassium-doped fulleride K 3 C 60 with T c of 18 K. Other alkali metals were found to induce superconductivity in fullerides as well. Up to now, the highest T c reported for FSCs is 33 K for Cs 2 RbC 60 153 at ambient pressure and 38 K for A15 Cs 3 C 60 under 0.93 GPa. 154 Compared with body-centered-cubic (bcc) A15 Cs 3 C 60 , face-centered cubic (fcc) Cs 3 C 60 showed a superconducting transition at 35 K under 0.73 GPa for a less ordered structure. Except for fcc Cs 3 C 60, other fcc FSCs were ambientpressure SCs, whose superconductivity was in the BCS regime. They exhibited s-wave symmetry and singlet pairing states. 155 Positive dependence of T c on the lattice constant suggested phonon-mediated pairing in these FSCs [156][157][158] : as the volume of per C 60 3− anion increased, which led to a larger interfullerene separation, T c was enhanced as the consequence of the increase in N(ε F ). 159 Besides, observation of Hebel-Slichter peaks in NMR [160][161][162] and μSR spectra 163,164 and isotopic effects 165 supported the phonon mechanism. While in A15 Cs 3 C 60 , unexcepted results were obtained. T c increased with pressure, and enhancement of interfullerene separation decreased T c . The absence of the Hebel-Slichter peak also suggested it was an unconventional SC. 166 Its phase diagram was similar to cuprates and heavy fermions, which indicated that electronic correlations could work together with the phonon mechanism. 157 Besides, Harshman et al. 167 pointed out that Coulombic interactions between alkali cations could be the origin of the superconductivity.

| Magic-angle graphene
In 2007, Lopes dos Santos et al. 168 proposed superconductivity potential in twisted bilayer graphene (TBG). Later, tight-binding calculation results by Suárez Morell et al. 169 indicated the appearance of flat bands in TBG, which was considered the signature of a superconducting transition. Bistritzer et al. 170 used a continuum model Hamiltonian and predicted that the two layers of TBG would be strongly coupled, and a flat band can be obtained at the twist angle of 1.05°. Motivated by these theoretical calculations, in 2018, Cao et al. 171 developed an unconventional SC based on a TBG superlattice, where moiré patterns were long-range ordered and tunable by the twisted angle. When the angle was 1.1°, called the first magic angle, a flat band near zero Fermi energy was formed due to interlayer hybridization. The device exhibited a Mott-like insulating state with half-filling bands due to electron localization. Figure 8A illustrates a typical TBG device, where two graphene sheets from the same flake are stacked and twisted at a certain angle. Unlike other OSCs, in TBG devices, electrostatic doping by gate voltages is necessary to adjust carrier density and induce zeroresistance states. Figure 8B shows the superconducting transitions in two magic-angle TBG (MATBG) devices (angles: 1.16°and 1.05°), which have T c up to 1.7 K. Superconductivity could only be observed when the Fermi energy E F was tuned from neutral to negative. If not, this phenomenon would be absent.
