Evidence for superconductivity in Li-decorated monolayer graphene

Significance

Although superconductivity is well-known in intercalated bulk graphite, the ultimate goal of inducing superconductivity in single-layer graphene has not yet been achieved. We have here developed an experiment that combines ultralow-temperature (5 K) and ultrahigh-vacuum (10⁻¹¹ torr) sample preparation with high-resolution angle-resolved photoemission spectroscopy (ARPES). We show that decorating monolayer graphene with a layer of lithium atoms enhances the electron–phonon coupling to the point where a superconducting state can be stabilized at low temperature. Measurements of the size of the superconducting gap by ARPES suggest a $T_c$ of about 5.9 K. This result constitutes the first observation, to our knowledge, of superconductivity in monolayer graphene. Given the massive scientific and technological interest in graphene, our findings will have significant cross-disciplinary impact.

Abstract

Monolayer graphene exhibits many spectacular electronic properties, with superconductivity being arguably the most notable exception. It was theoretically proposed that superconductivity might be induced by enhancing the electron–phonon coupling through the decoration of graphene with an alkali adatom superlattice [Profeta G, Calandra M, Mauri F (2012) Nat Phys 8(2):131–134]. Although experiments have shown an adatom-induced enhancement of the electron–phonon coupling, superconductivity has never been observed. Using angle-resolved photoemission spectroscopy (ARPES), we show that lithium deposited on graphene at low temperature strongly modifies the phonon density of states, leading to an enhancement of the electron–phonon coupling of up to $\lambda \simeq 0.58$. On part of the graphene-derived ${\pi }^{\ast }$-band Fermi surface, we then observe the opening of a $\mathrm{\Delta }\simeq 0.9$-meV temperature-dependent pairing gap. This result suggests for the first time, to our knowledge, that Li-decorated monolayer graphene is indeed superconducting, with $T_c\simeq 5.9$ K.

Although not observed in pure bulk graphite, superconductivity occurs in certain graphite intercalated compounds (GICs), with $T_c$ values of up to 11.5 K in the case of CaC₆ (1, 2). The origin of superconductivity in these materials has been identified in the enhancement of electron–phonon coupling induced by the intercalant layers (3, 4). The observation of a superconducting gap on the graphitic ${\pi }^{\ast }$-bands in bulk CaC₆ (5) suggests that realizing superconductivity in monolayer graphene might be a real possibility. This prospect has, indeed, attracted intense theoretical and experimental efforts (6–12). In particular, recent density functional theory calculations have suggested that, analogous to the case of intercalated bulk graphite, superconductivity can be induced in monolayer graphene through the adsorption of certain alkali metals (8).

Although the Li-based GIC—bulk LiC₆—is not known to be superconducting, Li-decorated graphene emerges as a particularly interesting case with a predicted superconducting $T_c$ of up to 8.1 K (8). The proposed mechanism for this enhancement of $T_c$ is the removal of the confining potential of the graphite C₆ layers, which changes both the occupancy of the Li $2s$ band (or the ionization of the Li) and its position with respect to the graphene layer. These modifications lead to an increase of the electron–phonon coupling constant from $\lambda =0.33$ to $\lambda =0.61$, in going from bulk to monolayer LiC₆. It has been argued that the LiC₆ monolayer should exhibit the largest values of both λ and $T_c$ among all alkali–metal–C₆ superlattices (8). Nevertheless, although there is thorough experimental evidence for adatom-enhanced electron–phonon coupling in graphene (7, 11, 13), superconductivity has not yet been observed in decorated monolayer graphene.

Angle-resolved photoemission spectroscopy (ARPES) measurements of the electronic dispersion of pristine and Li-decorated graphene at 8 K, characterized by the distinctive Dirac cones at the corners of the hexagonal Brillouin zone (Fig. 1E), are shown in Fig. 1 A and B. Li adatoms electron-dope the graphene sheet by charge transfer doping, leading to a shift of the Dirac point to higher binding energies. As evidenced by the evolution of the graphene sheet carrier density in Fig. 1F, this trend begins to saturate after several minutes of Li deposition. Concomitantly, we observe the emergence of a new spectral weight (Fig. 1E) at the Brillouin zone center (the comparison of the $\mathrm{\Gamma }$-point ARPES dispersion for pristine and 10-min Li-decorated graphene is shown in Fig. 1 C and D). The origin of this spectral weight is probably the Li-2s band expected for this system (8) superimposed with the folded graphene bands caused by a Li superstructure, which were observed in Li and Ca bulk GIC systems (5, 14). This spectral weight, which disappears above $\sim 50$ K and is not recovered on subsequent cooling, is associated with the strong enhancement of electron–phonon coupling (discussed later, see Fig. 3 and SI Appendix).

