Visualization of Macroscopic Ising Superconducting State in Superconductor‐Graphene Junctions

Graphene‐based two‐dimensional van der Waals Josephson junctions with superconductors are hopeful for realizing versatile quantum devices. However, research on the junctions with Ising superconductors in atomic‐layer transition metal dichalcogenides, whose superconductivity is resilient to strong in‐plane magnetic fields, has remained elusive. Here the scanning tunneling microscopy study of Ising superconductivity in single‐layer (SL) NbSe2 island and its long‐range proximity effect to the adjacent graphene with high spatial and energy resolution is reported. It is found that SL NbSe2 island manifests as an Ising superconductor while the island area is larger than about 800 nm2. Moreover, the superconducting proximity effect from the NbSe2 island generates a superconducting gap in graphene, which can extend to over several tens of nanometers without obvious decay. Such a long‐range proximity effect makes the intrinsically non‐superconducting graphene as a superconductor. More intriguingly, such a superconducting gap can survive under strong in‐plane magnetic fields, following the Ising behavior of that in SL NbSe2. This work reveals a brand‐new macroscopic Ising superconducting regime, opening perspectives for superconductor‐based quantum devices with outstanding functionality.


Introduction
In conventional superconductor-normal metal junctions, Cooper pairs are expected to penetrate from superconductor to metal DOI: 10.1002/qute.202300087 via an Andreev reflection, resulting in a superconducting state in the metal. [1] Such a phenomenon, known as the superconducting proximity effect, has attracted intensive studies in the past decades, because of the significant effect on both the fundamental research and the design of versatile quantum devices. [2][3][4][5][6][7][8] Among all, graphene-based two-dimensional (2D) van der Waals (vdW) Josephson junctions with Ising superconductors are outstanding. On the one hand, high quality graphene generally displays ballistic characteristics, which is expected to generate an extremely low contact resistance in graphene-based vdW junctions. [9][10][11][12][13] On the other hand, the Ising superconductivity has been proved to exist in atomic-layer transition metal dichalcogenides (TMDs) such as gated MoS 2 , [14,15] NbSe 2 , [16][17][18][19] TaS 2 , [20] as well as stanine. [21] Therefore, junctions constituted by a combination of Ising superconductor and graphene are expected to act as an ideal platform with a macroscopic superconducting state against strong external in-plane magnetic fields, opening perspectives for building superconductor-based quantum devices. However, to the best our knowledge, research on the superconducting proximity effect from Ising superconductor to graphene with high spatial resolution and the response of such superconductivity under external magnetic fields are still lacking up till now, which needs further exploration.
In the current work, we report on the scanning tunneling microscopy (STM) and spectroscopy (STS) study of the Ising pairing in 2D superconductor NbSe 2 and its proximity effect to the adjacent graphene with high spatial and energy resolution. The single-layer (SL) H-NbSe 2 island exhibits as an Ising superconductor when the island area is beyond 800 nm 2 . The proximity effect from the superconducting NbSe 2 island generates a superconducting energy gap in the adjacent graphene layer, which can extend to over several tens of nanometers without obvious decay. More intriguingly, such a superconducting gap can survive under strong in-plane magnetic fields even up to 2 T, following the Ising behavior of that in SL NbSe 2 . Considering that there is a high density of superconducting NbSe 2 islands in our as-grown samples, the whole NbSe 2 /graphene system behaves as a macroscopic Ising superconductivity. Our results pave the way for realizing a brand-new macroscopic Ising superconducting regime. Figure 1a shows the schematic atomic structure of SL H-NbSe 2 with the top and side views, and a 3 × 3 superlattice is marked. A niobium atom locates inside a trigonal prismatic cage formed by six nearest-neighbor selenium atoms. Since the SL NbSe 2 has out-of-plane mirror symmetry but broken in-plane inversion symmetry, the strong atomic spin-orbit coupling (SOC) in SL NbSe 2 locks the electron spins near the K and K′ valleys in an out-of-plane orientation, i.e., Ising SOC, thus resulting in the broken of spin degeneracy at a finite momentum. In the superconducting regime, such spin-momentum locking effect naturally gives rise to the Cooper pairing between an electron around K valley and its time-reversed pair with opposite spin and momentum around K′ valley, [16][17][18][19][20] as linked by double-headed arrows in Figure 1b.

