Scanning Tunneling Spectroscopy of Lithium‐Decorated Graphene

Lithium decoration of graphene on SiC(0001) is achieved in a surface science approach by intercalation and adsorption of the alkali metal. Spectroscopy of the differential conductance with a scanning tunneling microscope at the Li‐decorated graphene surfaces does not give rise to a pairing gap at the Fermi energy, which may be expected because of the previously predicted superconducting phase [Profeta et al., Nat. Phys. 2012, 8, 131]. Rather, pronounced gaps in the spectroscopic data of intercalated samples reflect the excitation of graphene phonons. Rationales that possibly explain this discrepancy between experimental findings and theoretical predictions are suggested.


Introduction
Inspired by the observation of superconductivity in graphiteintercalated compounds, [1][2][3][4][5][6] simulations explored the possibility to induce the superconducting phase of free graphene by alkali metal decoration. [7]The compound LiC 6 where Li atoms occupy the center of C honeycomb cells at one side of free graphene was predicted to exhibit superconductivity with a critical temperature of T c = 8.1 K.The superconducting phase was traced to favorable ingredients.Lithium intercalation induces a 2s-band at the Fermi energy (E F ) and thereby enlarges the density of states (DOS).The Li 2s-band moreover promotes the coupling to low-energy out-of-plane graphene phonons and Li vibrational quanta.The calculations for Li 2 C 6 where Li resides at both sides of the graphene sheet, predicted superconductivity with a T c between 17 and 18 K.In a subsequent photoemission experiment performed on graphene-covered SiC(0001) with purely adsorbed Li, [8] a temperature-induced energy gap opening at E F of the band close to the K-point of the Brillouin zone (BZ) was reported and interpreted as the pairing gap of the predicted superconductivity.By using an analytical expression derived within the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity [9] DOI: 10.1002/andp.202300249 the measured gap width was translated into an associated critical temperature of T c = 5.9 K, in reasonable agreement with the prediction for LiC 6 . [7]hese previous theoretical results and experimental observations were the key motivation for the studies presented here.Graphene on SiC(0001) is decorated from different sides by intercalation and adsorption of Li.Spectroscopy of the differential conductance (dI∕dV) with a scanning tunneling microscope (STM) reveals pronounced gaps around E F of the intercalated samples that are assigned to the excitation of graphene phonons.However, a pairing gap indicating a superconducting state remains absent from the spectra of all samples.These findings apparently contrast previous results [7,8] and possibilities for reconciliation are discussed.