The MATBG devices showed a Berezinskii-Kosterlitz-Thouless transition and typical currentvoltage behaviors, commonly observed in 2D SCs. 173 As quantum oscillations tests showed small Fermi surfaces leading to low carrier density, high T c of the devices indicated strong electron pairings. T c of various SCs was plotted as a function of Fermi temperature T F in Figure 9. For most unconventional SCs, the values of T c /T F are in the range from 0.01 to 0.05, and those for BCS-type SCs are much lower by serval orders of magnitude. The location of a MATBG device is close to a trend line consisting of cuprates, heavy-fermion, and organic CT salt-based SCs, suggesting the importance of electron correlation in its superconductivity. Another parameter to be compared is the T c /T BEC value, where T BEC is the Bose-Einstein condensation temperature. of electrons in MATBG, which agrees with its comparable coherence length to average interparticle distance. Nematic fluctuations may also contribute to the superconducting transition since transverse resistance tests suggested a wedge-like normal state and anisotropic responses toward the in-plane magnetic field were observed. 174 Three years after the discovery of MATBG, the same group reported the realization of superconductivity in a magic-angle twisted trilayer graphene (MATTG), where electronic structures and properties were more tunable than MATBG. 175 In a MATTG device, three layers are symmetrically stacked with opposite twisted angles θ and −θ. Like MATBG, MATTG entered the superconducting state with the application of gate voltages and exhibited a richer phase diagram. Through gating, the coupling strength of MATTG can become intense, supported by the T c /T F value over 0.1 and short coherence length. The mathematical reduction of its flat bands resulted in a larger magic angle of 1.6°. Besides, MATTG showed a more robust superconductivity tolerance towards the in-plane magnetic field exceeding the Pauli limit, which MATBG cannot break. In BCS SCs, divergent N(ε F ) shall facilitate superconducting order. Thereby, superconductivity suppression by Van Hove singularity suggested its unconventional nature. Recently, Park et al. 172 discovered that with more symmetrically arranged layers (four or five), which stacked with alternated twisted angle θ and −θ ( Figure 8C), the graphene still exhibited superconducting states, thus suggesting magic-angle graphene as a new family of SCs. The flat bands and C 2z symmetry observed in these SCs indicated their essential contribution to superconductivity since no such phase was obtained in other graphene moiré systems. For MATBG, only a pair of flat bands were found, while for others, Dirac points by additional bands made their electronic structures firmly tuned by an out-of-plane displacement field. The Pauli limit breaking and nematicity lacking were observed as well. Adding stacking layers increased the corresponding largest magic angle and extended the superconducting phase space, but T c increment was absent, which may be due to the Dirac bands. On the other hand, cooper pairs in graphene devices with over three layers were nonsinglet, making pairing in MATBG questionable since they should show similar behaviors.
During the investigation of these devices, some experimental observation is unusual. For example, data in Pauli limit violations does not agree with the principal expectation, and the reason for the slight variation in orbital g-factor with diverse displacement fields is still unknown. Limited developed materials cannot provide enough results for mechanism analysis. Superconductivity potential in twisted graphene with more layers should be explored to study the relationship between physical properties and stacking layers. And a deeper understanding of the role of many-body correlations is required. To summarize, significant effects have been conducted to develop a series of OSCs. Besides OSCs mentioned above, there are other superconducting organic materials. For example, single molecules like p-iodanil and hexaiodobenzene become SCs under extremely high pressures 176,177 ; and copper (II) benzenehexathiolate (Cu-BHT) was found to be the first superconducting coordination polymer. 178 Although relevant reports are few, these results suggest a wide range of OSCs and inspire us to extend OSC types. Recent years have seen plenty of studies trying to reveal the superconducting nature and improve the sample quality of OSCs. However, some puzzling questions remain unsolved, like paring states in CT salt based SCs and structure analysis of aromatic SCs. Therefore, the future goal is to understand the cause of these unconventional properties and explain the discrepancy in experimental results. Employing innovative measurement tools and tunable organic materials can offer better opportunities to learn structure-property relationships and investigate exact parameters leading to uncommon results. Further studies should develop a microscopic model to explain all the observed phenomena.

| QUANTUM SPIN LIQUIDS
Conventional magnets usually exhibit disordered states when temperature T is high. At relatively low T, their ground states would become long-range magnetically ordered (LRO) with symmetry breaking due to spin interactions, and spin entropy would vanish to zero when T → 0. 179 However, in some unusual materials, spin entropy would reside at T → 0 without symmetry breaking and magnetic order formation for spin frustration. Such exotic states are called quantum spin liquids (QSLs). 180,181 QSLs are topological states with fractional excitations and consist of many degenerate states, leading to high spin entropy at low T. 182,183 Spin frustration in QSLs usually comes from long-range spin entanglement or competitive spin interactions by geometrical frustration. Figure 10 shows the spin arrangements in typical QSLs whose lattices can be triangular, Kagome, honeycomb. 184 Therefore, QSL states are usually discovered in Mott insulator, 185,186 and resonating-valence-bond (RVB) states are obtained as the consequence of the prevention of electron spin freezing by conflicted interactions on bonds. 187 Since Andersen proposed the RVB theory for triangular lattices with interacting Heisenberg spins in 1973, 188 QSLs have become a great interest in modern condensed physics of matter due to new excitations and exotic properties as promising candidates in quantum information transportation and computing. 189 Besides, doping of QSLs may provide a new strategy for realizing SCs. Compared with inorganic QSLs, the properties of organic QSLs are more flexible by controlling their components and structures, helping to understand exchange spin interactions in QSLs. Many organic QSL candidates have been experimentally realized. Here we would like to introduce these materials according to the following types: CT salts, metal-doped hydrocarbons, and metal-organic frameworks.