Ising Superconductivity of SL NbSe 2
In our experiments, high-quality atomic-layer NbSe 2 islands were prepared on graphene-covered SiC(0001) substrates by using a molecular beam epitaxy (MBE) method (see Experimental Section). [22][23][24] Figure 1c shows a large-scale STM image of the SL NbSe 2 island with the sample temperature T = 0.35 K. A close examination of the atomically resolved STM images reveals that the topmost Se atoms, which dominate the topography as bright protrusions, condensed into commensurate 3 × 3 charge density wave (CDW) superlattices, [25][26][27][28][29][30] as shown in Figure 1d,e. Moreover, the low-bias STS spectra recorded at the center of large-sized SL NbSe 2 island can be well fitted by the Bardeen-Cooper-Schrieffer (BCS) gap function, [16,28] yielding the superconducting energy gap Δ SL ≈ 1.2 meV and the lifetime broadening energy Γ ≈ 0.2 meV (Figure 1f, see Figure S1, Supporting Information for more details). Similar results have been widely observed by changing different samples and STM tips after calibration, which can help us rule out any possible artifacts ( Figures S2-S6, Supporting Information). It's worth noting that such a superconducting energy gap is larger than that in previous STM measurements. [28][29][30][31] A certain density of atomic disorders ( Figure S7, Supporting Infor-mation), as well as the interlayer spacing between SL NbSe 2 and graphene, may attribute to such a difference, based on previous studies. [28,31]

Size-Dependent Ising Superconductivity of SL NbSe 2
Now we systemically study the size-dependent superconducting properties of SL NbSe 2 islands. Figure 2a-c shows three representative STM images of SL NbSe 2 islands with similar shapes and different sizes. We first capture the area S of an island via the WSxM software [31] (see Figure S8, Supporting Information for more details). And then, the effective length d eff of the island can be determined as √ S. [32,33] Figure 2d shows a series of STS spectra recorded at the center of SL NbSe 2 islands with the variation of S (more STM images and STS spectra are given in Figures S9 and S10, Supporting Information). First, we confirm that an STS spectrum exhibits superconductivity when the spectrum exhibits a BCS-like behavior with particle-hole symmetric coherence peaks. In such a case, there are obvious superconducting features when S > 800 nm 2 approximatively, along with the superconducting gaps uniform throughout the island even approaching to the island edges. On the contrary, when S < 800 nm 2 approximatively, the superconductivity is completely quenched, and instead, exhibits an insulating behavior. Owing to the existence of confinement-controlled interactions, the insulating behavior of SL NbSe 2 islands with S < 800 nm 2 may be attributed to the Coulomb gap. Very recently, similar phenomena were also observed via STM/STS measurements. [31] To systemically investigate the superconducting properties of SL NbSe 2 , we carry out the STS measurements on SL NbSe 2 islands with different temperatures and external magnetic fields in the out-of-plane/in-plane orientation, as summarized in Figure 2e and Figure S11 (Supporting Information). As increasing the sample temperature or applying an external outof-plane magnetic field, the superconducting coherence peaks recorded on SL NbSe 2 are effectively suppressed, together with an enhancement of the zero-bias conductance, yielding the critical out-of-plane magnetic field of about 3.4 T. In such a case, the coherence length of SL NbSe 2 can thus be estimated as = √ 0 ∕2 H c2 ≈ 9.8 nm, where 0 is the superconducting magnetic flux quantum. However, we can hardly observe vortices under out-of-plane magnetic fields, which may be owing to the undersized NbSe 2 or graphene regions as well as the unstable features of vortices in this regime. [28] However, the response of superconductivity in SL NbSe 2 by applying an in-plane magnetic field is quite abnormal. As shown in Figure 2e, the STS spectra recorded on the superconducting SL NbSe 2 islands are almost invariant as increasing the in-plane magnetic field from 0 to 2 T at the sample temperature of 0.35 K (the highest in-plane magnetic field available in our STM system is 2 T). For comparison, we also carry out the similar measurements on bilayer NbSe 2 , the Ising superconducting signatures of which are strongly suppressed because of the spin-layer locking. As shown in Figures S12 and S13 (Supporting Information), the superconducting gap in bilayer NbSe 2 can be obviously suppressed when the in-plane magnetic field reach to 1.6 T, quite different from that in the SL. Such results indicate the existence of an extremely large in-plane upper critical field in the SL regime. Theoretically, the upper critical field means the ability of a superconductor to withstand external magnetic field. Superconductivity in conventional BCS superconductors can be quenched by applying an external magnetic field, owing to both the orbital and spin Zeeman effects. In the limit of SL thickness, both the interlayer coupling and the orbital effect are absent, and therefore, the in-plane upper critical field is only determined by the spin-flip effect, which is characterized as the Pauli paramagnetic limit of B p ≈ 1.86 T c . When applying an in-plane magnetic field beyond B p , the Zeeman splitting energy is supposed to overcome the binding energy of a Cooper pair, thus driving the superconductor into a metal. [34][35][36][37] However, the Ising SOC in SL NbSe 2 , which pins the electron spins perpendicular to the sample surface, can efficiently reduce the pair-breaking effect and stabilize the superconducting state against the in-plane magnetic fields far beyond the Pauli paramagnetic limit, [14][15][16][17][18][19][20][21] as schematically shown in the inset of Figure 2e. Therefore, the superconductivity in SL NbSe 2 can survive under high external in-plane magnetic fields. Very recently, transport measurements demonstrated that the in-plane upper critical field of SL NbSe 2 can reach up to 35 T. [36] Figure 2. a-c) Typical STM images of SL NbSe 2 islands on graphene with the island areas of about 1196, 761, and 101 nm 2 , respectively (V s = −1.5 V, I t = 9 pA). d) Characteristic local STS spectra recorded at the center of the islands with different island areas. The particle-hole symmetric coherence peaks in superconductors are marked by the arrows. All the STS spectra are offset for clarity with the dI/dV = 0 positions marked by the black dotted lines. The spectra show superconductivity when S > 800 nm 2 approximatively. e) The evolution of STS spectra of SL NbSe 2 as a function of the in-plane magnetic field from 0 to 2 T. The STS spectra are almost unchanged. Inset: In the in-plane magnetic field, electrons of SL NbSe 2 around the K and K' valleys experience opposite effective magnetic fields B SOC .