Results and Discussion
To experimentally approximate the free state of graphene, which entered the simulations predicting superconductivity upon Li decoration, [7] graphene atop a C buffer layer (BL) on SiC(0001) was used.14][15][16][17][18][19] The samples considered in the present studies are illustrated in Figure 1b,c,d.The entirely Li-intercalated sample (Figure 1b) gives rise to a graphene sheet that is decorated with the alkali metal at its bottom, i.e., at the vacuum-averted side; this sample is referred to as Li-gr in the following.Intercalation and adsorption of Li on clean graphene-covered SiC(0001) leads to Li decoration of graphene from both sides (Figure 1c, Li-gr-Li), while low-temperature deposition of Li ensures the presence of a purely adsorbed phase (Figure 1d, gr-Li).
Figure 2a shows an overview STM image of Li-intercalated graphene (Li-gr) on SiC(0001).Several findings evidence that the deposited Li entirely intercalated and occupies the substrate-BL and BL-graphene interfaces (Figure 1b).First, adsorbed Li atoms or clusters, that is, Li residing at the graphene surface have not been observed.Second, atomically resolved STM images of the surface reveal the graphene honeycomb lattice (Figure 2b).Third, the Fourier transform (Figure 2c) of the STM data depicted in Figure 2a shows the (1 × 1) pattern induced by the atomic C lattice of graphene (circles in Figure 1c) with inferred lattice constant a = 0.243 ± 0.02 nm together with a  3a.This superstructure was previously reported and associated with intercalated Li occupying both the SiC-BL and BL-graphene interface. [8]A similar superstructure was likewise observed for intercalated Li at graphenecovered Ir(111). [20]Fourth, the (6 × 6) superstructure that is characteristic for clean graphene is absent.Its origin is interpreted as the interplay between lattice mismatch and strong bonding at the SiC-BL interface. [19]Therefore, the absence of the (6 × 6) superstructure is indicative of Li residing at this interface. [10,21]Before presenting the electronic structure of the surface, the circular depressions visible in the STM image of Figure 2a shall be commented on.The maximum apparent depth is ≈ 25 pm at the given bias voltage and tunneling current.Defects of the top graphene sheet can be excluded because the intact honeycomb lattice spans the depressions.Therefore, the depressions most likely result from a locally incomplete Li film at the BL-graphene interface.Similar observations were reported previously for Li [22] and H [23] intercalation.
Figure 3a shows a representative dI∕dV spectrum of Ligr (Figures 1b and 2).The minimum at ≈ −0.8 V [arrow in Figure 3a] is assigned to the Dirac point. [8,24]For the clean, nonintercalated sample, the Dirac point spectroscopic signature is found at ≈ −0.4 V. [10] The shift of the Dirac point energy by ≈ 0.4 eV further below E F is attributed to the additional n-doping of graphene induced by the Li intercalation.
Performing scanning tunneling spectroscopy (STS) experiments in the narrow bias voltage range |V| ≤ 100 mV with better resolution gives rise to a pronounced gap with symmetrically positioned flanks at ±60 mV and ±75 mV (Figure 3b) as extracted from the clearly resolved pair of peaks and dips in the d 2 I∕dV 2 spectrum (Figure 3c).These spectroscopic features are caused by the excitation of graphene phonons at the M-point of the graphene BZ (inset to Figure 3a), namely the outof-plane acoustic (ZA) phonon with an energy of 60 meV and the out-of-plane optical (ZO) as well as the transverse acoustic (TA) phonon with an energy of 75 meV. [25,26][29][30][31][32] Indeed, for graphene on SiO 2 extraordinarily strong phonon signals were reported from STS studies. [27]he nearly-free status of graphene on SiO 2 entailed the depletion of final states close to the BZ Γ-point for the inelastic tunneling electrons, which instead reach ample DOS at E F due to the Dirac cone -bands at K by phonon-mediated tunneling.In the present case, intercalating Li only at the substrate-BL interface did not push the graphene phonon signals above the detection limit in dI∕dV spectroscopy, [10] although many works reported the intercalation-induced free state of the BL, [21,[33][34][35][36][37][38][39][40][41][42][43][44] which, expectedly, would give rise to the free state of graphene atop the BL.The results reported here seem to suggest, however, that a residual BL-graphene coupling has to be suppressed by Li intercalation at the BL-graphene interface to attain a quasi-free state of graphene.