| Charge transfer salts
Due to dimerized ET molecules, lattices of ET dimers that carry magnetic moments can be considered triangular. 190 The ratio of intradimer transfer integrals t′/t indicates the strength of spin frustration. For most κ-(ET) 2 X salts, the ratio is away from 1 for their highly anisotropic lattices. However, for the first organic QSL candidate κ-(ET) 2 Cu(CN) 3 (donated as κ-CuCN), the lattice was regularly triangular with t′/t of 1.09, indicative of intense competing interactions between spins (see Figure 11A), which led to the absence of LRO states at low T. 191 κ-CuCN was first studied by as a superconductor with T c of 3.8 K. 193,194 Given that κ-CuCN showed better superconductivity under in-plane uniaxial strain than pressure, Shimizu et al. 195,196 tested its magnetic behaviors at ambient pressure. Its magnetic susceptibility χ(T) data were well fitted by an S = 1/2 Heisenberg antiferromagnetic (AF) triangular-lattice model, as seen in Figure 11B. 192 The Hamiltonian H reads as: , where J 1 and J 1 ′ are first-nearest-neighbor couplings for vertical and zigzag bonds, respectively, which equals in most QSL systems; J 2 stands for second-nearest-neighbor couplings.
In κ-CuCN, the 6/6 and 7/7 Padé approximants were employed, and the exchange interaction energy J/k B (k B is the Boltzmann constant) of localized spins was around 250 K, indicative of strong AF interactions. The NMR spectra with no broadening and splitting under cooling were interpreted as no magnetic order generation low tõ 30 mK, significantly smaller than its J/k B .
However, opposite results about κ-CuCN excitations were obtained: Linear temperature-dependence of heat capacity at low T suggested gapless fermionic excitations, 197 192 though no experimental evidence has been gained yet. While Yamashita et al. 198 proposed that the excitation should be gapped for its low-T thermal conductivity performance. The origin of the difference remains unsettled. Besides, an anomaly at 6 K in both tests suggested a second-order phase transition, also indicated by the spin-lattice relaxation rate 192 and thermal expansion measurements. 199 Miksch et al. 200 pointed out that the spin gap opening triggered the quick drop in spin susceptibility below 6 K, and its ground state should be a valence-bond solid state with broken symmetry.
Contamination from Cu 2+ is annoying for research. κ′-(ET) 2 Cu 2 (CN) 3 (κ′-CuCN), a compound containing Cu 2+ with a structure similar to κ-CuCN, could be obtained during the preparation of κ-CuCN. 194,201 Angledependent Raman tests also detected N(CN) 2 − anion in κ′-CuCN. 202 These impurities made the property exploration of κ-CuCN much more difficult. To avoid that, Hiramatsu et al. 203 synthesized a new QSL candidate, κ-(ET) 2 Ag 2 (CN) 3 (κ-AgCN), by replacing Cu with Ag due to its stability and exclusion of Ag 2+ . Similarly, Mott-like insulating κ-AgCN would enter a superconducting state under pressure with T c of 5.2 K. The value J/k B was lower than that of κ-CuCN but enough for stabilizing its QSL state, which was confirmed by NMR tests showing no magnetic transition down to 0.1 K. Similar heat capacity behaviors at low T were observed in κ-AgCN. Figure 12 shows the crystal structures of two compounds, both with disordered C/N. κ-AgCN also has an equivalently triangular lattice with t′/t of 0.967, indicative of frustrated spins. Its geometrical relationship between the spin site (key) and anion opening (keyhole) was keyon-rim while that for κ-CuCN was key-on-hole, leading to loosely packed ET dimers in κ-AgCN. Due to the suppressed anion and integral t′, a larger U/W ratio was obtained, where W was bandwidth. Besides, lattice constant expansion for a larger ionic radius of Ag + than Cu + induced a more considerable negative chemical pressure. As a result, higher critical pressure of 0.95 Gpa was needed for the emergence of superconductivity in κ-AgCN, but that for κ-CuCN was 0.36 Gpa. Therefore, at the same T of 1 K, κ-AgCN exhibited a robust QSL state with a wider pressure range.