Fig. 1.

Charge transfer doping of graphene by lithium adatoms. Dirac-cone dispersion measured by ARPES at 8 K (A) on pristine graphene and (B) after 3 min of Li evaporation along the K-point momentum cut indicated by the white line in the Fermi surface plot in E. The Dirac cone–Fermi surface was measured at this specific K point and then replicated at the other K points by symmetry (note that high-symmetry points are here defined for the Brillouin zone of pristine graphene and not of $\sqrt{3}\times \sqrt{3}R30°$ reconstructed Li-graphene, which is, instead, the notation in ref. 8). The point at which the spectroscopic gap is studied is indicated by the shaded white circle. The Dirac point, (A) already located below $E_F$ on pristine graphene because of the charge transfer from the SiC substrate, further shifts to higher energies with (B) Li evaporation. The presence of a single well-defined Dirac cone indicates a macroscopically uniform Li-induced doping. (C) Although no bands are present at the $\mathrm{\Gamma }$-point on pristine graphene, spectral weight is detected on 10-min Li-decorated graphene in D and E. As illustrated in the 8 K sheet carrier density plot vs. Li deposition time in F, which accounts for the filling of the $\pi \ast$ Fermi surface, the spectral weight at $\mathrm{\Gamma }$ is observed for charge densities $n_{2D}\gtrsim 9\times {10}^{13}$ cm^-2 (but completely disappears if the sample temperature is raised above $\sim 50$ K and is not recovered on subsequent cooling) (SI Appendix).

Fig. 3.

Analysis of electron–phonon coupling in Li-decorated graphene. (A) Dirac dispersion from 3-min Li-decorated graphene along the k-space cut indicated in the Fermi surface plot in E that exhibits kink anomalies caused by electron–phonon coupling (white line indicates MDC dispersion). (B–D) MDC dispersion and bare bands obtained from the self-consistent Kramers–Kronig bare-band fitting (KKBF) routine (20, 21) for several Li coverages (Methods and SI Appendix); the real part of the self-energy $\Sigma \prime$ is shown in Right (orange indicates $\Sigma \prime$ from the KKBF routine analysis, and black indicates $\Sigma \prime$ corresponding to the Eliashberg function presented below). (F–H) Eliashberg function ${\alpha }^{2}F\left(\omega \right)$ from the integral inversion of $\Sigma \prime \left(\omega \right)$ (22) and electron–phonon coupling constant $\lambda =2{\displaystyle \int d\omega \hspace{0.17em}{\alpha }^{2}F\left(\omega \right)/\omega }$ (Methods and SI Appendix); in H, the theoretical results from ref. 8 for a LiC₆ monolayer are also shown (gray shading). (I) Experimentally determined contribution to the total electron–phonon coupling (black circles) from phonon modes in the energy ranges 100–250 meV (blue shading and white circles) and 0–100 meV (orange shading); the coupling of low-energy modes strongly increases with Li coverage.

Next, we use high-resolution, low-temperature ARPES to search for the opening of a temperature-dependent pairing gap along the ${\pi }^{\ast }$-band Fermi surface as a direct spectroscopic signature of the realization of a superconducting state in monolayer LiC₆. To increase our experimental sensitivity, as illustrated in Fig. 2A, using the approach introduced for FeAs (17) and cuprate (18) superconductors, we perform an analysis of ARPES energy distribution curves (EDCs) integrated in $dk$ along a 1D momentum–space cut perpendicular to the Fermi surface. This method also provides the added benefit that the integrated EDCs can be modeled in terms of a simple Dynes gap function (19) multiplied by a linear background and the Fermi–Dirac distribution, all convolved with a Gaussian resolution function (Methods and Eq. 4). As shown in Fig. 2A and especially, Fig. 2B, for data from the k-space location indicated by the white circles in Figs. 1E and 3E, a temperature dependence characteristic of the opening of a pairing gap can be observed near $E_F$. The leading-edge midpoints of the Li-graphene spectra move away from $E_F$ (Fig. 2B) in cooling from 15 to 3.5 K, which is at variance with the case of Au spectra crossing precisely at $E_F$ according to the Fermi–Dirac distribution (Fig. 2D). Fitting these data with Eq. 4 returns a gap value of $\mathrm{\Delta }=0.9\pm 0.2$ meV at 3.5 K (with $\mathrm{\Gamma }\simeq 0.09$ meV). [Note that the parameter $\mathrm{\Gamma }$ in the Dynes fitting function is not treated as a free-fitting parameter, because the broadening of the coherence peaks and filling in of the gap are dominated by the experimental energy resolution. However, setting this parameter to small realistic values ($\mathrm{\Gamma }\sim 0.1\mathrm{\Delta }$) improves the fit at the center of the gap (i.e., at E = 0 in the symmetrized data) without affecting the value of the gap itself.] Given its small value compared with the experimental resolution, the gap opening is best visualized in the symmetrized data in Fig. 2C, which minimize the effects of the Fermi function. Finally, we note that the gap appears to be anisotropic and is either absent or below our detection limit along the $K-M$ direction (SI Appendix, Fig. S4).