Figure 3d shows a close-up view of an experimental dI∕dV spectrum (top data set) in a still narrower bias voltage range with further increased resolution.Obviously, a zero-bias gap is absent.Rather, the dI∕dV signal varies by less than 10 % for |V| ≤ 15 mV.In order to exclude an insufficiently low sample temperature that may cause the suppression of the expected pairing energy gap, a dI∕dV spectrum was simulated (Appendix A).It relies on the previously reported BCS gap width Δ = 0.9 ± 0.2 meV at 3.5 K and T c = 5.9 K. [8] In addition, tip and sample temperature (5 K) as well as the modulation broadening in the present experiments were considered (Appendix A). Figure 3d shows that even after adding an artificial scattering of data points comparable to the experiments, the BCS energy gap is visible in the simulated data.
The Li deposition experiments were continued in order to cover graphene with Li also from its vacuum side (Figure 1c). Figure 4 shows STM images and STS data of such Li-gr-Li samples with increasing surface coverages Θ (1) Li .The adsorption of Li at the graphene surface is evidenced by the absence of the atomically resolved graphene lattice.For the lowest coverage, an irregular honeycomb pattern is visible in STM images (Figure 4a).Tentatively, this pattern may be assigned to a distorted Li lattice where Li atoms occupy sites at or close to the center of the graphene honeycomb unit cells.The inset to Figure 4a shows a close-up view of the Li-covered graphene surface with dots marking the suggested Li atom positions.The interatomic distances match well the distance between adjacent honeycomb cell centers of the graphene lattice.Defining 1 monolayer (ML) as 1 Li atom per C hexagon, the lowest coverage studied is estimated as Θ Li ≈ 2 ML.Spectra of dI∕dV were acquired atop various positions of the sample surface and for different bias voltage ranges (Figure 4bd).The spectral data are essentially independent of the site and, therefore, only two representative data sets are displayed for each bias voltage range.In the wide voltage range (Figure 4b) the spectra are rather flat with rising edges for |V| > 1 V.In the intermediate range |V| ≤ 125 mV, dI∕dV data exhibit steplike changes at ±60 mV and ±75 mV, which are assigned to the excitation of ZA and ZO, TA graphene phonons at the BZ M-point, as observed for the purely Li-intercalated sample (Figure 3b).An energy gap indicating the superconducting phase is absent, however, as clearly evidenced by spectra in the narrow range |V| ≤ 8 mV with increased resolution (Figure 4d).A similar situation is encountered for the higher coverages Θ Consequently, evidence for a superconducting phase of the Ligr-Li sample is absent in STS experiments.It is noteworthy that the Li-gr-Li sample prepared in the experiments is comparable with the Li 2 C 6 structure that was predicted to superconduct with T c = 17-18 K. [7] Before entering into the discussion of the findings for the Li adsorption phase, a remark on the spectra of the pure intercalation (Figure 3b) and the combined intercalation-adsorption (Figure 3c) phases is noteworthy.An asymmetry of the phonon excitation efficiency with the bias polarity is observed for all samples.Moreover, the ZA phonon induces larger relative changes in dI∕dV for Li-gr than for Li-gr-Li samples.These observations are further discussed in Appendix B.
In order to exclusively cover graphene with Li (Figure 1d), intercalation of Li was suppressed by low-temperature deposition.The prepared sample is expected to match very well the sample used in the previous photoemission experiments. [8]ifferent Li coverages were prepared.The coverage was calibrated via deposition on a clean Au(100) surface (Appendix C), where ΘLi = 1 ML is defined by a closed Li film on Au(100).Graphene-covered SiC(0001) samples with ΘLi < 0.5 ML gave rise to unstable tunneling junctions, presumably due to mobile and diffusing Li on graphene.The situation improved for ΘLi ≥ 0.5 ML.