Furthermore, partial replacement of Cu by Ag atoms in κ-CuCN realized a QSL state. Yoshida et al. 204 developed three mixed compounds κ-(ET) 2 Ag 2x Cu 2(1-x) (CN) 3 (0.24 < x < 0.71) and found their t'/t values would increase with x. When x was 0.49, despite low geometrical frustration suggested by a t′/t value of 1.253, the compound (donated as κ-AgCu) remained a magnetically disordered state down to 2 K, suggesting it was a promising QSL candidate. κ-AgCu exhibited a key-on-hole relationship, and its Ag and Cu atoms were uniformly distributed but disordered. Compared to its parent compounds κ-CuCN and κ-AgCN, κ-AgCu showed similar Mott and superconducting transitions and a moderate U/W ratio. On the contrary, component substitution in another QSL candidate β′-EtMe 3 SbPd(dmit) 22 205 (donated as β′-EtSb, Et = C 2 H 5 , Me = CH 3 , dmit = 1,3-dithiole-2-thione-4,5-dithiolate) did not favor a non-LRO state. In β′-EtSb, Pd(dmit) 2 molecules dimerized and formed a nearly triangular lattice, preventing spin ordering. When Sb in β′-EtSb was replaced by P, the compound β′-EtMe 3 PPd(dmit) 22 showed a valence-bond solid state and became superconducting under pressure, even though it had the same spin-lattice system as β′-EtSb. 206 Besides, a series of β′-XPd(dmit) 22 salts (X was Me 4 As, Me 4 P, MeP, Et 2 Me 2 P, or Et 2 Me 2 Sb) exhibited magnetic order under cooling despite that their t′/t values were close to that of β-EtSb. 207,208 According to these results, Ag/Cu and C/N disorders were proposed to facilitate the emergence of QSL states. Noting that disorders may stabilize the QSL states of salts, Furukawa et al. 209 developed a QSL candidate κ-(ET) 2 CuN(CN) 2 Cl (κ-Cl) by the introduction of disorder through X-ray irradiation. The pristine κ-Cl was an LRO Mott insulator with t′/t around 0.4-0.5, indicative of moderately frustrated spins. Given that x-ray irradiation can cause disorders in anion layers, 210,211 the resistivity of κ-Cl was reduced with longer irradiation time, and saturation in the disorder effect was observed after 500-h illumination. Differing from the original κ-Cl, the absence of new peaks in NMR spectra of 500-hirradiated κ-Cl suggested long-range entangled spins down to 340 mK, two orders of magnitude lower than the Neel temperature of the original one. No rapid changes in T 1 −1 also indicated the lack of spin freezing during cooling, confirming the QSL state in irradiated κ-Cl. Due to a more homogeneous system, above 1 K, irradiated κ-Cl only exhibited a characteristic behavior T 1 −1 ∝T 0.5 , commonly observed at high T for other QSL candidates, which also showed two other behaviors at low T accompanied by inhomogeneity nature. Its possibility of mobile spinons was proposed, and the proximity to Mott boundary indicated that a spinondeconfined chargon-glass insulator might dominate the QSL state. Furthermore, disorder generated by randomly frozen BABCO-rotors induced the QSL state in EDT-TTF-CONH 2 +2 BABCO−(EDT-BCO), where the cations carrying S = 1/2 spins formed a triangular lattice with spatial anisotropy. 212 The DFT calculation suggested that the anisotropy was not strong enough for dimensionality reduction, and this less frustrating system was expected to show chiral or collinear LRO states. However, tests including ESR, NMR, and µSR could not provide evidence for the formation of magnetic order but supported the appearance of a QSL state. The upturn below 50 K in χ was due to its intrinsic characteristic instead of impurities or magnetic order due to the same temperature-χ relationship of various batches. The emergence of long-range fluctuating spins was attributed to BCO randomness precluding the predicted ordering of EDT layers. 213,214 Hence, these experimental findings show the critical position of disorder in the presence of QSL states.