Fig. 2.

Spectroscopic observation of a pairing gap in Li-decorated graphene. (A) Dirac dispersion from 10-min Li-decorated graphene measured at 15 and 3.5 K at the k-space location indicated by the white circles in Figs. 1E and 3E; the temperature dependence is here evaluated for EDCs integrated in the 0.1-Å^-1 momentum region about $k_F$ shown by the white box in Lower, with (Upper) the only changes occurring near $E_F$. (D) Although Au spectra cross at $E_f$ as described by the Fermi–Dirac distribution, (B) the crossing points of the Li-graphene spectra are shifted away from $E_F$ (cyan dashed line) because of the pull back of the leading edge at 3.5 K. A fit to the Dynes gap equation (Methods) yields a gap of $\mathrm{\Delta }\simeq 0.9$ meV at 3.5 K (and 0 meV at 15 K). The superconducting gap opening is best visualized in the symmetrized data in C [i.e., by taking $I\left(\omega \right)+I\left(-\omega \right)$, which minimizes the effects of the Fermi function, even in the case of finite energy and momentum resolutions (15, 16); blue and red symbols in C represent the smoothed data, whereas the light shading gives the rmsds of the raw data]. The qualitatively similar behavior observed on polycrystalline niobium—and returning a superconducting gap $\mathrm{\Delta }\simeq 1.4$ meV—is shown in E and F.

The detection of a temperature-dependent anisotropic gap at the Fermi level with a leading-edge profile described by the Dynes function—with its asymmetry about $E_F$ and associated transfer of spectral weight to just below the gap edge—is suggestive of a superconducting pairing gap. The phenomenology would, in fact, be very different in the case of a Coulomb gap, which is typically observed in disordered semiconductors (23–25) because of the combination of disorder with long-range Coulomb interactions. A Coulomb gap would lead to a rigid shift of the spectra leading edge (isotropic in momentum) and result in a vanishing of the momentum-integrated density of states at E_F. Similarly, the observed gap is unlikely to have a charge density wave origin, because the observed gap is tied to the Fermi energy as opposed to a particular high-symmetry wavevector (the latter might occur at the M points, when graphene is doped all of the way to the Van Hove singularity, resulting in a highly nested hexagonal Fermi surface; or the K points, in the case of a $\sqrt{3}\hspace{0.17em}\times \sqrt{3}\hspace{0.17em}R\hspace{0.17em}30°$ reconstruction, leading to a Dirac point gap). Finally, we note that these measurements do not allow us to speculate on the precise symmetry of the gap along a single Dirac cone–Fermi surface or the relative phases of the gap on the six disconnected Fermi pockets. As such, our results do not rule out any of the recent proposals for a possible unconventional superconducting order parameter in graphene (9, 26, 27).

To further explore the nature of the gap observed on Li-decorated graphene (and also show our ability to resolve a gap of the order of 1 meV), in Fig. 2 E and F, we show as a benchmark comparison the analogous results from a bulk polycrystalline niobium sample—a known conventional superconductor with $T_c\simeq 9.2\hspace{0.17em}\text{K}$. The Dynes fit of the integrated EDCs Fermi edge in Fig. 2E determines the gap to be $\mathrm{\Delta }=1.4\pm 0.2$ meV (with $\mathrm{\Gamma }\simeq 0.14$ meV), in excellent agreement with reported values (28). Although the leading-edge shift (Fig. 2E) and the dip in the symmetrized spectra (Fig. 2F) are more pronounced than for Li-graphene owing to the larger gap, the behavior is qualitatively very similar. This similarity provides additional support to the superconducting origin of the temperature-dependent gap observed in Li-decorated graphene.