Figure 5a shows a representative STM image of Li-covered graphene with Θ(1) Li ≈ 0.5 ML.The protrusions with an average size of 2.99 ± 0.73 nm and apparent height of 0.95 ± 0.10 nm (at 1 V) are assigned to Li clusters.Spectra of dI∕dV depend on the spectroscopy site as demonstrated by the STS data presented in Figure 5b.Spectra on different Li clusters (1,2,4) and above interstitial sites (3) differ.The origin of the spectral signatures is unclear at present.Expectedly, the electronic structure of the surface is complex due to the presence of electron states at the pristine substrate-BL interface [10,11] together with Li 2s [8] bands.Common to all spectra, however, is a gapless variation of dI∕dV around 0 V, which can be inferred from the representative dI∕dV spectrum in the inset to Figure 5b.In particular, also a phononinduced gap in dI∕dV data as observed for the entirely intercalated samples is absent, which corroborates the importance of reducing the residual BL-graphene interaction for efficient graphene phonon excitation.
At higher coverage (Figure 5c, Θ(2) Li ≈ 1 ML) the average size of Li clusters has slightly increased (dimension: 3.98 ± 0.85 nm, apparent height at 1 V: 0.87 ± 0.11 nm).The dI∕dV spectra still depend on the actual surface site (Figure 5d), albeit to a less pronounced extent than observed for samples with coverages Θ(1) Li (Figure 5b).Spectral data of the clusters (1-3) are rather similar, Li ≈ 2 ML (25 mV, 30 pA, 15 nm × 15 nm).j,k,l) Spectra of dI∕dV in different bias voltage ranges acquired atop two sites of the sample in (i).The feedback loop was deactivated at j) 1.5 V, k) 125 mV, l) 10 mV and 50 pA.The ac modulation was (b,f,j) 3 mV rms , (c,g,k) 1 mV rms and (d,h,l) 100 V rms .
which may hint at a spatially more uniform Li 2s DOS across the surface at higher Li coverage.For sites between the clusters (4) differences in dI∕dV data are discernible.An energy gap indicating the expected superconducting phase is absent from dI∕dV spectra at all surface sites, as exemplarily demonstrated for site 1 (inset to Figure 5d).
It is noteworthy that a template effect of graphene or its (6 × 6) moiré pattern for guiding the Li adsorption was not observed.
It is likely that the Li-graphene interaction is weak, which in turn favors Li cluster assembly independent of the underlying lattice.
of the manner of graphene decoration with Li -exclusively at its bottom (Li-gr) or top (gr-Li) side as well as at both sides (Li-gr-Li) -an energy gap at E F due to superconductivity is not indicated by dI∕dV spectroscopy with an STM.Apparently, these spectroscopic findings are in contradiction to previous predictions [7] and photoemission experiments. [8]hile a clear-cut explanation to these seemingly antagonistic results is not available to date, tentative rationales are discussed here.
The photoemission work [8] showed that the temperaturedependent gap opening at E F occurs in the -band close to the K-point of the BZ.At the same time, a strong increase of spectral weight at the BZ Γ-point due to the occurrence of the Li 2s-band was reported.The contribution of electron states to dI∕dV data depends exponentially on the electron wave vector k ∥ according to exp(−2z) (z: tip-surface distance) with (m: free-electron mass, E: energy of the tunneling electron relative to E F , G ∥ : reciprocal surface lattice vector).Therefore, the enhanced Li 2s electron DOS at Γ is expected to surmount the signal of the pairing gap at K in spectra of dI∕dV.
The anisotropy of the pairing gap [8] may likewise impede its observation in STS.The tunneling process averages over different spatial directions and, thus, reduces the effective gap width, possibly below the detection limit.
For the purely intercalated sample [Li-gr, Figure 1c] a different explanation for the absence of the pairing gap may apply.The Li 2s-states are strongly confined to the BL-graphene interface leading to their energy shift clearly above E F and the entailed ionization of the Li atoms.For Li-intercalated graphite this situation was shown to cause the suppression of the superconducting phase. [45]nother explanation that may reconcile electron tunneling and photoelectron spectroscopy on more general grounds is related to an electron transport phenomenon, which applies to STS but not to photoemission, namely the branching of inelastic and elastic electron transport channels.[32] Therefore, Li-gr and Li-gr-Li samples where graphene phonon signals in dI∕dV spectroscopy are strong (Figures 3 and 4) due to an elevated inelastic electron transport channel would not unveil the pairing gap because of weak elastic electron transport.