To avoid structural disorder, Tomeno et al. 215 prepared the first disorder-free QSL candidate κ-(ET) 2 CuAuCN 2 Cl, where an isotropic triangular spin-lattice system was formed. Positive pressure dependence of Mott transition temperature strongly confirmed its QSL state. While in κ-(ET-TTF) 2 Hg(SCN) 2 Cl, which had anisotropic lattice and no apparent disorder, observation of the QSL state was supported by the continuous change of T 1 −1 and unchanged NMR spectra down to 25 mK. 216 The magnetic field application controlled its NMR spectra due to inhomogeneity contribution. At relatively low T, impurity spins would polarize and freeze out the relaxation channels, and external fields can enhance the ordering suppression. Based on these results, it was evident that frustrated geometry was the main reason for hindering spin ordering in compounds. Besides, quantum fluctuation is another ingredient to stabilize QSL states, as suggested in κ-H 3 (Cat-EDT-TTF) 2 (κ-H) and κ-(ET-TTF) 2 B(CN) 4 (κ-BCN). Isono et al. 217 discovered that κ-H remained paramagnetic down to 50 mK by SQUID and torque tests. However, they ascribed the non-LRO state to spin frustration regardless of its highly anisotropic lattice. In contrast, Yoshida et al. 218 proposed that a highly distorted triangular lattice could suppress geometrical frustration and produce reduced dimensionality. They found that the χ(T) data of κ-BCN was fitted by an S = 1/2 spin Heisenberg model with an interaction energy of 2-3, close to the 1D limit. Observation of constant T 1 −1 from 5 to 100 K, usually presented in 1D QSLs, suggested its 1D nature as well since T 1 −1 ∝T 0.5 power-law behaviors usually occurred in 2D QSLs based on κ-(ET) 2 X salts. 219 Enhanced quantum fluctuation by low dimensionality led to a Mott insulating and nonmagnetic state in κ-BCN down to 5 K, below which a phase transition to a gapped state appeared with magnetic disorders, shown by a drop in T 1 −1 . As in Figure 13A, ITS band structure calculation revealed a band splitting with half-filled upper branches at 100 K, and the bandwidth was 0.39 eV, significantly smaller than that of other κ-(ET) 2 X SCs. A relatively high t′/t value was interpreted as the 1D-like character and was enhanced with a T decrease, ascribed to the large displacement of ET molecules by B(CN) 4 anions. Figure 13C compared two parameters of some typical κ-(ET) 2 X salts: t′/t and U/t. As κ-BCN has located away from the Mott boundary, the Mott transition was absent even under high pressures. With t′/t near unity, κ-CuCN showed a stable QSL state. While for κ-BCN with t′/t of 1.44, even though the anisotropic lattice weakened spin frustration, quantum fluctuation would be enhanced due to a lower-dimensional structure, thus stabilizing the QSL state. Compared to κ-BCN, the J/k B value of κ-H was significantly higher, around 80~100 K. Considering its lattice structure, where the anisotropy parameter t′/t was 1.48, almost the same as κ-BCN, quantum fluctuations and competing spin interactions should work together for the emergence of the QSL state in κ-H. As structural deformations and disorders influence QSL states in these 2D triangular-lattice salts, a 3D spin frustrated system is desirable for its isotropic spins and structure. Mizuno et al. 220 first reported a 3D QSL state in (TBA) 1.5 (−)-NDI-Δ, where TBA was tetrabutylammonium and NDI was naphthalene diimide. Figure 14 illustrates the triangular molecular structure of (−)-NDI-Δ consisting of three NDI units, where intermolecular orbital overlap produces a K4 structure. Considering unpaired electrons, we can transform the structure into a hyperkagome spin-lattice system made up of triangles of S = 1/2 electrons. With AF interactions revealed by negative Weiss constant, spin frustration was expected to induce a quantum-disordered state, presented by data in Figure 14C,D, showing the lack of magnetic transition down to 70 mK. It should be noted that the confirmation of the QSL state in a salt requires comprehensive measurements because their magnetic features are not universal. Novel properties may occur due to complicated interactions. For example, the magnetic susceptibility of λ-(BEDT-STF) 2 GaCl 4 suggested spin-liquid-like behaviors towards temperature. 221 But the observed saturation of T 1 −1 was against other QSLs, indicative of an exotic disordered state. In summary, in CT-salt-based QSL candidates, a triangular arrangement of spins is essential to induce competitive spin interactions. Besides, other factors like disorder, inhomogeneities, and quantum fluctuation could contribute to the realization of a QSL state, providing new strategies to develop QSL materials. However, data collection usually needs ultra-low temperature operation, making studies challenging. The nature of excitations in QSLs is still unclear for controversial test results. The origin of the large discrepancy in thermal conductivity tests remains an open question. Yamashita et al. 222,223 reported that fast cooling suppressed the phonon thermal conductivity, which would reside under slow cooling. Nevertheless, the conclusion was doubted by Kato et al. 224 because they detected no evident cooling rate dependence in crystal determination, NMR, and resistivity tests. More efficient tools and efforts are needed to reveal the potential mechanism in these QSLs.