Proximity Effect of Ising Superconductor-Graphene Junctions
Now we concentrate on the proximity-induced Ising superconductivity of SL NbSe 2 with S > 800 nm 2 to the adjacent graphene. Figure 3a shows a representative STM image of SL NbSe 2 islands on graphene with their separations of about Δx = 25 nm. The two isolated SL NbSe 2 islands, together with the uncovered graphene region between the islands, form a typical 2D vdW Ising superconductor-normal metal-Ising superconductor (INI) Josephson junction, as depicted in Figure 3b. The STS spectra recorded across such an INI Josephson junction exhibit spatially homogeneous superconducting gaps in graphene (Figure 3c). The gap energy in graphene is about 0.9 meV, slightly smaller than that in SL NbSe 2 of about 1.2 meV (Figure 3d,e).
The superconductivity of graphene can be well understood via an intraband retro-type Andreev reflection (in our NbSe 2 /graphene/SiC samples, the Fermi energy is several hundreds meV away from the charge neutrality point of graphene), as shown in Figure 3f. An incident electron from graphene K valley can be reflected back as a hole in K′ valley at the NbSe 2 /graphene interface owing to the time reversal symmetry, and hence, creating a Cooper pair in graphene at the Fermi level. [9,[38][39][40][41][42][43] The Cooper pair then becomes a pair of time-reversed electron states that propagates into graphene over a distance, with the characteristic superconducting coherence length predominantly depending on the properties of graphene. [9,42] Generally, epitaxial graphene on SiC displays a ballistic regime with an exceptionally long mean free path of over the order of 100 nm. [44,45] Intriguingly, uniform superconducting gaps are also captured at the INI Josephson junction with the variant lengths of the uncovered graphene Δx ≈ 11, 31, and 58 nm, as shown in Figure 4bd, respectively (the corresponding zero bias conductance and BCS fitted gap values of SL NbSe 2 and graphene are given in Figures S14 and S15, Supporting Information). It's worth noting that the energy separations of the two coherent peaks in STS spectra of SL NbSe 2 are strongly dependent on the measured islands, which may be owing to the different size of these islands and defect concentration within each island. Moreover, Δx can be artificially tuned to about 150 nm (several times larger than the  adjacent two SL NbSe 2 islands and the uncovered graphene region between the islands. b-d) Spatially resolved energy separations of the two coherent peaks E cp in the superconducting spectra of graphene. The distances (Δx) of the two adjacent island edges are 11, 31, and 58 nm, respectively. e) The evolution of STS spectra in graphene as a function of the in-plane magnetic field from 0 to 2 T. The STS spectra are almost unchanged. coherence length of SL NbSe 2 ) via an STM tip manipulation technique. [24] In this case, the superconducting gaps can also be captured on graphene, only with a slight decay of superconducting signatures when approaching to the center ( Figure S16, Supporting Information).
However, the decay length of superconductivity from an individual SL NbSe 2 leaking into graphene is only several nanometers in previous research, [31] which is much smaller than that in our observations. This may be because the proximity effect at a NbSe 2 -metal junction is due to Andreev reflection, while at a NbSe 2 -metal-NbSe 2 junction, Andreev reflections occur at both the interfaces multiple times, which would lead to an enhanced proximity effect. [46] The exact mechanism of such a long-range proximity effect needs further exploration. Considering that the spatial distances between two island edges of our samples mostly concentrate on several tens of nanometers, such a high density of SL NbSe 2 islands gives rise to macroscopic superconductivity in graphene, which is useful for building of graphene-based superconductor quantum devices.
To understand the proximity-induced superconductivity of graphene, we measure the low-energy STS spectra on graphene as a function of sample temperature and external out-of-plane/inplane magnetic fields. Similar to the evolution of superconducting spectra in SL NbSe 2 , there is a suppression of coherence peaks and an enhancement of the zero-bias conductance in graphene as increasing sample temperature or applying an outof-plane magnetic field ( Figure S17, Supporting Information), yielding the critical superconducting temperature of graphene T c ≈ 1.9 K ( Figure S18, Supporting Information). The most salient feature is that the STS spectra recorded on graphene show no obvious variation by applying an in-plane magnetic field, as shown in Figure 4e. We find that the evolution of the energy separations between two superconducting coherent peaks ΔE CP under in-plane magnetic fields in graphene is almost invariant even when the in-plane magnetic field up to 2 T, regardless of the crystallographic orientation between NbSe 2 and graphene (see Figures S19 and S20, Supporting Information). Although the Pauli limit for graphene, B p ≈ 1.86 T c ≈ 3.5 T, is beyond our STM limitation, this phenomenon still provides evidence of the Ising signature in graphene, following the behavior of that in SL NbSe 2 ( Figures S21, Supporting Information).
To reveal the exact nature of proximity effect in graphene surviving under a large in-plane magnetic field, we first prepared SL NbSe 2 on 6H-SiC(0001) that was covered by multilayer graphene sheets. [47] Similar proximity effect can also be observed, demonstrating that the 2D signature of graphene is not necessary to maintain superconductivity under a large in-plane magnetic field. We can also rule out the mechanism of Dirac physics, since the Dirac point of graphene is not at the Fermi energy, owing to the existence of charge transfer effect. Moreover, the proximity effect of spin-orbit coupling in NbSe 2 can hardly leak into graphene for several tens of nanometers. [48] Taken together, we believe that the Ising superconductivity of SL NbSe 2 with spin-momentum locking Cooper pair is key to such an abnormal proximity effect, which needs more experimental and theoretical explorations.