Conclusion
Spectroscopy of dI∕dV with an STM lacks the expected superconducting energy gap of Li-decorated graphene on SiC(0001).Its absence in STS experiments may tentatively be traced to the suppression of electron states with elevated surface wave vectors, to the anisotropy of the energy gap, to the actual Li-induced electronic structure of the samples or the quenching of the elastic current in favor of inelastic graphene phonon excitation.Nonequilibrium electron transport calculations are highly desired to elucidate the discovered discrepancy with previous predictions and experiments.

STM and STS:
The experiments were performed with an STM operated in ultrahigh vacuum (10 −9 Pa) and at low temperature (5 K).Topographic STM data were acquired in the constant-current mode and processed using WSxM. [46]Scanning tunneling spectroscopy of dI∕dV proceeded by adding an ac sinusoidal voltage modulation (750 Hz) with rootmean-square (rms) amplitudes ranging from 100 to 5 mV rms to the dc bias voltage.The first harmonic of the current response was detected with a lock-in amplifier.The bias voltage was applied to the sample giving rise to occupied (unoccupied) sample states at negative (positive) voltage.

Sample and Tip Preparation:
The n-doped 4H-SiC(0001) crystal was cleaned by annealing (870 K).The prepared surface consists of two C layers stacked on top of each other in the Bernal configuration, graphene (top) and the buffer layer (bottom).Lithium was evaporated from a resistively heated dispenser.For intercalation, the clean sample was exposed to Li at elevated temperature (570 K).Exclusive adsorption of Li on the graphene surface was achieved by the deposition at low temperature (8 K) through openings of the cryostat radiation shields on the sample mounted to the STM.A chemically etched W wire was used as the tip material for experiments on Li-gr and Li-gr-Li samples.Field emission on a Au target was expected to coat the W tip apex with a Au film.For gr-Li samples a cut Au wire served as the tip.49][50][51]  Li ≈ 0.67 ML (feedback loop parameters: 125 mV, 50 pA, 1 mV rms ).The arrows mark step heights relative to dI∕dV ≡ 0 (dashed line).deed, gating the graphene sheet of Ref. [29], which sets the global carrier density or doping of graphene, led to different signal strengths of a given graphene phonon mode dependent on the gate voltage.A clear-cut picture underlying the observations is reserved to nonequilibrium electron transport calculations, which are hopefully sparked by the experimental results presented here.

Figure 1 .
Figure 1.Illustration of Li-decorated graphene on SiC(0001).a) Intercalation of Li at the substrate-BL interface (BL: buffer layer, gr: graphene).b) Intercalation of Li at the substrate-BL and BL-graphene interfaces (Ligr).c) Intercalation of Li as in (b) including a Li adsorption phase at the graphene surface (Li-gr-Li).d) Exclusive Li adsorption phase on the graphene surface (gr-Li).

Figure 3 .
Figure 3. Spectroscopic data of Li-intercalated graphene (Li-gr) on SiC(0001).a) Spectrum of dI∕dV with feedback loop parameters 1 V, 78 pA, 5 mV rms .The arrow marks the position of the Dirac point.Inset: Brillouin zone of graphene with indicated high-symmetry points.b) As (a) in a narrower V range (150 mV, 75 pA, 1 mV rms ).The steep changes in dI∕dV (arrows) are assigned to out-of-plane acoustic (ZA) and optical (ZO) as well as transverse acoustic (TA) phonon modes at the M-point of the BZ.c) Numerical derivative of (b).d) Top: As (a) in a still narrower V interval (15 mV, 78 pA, 100 V rms ).Bottom: Simulated dI∕dV spectrum for a tip and sample temperature of 5 K (Appendix A).Raw (Smoothed) data are depicted as dots (solid lines) in (a-d).

Figure B1 .
Figure B1.Inelastic electron tunneling spectroscopy of graphene phonons.a) Spectrum of dI∕dV of Li-intercalated graphene (Li-gr) on SiC(0001) (feedback loop parameters: 150 mV, 75 pA, 1 mV rms ).The arrows mark changes in dI∕dV induced by ZA and ZO, TA phonons at the M-point of the BZ.The dashed line indicates dI∕dV ≡ 0. b) As (a) for an entirely intercalated sample with an additional Li adsorption phase (Li-gr-Li) of coverage Θ (1)