| Metal-doped hydrocarbons
AH molecules exhibit natural packing orientations due to interplay between intermolecular orbitals. They are expected to host QSL states for their low dimensionality and geometrically frustrated structures. In 2017, Takabayashi et al. 225 reported that a cesium salt Cs (C 14 H 10 ) could remain paramagnetic down to 1.8 K. As illustrated in Figure 15, metal intercalation induced structural expansions and changes in phenanthrene packing. Triangularly arranged units of (C 14 H 10 ) •− anions with S = 1/2 spins formed bipartite-packed spiral tubes, whose four perpendicular neighbors enclosed. As a result, a magnetic network of coupled tubes was constructed, and zig-zag chains were observed along the b axis. Heisenberg AF coupling between these tubes gave rise to a highly frustrated 3D topological state with two differently oriented spin chains. A Curie-Weiss model was observed by fitting χ(T) data above 100 K, suggesting strong exchange interactions. Heavily entangled energy levels led to a two-orbital system with 1/4 band filling, and correlated calculations indicated a U/W value on the order of 2-3. Therefore, Mott localization was observed. Magnetic property tests revealed no sign of a transition into an ordered state at T much lower than its J/k B. Its similar magnetic response to a 1D magnetic model suggested a gapped spin state. However, this model cannot explain the inverse temperature dependence of EPR linewidth, which was expected to facilitate ordering due to enhanced spin correlations and A similar network of magnetic exchange interactions was observed in K 2 (triphenylene)(DME) as well, where DME was 1,2-dimethoxyethane. 226 The packing motif of ions suggested a low-dimensional electronic structure, and the network implied the introduction of frustration by triphenylene units. These effects stabilized the QSL state over a wide temperature range. K + -π coordination effects and intramolecular crowding removed the LUMO degeneracy, leading to a half-filled system. With intense electron correlation, a Mott insulating state was experimentally observed. Because of close intermolecular contacts within van der Waals distances, AF exchange was significantly stronger than Cs(C 14 H 10 ). The complicated exchange network made it hard to identify the fitting model of the magnetic data because both a spin chain and a spin ladder model were applicable.
The reported AH-based QSL materials exhibit a frustrating 3D-interlinked network of AH ions and tunable exchange interactions by metal-π interactions. With quantum fluctuation enhanced by low dimensionality, their spin ordering is prevented. These works imply controllable quantum states of materials based on all carbon π-electrons and show the promising potential of AH molecules in the preparation of organic QSL materials.