Conclusion
In summary, we systemically study the 2D vdW SNS Josephson junctions based on Ising superconductors. The SL H-NbSe 2 island shows a size-dependent Ising superconducting behavior, and the island areas larger than about 800 nm 2 can generate a long-range proximity effect of over several tens of nanometers to the adjacent graphene without decay. Such a long-range proximity effect induces graphene to exhibit an obvious superconducting gap. The discrete H-NbSe 2 islands, together with the underlying graphene, construct a system that can realize a macroscopic superconducting state beyond the Pauli paramagnetic limit. Our results pave the way for exploring the new systems with versatile superconducting quantum devices.

Experimental Section
The sample preparation and STM measurements were carried out by a custom-designed Unisoku STM system (USM-1300). First, graphene was obtained by thermal decomposition of 4H-SiC(0001) at 1200°C for 45 min. And then, the NbSe 2 islands were epitaxially grown on graphene/SiC(0001) substrate by evaporating Nb and Se from an electron beam evaporator and a Knudsen cell evaporator, respectively. The flux ratio of Nb and Se was ≈1:20, in order to guarantee a rich Se environment. The growth rate of NbSe 2 was 0.002 layer min −1 . The graphene/SiC(0001) substrate was maintained at 500°C during the growth, followed by a post-annealing process at 400°C for 20 min. The STM and STS measurements were performed in the ultrahigh vacuum chamber (≈10 −11 Torr) with constant-current scanning mode. The experiments were acquired at the temperature of 0.35 K. An electrochemically etched tungsten tip was used as the STM probe, which was calibrated by using a standard graphene lattice, a Si (111)-(7 × 7) lattice, and a Pb film ( Figure S5, Supporting Information). The STS measurements were taken by a standard lock-in technique with the bias modulation of 0.3 mV at 973 Hz.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.