| Metal-organic frameworks
Metal-organic frameworks (MOFs) have been of great interest in condensed physics due to their topological structures and exotic quantum phenomena. 227,228 Their structural and physical properties are easily adjustable by tuning metal cations and organic ligands. Small differences could lead to significant changes in performance. For example, Day et al. 229 found that slightly different stacking motifs of Ni 3 (HITP) 2 and Cu 3 (HHTP) 2 led to a notable conductivity discrepancy, where HITP was hexaaminotriphenylene, and HHTP was hexahydroxytriphenylene. Besides extensive studies on their electrical properties, the magnetic performance of MOFs is recently gaining much attention from physicists. With numerous building units, enhancement in spin-exchange interactions in MOFs could be achieved, resulting in novel physical effects. For 2D MOFs with honeycomb lattices, Kagome networks of metal cations are made up of triangles, which suggest frustrated spins and topological interactions between magnets, making these MOFs potential QSL candidates. [230][231][232] In 2017, apart from superconductivity discovered in Cu-BHT, Huang et al. 178 also reported the order absence down to 2 K according to its χ(T) data, which fitted the Curie-Weiss law well. The law describes χ(T) of a paramagnetic ferromagnet above the Curie temperature θ, and is expressed as the equation: where C is a Curie constant. A rather negative θ of −1400 K indicated strong interactions between Cu 2+ magnetic moments. Later, Misumi and coworkers 233 systematically investigated the magnetic properties of another QSL Cu 3 (HHTP) 2 . As Figure 16 shows, the 2D Kagome network of Cu 2+ ions with S = 1/2 spins could be regarded as the combination of corner-sharing triangular ion lattices, known as the primary origin of QSL states. As expected, no signals of magnetic ordering were detected in χ(T) and specific heat capacity tests down to 38 mK. Though diamagnetic Cu + ions originating from structural defects were discovered by XPS spectra, they shall not affect MOF properties much. The obtained θ of Cu 3 (HHTP) 2 was close to the predicted value of an S = 1/2 spin system, indicating that Cu 2+ ions mainly contributed to its magnetic characteristics and presented weak spin interactions. Another MOF Zn 3 (HHTP) 2 was prepared and showed room-temperature diamagnetism for the lack of spins in the system. By property comparison, they regarded Cu 3 (HHTP) 2 as an S = 1/2 Heisenberg antiferromagnet due to its similar magnetic heat capacity and entropy values.
On the other hand, disorders suppress spin ordering in 2D MOFs as in ET salts. Berry et al. 234 reported paramagnetic behaviors in Ni 3 (HIB) 2 and Cu 3 (HIB) 2 (HIB is hexaiminobenzene). While no signals of spin freezing were detected in these MOFs with high θ/ T order values over 10, which satisfied the frustration condition, the origin of the order absence was attributed to their stacking faults. Their X-ray data exhibited peak asymmetries and broader reflections compared to ideal crystals, indicative of imperfect molecular arrangement. In Cu 3 (HIB) 2 , observation of a magnetic-field-tunable ground state and lowtemperature magnetic entropy was interpreted as the result of significant structural disorder, precluding spin ordering. While for Ni 3 (HIB) 2 , a common signature of a QSL state, the T-linear term in specific heat data emerged from the cooperation of an extra degree of freedom and interlayer disarrangement. As these 2D MOF QSL candidates all have Kagome lattices, 3D MOFs with the same coordination configuration are potential QSLs for their hyperkagome lattices, which could lead to the triangular arrangement of spins as well. Inspired by the discovery of 3D (TBA) 1.5 (−)-NDI-Δ, 220 Zhang et al. 235 developed a 3D MOF QSL (C 2 H 5 ) 3 NH 2 Cu 2 (C 2 O4) 3 . As shown in Figure 17, the compound had a (10,3) lattice, a network isomer of 2D (6,3) honeycomb lattices. The metal atoms had different chirality, and their arrangement generated a strong AF interaction between spins, as suggested by rather negative θ. Anisotropic AF interactions produced a Jahn-Teller distortion in CuO 6 octahedra and strongly coupled metal dimers. As a result, an pair of Cu-O bonds was significantly elongated. Longer Cu2-Cu2 distance led to rather weaker J′ than other interactions. Therefore, reduced magnetic lattice endowed the compound with a 2D quasi-honeycomb QSL, supported by the calculated dimensionless Wilson ratio R W of 0.19, which was comparable to 2D Herbertsmithite.
Since several Kagome or hyperkagome-lattice MOFs were reported to show paramagnetic behaviors at low T, QSL states may be a shared feature for MOFs with such topologies. Through employing various combinations of metal cations and organic ligands, structures and AF interactions of spins can be controlled to generate more QSL candidates. Structural and spin factors are essential in these QSLs, but their exact efforts are still unknown. For example, how will non-Kagome-lattice MOFs behave if numerous structural disorders or defects are introduced? How will the magnetic responses of MOFs change if spin states vary? These unsolved questions require further characterization measurements. Despite these puzzles, the discovery of QSLs in MOFs shows their promising prospects in condensed physics and provides a highly tunable platform for the production of more QSL candidates.
In summary, intense geometrical frustration is fundamental for spin liquids, and ingredients like structural deformation, defects, and impurities can facilitate their presence. However, their effects on the presence of QSLs and their contribution to magnetic behaviors are not quantified to discover the nature of QSLs, requiring further examination. Most studies concentrate on their magnetic behaviors, and detailed and systematic mechanism investigation is rare. The functions of each factor should be determined to reveal their influence on magnetism. It is known that conflicted spin interactions prevent the formation of magnetic order, but a complete illustration of this process for one particular system is ignored. In the view of mechanism description, more attention should be paid to explain how spins interact with each other. Theoretically, the strong correlation of QSL systems makes it hard to understand their performance. While a few new models have been put up to describe the behaviors, they cannot cover all the emergent novel phenomena, expecting a reliable basic theoretical framework for complete understanding. On the hand, methods for confirming QSLs require ultra-low temperature tests, which raise experimental costs, and a feasible characterization tool is urgently commanded. Naka et al. [236][237][238][239] proposed spin polarization in κ-(ET) 2 X salts and spin current is a possible tool to clarify the existence of QSL states. As inorganic QSLs have triangular, Kagome, honeycomb lattices, 240 studying Kitaev interactions of materials based on honeycomb lattices may provide new opportunities for discovering new types of organic QSLs, since inorganic Kitaev QSL H 3 LiIr 2 O 6 was successfully developed. 241 F I G U R E 17 (A) Structure of the three-dimensional (3D) metal-organic framework (MOF), dark blank lines highlighted the elongated Cu-O bonds, (B) Arrangement of magnetic interactions between Cu atoms. Reproduced with permission: Copyright 2018, American Chemical Society. 235 Anderson's theory points out the potential of QSLs in high-temperature SCs. Superconductivity in several organic QSLs was observed under pressures, such as κ-CuCN, κ-AgCN, κ-AgCu, κ-Cl, and Cu-BHT, though their T c was not much high. Based on these results, Hiramatsu et al. 203 proposed several principles for the design of QSL candidates neighboring superconducting states: low spin states are preferred because higher spins would facilitate magnetic ordering; the ratio of U/W should be significant to localize electrons for developing Mott insulators, and Mott gap should be small; spin lattices should be close to triangles to induce frustrations; a high J/k B is favorable due to the requirement for QSLs that disordered states should remain at T way smaller than J/k B . Generally, in OSCs, electron correlations play a vital role in forming a zeroresistance pathway. QSLs are Mott insulators for localized charge, and spin interactions are responsible for the presence of magnetically disordered states at low T. These findings indicate that electron interactions are decisive for exotic quantum properties. Although these two states cannot coexist, QSLs nearby superconducting states can be demonstrated by suitable supramolecular architectures to control the interactions between electrons. Another possible method to realize superconductivity in QSL candidates is doping. Doping is an efficient way to modulate the electronic structures of compounds and develop novel effects. Encouraged by the observation of superconducting AHs upon metal doping and magic angletwisted graphene under electric-filed gating, scientists suggest that chemical doping seems a promising route to trigger superconductivity in the proximity of QSL states. This strategy is theoretically feasible 242,243 and experimentally proven in κ-(ET) 4 Hg 2.89 Br 8 (κ-HgBr), 244,245 where the isotropic triangular lattice of ET dimers led to QSL-like behaviors. However, the sub-lattice incommensurate of Hg ions produced a non-stoichiometric ratio, giving rise to hole doping in the ET layer and a pressure-driven Mott-like transition. As pressures increased, the ground state of κ-HgBr changed from a Mott insulator to a correlated metal, and became superconducting at low T. Thereby, we believe it is practical to realize a frustrated spin lattice and then achieve a QSL with nearby superconductivity.
To conclude, we review the recent development of organic QMs, including organic SCs and QSLs. While many experimental studies report inspiring progress in performance improvement, controversial results against conventional exciton theory suggest complicated electronic states and exciton interaction mechanisms. Effects responsible for these novel phenomena are ambiguous, and a theoretical model comprehensively describing the electromagnetic behaviors of these QMs is absent. A general belief is that electron interactions lead to these properties, but the detailed process requires deep investigation. To get insight into quantum mechanisms, the cooperation of innovative experimental tools and numerous simulations is necessary. Continued studies should be conducted to develop more organic QMs, thus facilitating the construction of a quantum information society.