If the spectroscopic gap observed in Li-graphene is, indeed, a superconducting gap, the responsible mechanism may likely be electron–phonon coupling, which was predicted by the theory for monolayer Li-graphene (8) and also, seen experimentally for the bulk GIC CaC₆ (5). In direct support of this scenario, we present a detailed analysis of the graphene ${\pi }^{\ast }$-bands in Fig. 3, showing that the Li-induced enhancement of the electron–phonon coupling is, indeed, sufficient to stabilize a low-temperature superconducting state. Graphene doped with alkali adatoms always shows a strong kink in the ${\pi }^{\ast }$-band dispersion at a binding energy of about 160 meV (11). For the Li-graphene studied here, the same effect is seen in the momentum distribution curve (MDC) dispersions and the corresponding real part of the self-energy $\Sigma \prime$ in Fig. 3 B–D. This structure stems from the coupling to carbon in-plane (C_xy) phonons (4, 8). Despite the apparent strength of this kink, the interaction with these phonon modes contributes little to the overall coupling parameter because of their high energy (note that ω is a weighting factor in the integral calculation of λ) (Methods). As illustrated by the white circles in Fig. 3I, the contribution to λ from these high-energy (100–200 meV) modes is determined to be $0.14\pm 0.05$, and it remains approximately constant for all Li coverages studied here. This value is, however, too small to stabilize a superconducting state in this system (8, 11).

With increasing Li coverage and the appearance of the spectral weight at $\mathrm{\Gamma }$, significant modifications to the low-energy part of the dispersion ($\lesssim 100$ meV) become apparent (Fig. 3 B–D). With 10 min of Li deposition (Fig. 3D), an additional kink is visible at a binding energy of ∼30 meV along with the associated peak in the real part of the self-energy $\Sigma \prime$. The extracted (Methods) Eliashberg functions and energy-resolved $\lambda \left(\omega \right)$ in Fig. 3 F–H show that, at high Li coverage, phonon modes at energies below 60 meV are coupling strongly to the graphene electronic excitations. The phonon modes in this energy range are of Li in-plane (Li_xy) and C out-of-plane (C_z) character (4, 8). This assignment is in agreement with predictions (8) as shown by the direct comparison between theory and experiment in Fig. 3H. [As for the theoretical and experimental Eliashberg functions ${\alpha }^{2}F\left(k,\omega \right)$ in Fig. 3H, the agreement may, at first glance, appear not as good as the one for $\lambda \left(\omega \right)$. We note, however, that, in this regard, the relevant information is in the macroscopic energy distribution of the ${\alpha }^{2}F\left(k,\omega \right)$ weight rather than in its detailed structure.] As for the total electron–phonon coupling λ for each coverage (black circles in Fig. 3I), our values measured on the ${\pi }^{\ast }$-band Fermi surface at an intermediate location between $\mathrm{\Gamma }-K$ and $K-M$ directions (Fig. 3E) provide an effective estimate for the momentum-averaged coupling strength. [The electron–phonon coupling parameter increases monotonically along the ${\pi }^{\ast }$-band Fermi surface in going from the $\mathrm{\Gamma }-K$ to the $K-M$ direction as observed in both decorated graphene (11) and intercalated graphite (29). Empirically, the value measured at the intermediate Fermi crossing corresponds to the momentum-averaged coupling strength along the ${\pi }^{\ast }$-band Fermi surface.] Remarkably, the value $\lambda =0.58\pm 0.05$ observed at the highest Li coverage (Fig. 3I) is comparable with $\lambda =0.61$ predicted for monolayer LiC₆ (8) as well as $\lambda \simeq 0.58$ observed for bulk CaC₆ (29)—it is, thus, large enough for inducing superconductivity in Li-decorated graphene. It is also significantly larger than the momentum-averaged results previously reported for both Li and Ca depositions on monolayer graphene [$\lambda \simeq 0.22$ and $\lambda \simeq 0.28$, respectively (11)]. We note that achieving such a large λ-value is critically dependent on the presence of the spectral weight observed at $\mathrm{\Gamma }$ when Li is deposited on graphene at low temperatures, presumably forming an ordered structure on the surface and not intercalating. As shown in SI Appendix, we find $\lambda =0.13\pm 0.05$ after the same sample is annealed at 60 K for several minutes, destroying the Li order and associated $\mathrm{\Gamma }$-spectral weight.

Taken together, our ARPES study of Li-decorated monolayer graphene provides evidence for the presence of a temperature-dependent pairing gap on part of the graphene-derived ${\pi }^{\ast }$ Fermi surface. The detailed evolution of the density of states at the gap edge as well as the phenomenology analogous to the one of known superconductors, such as Nb—as well as CaC₆ and NbSe₂, which also show a similarly anisotropic gap around the K point (30–34)—indicate that the pairing gap observed at 3.5 K in graphene is most likely associated with superconductivity. Based on the Bardeen–Cooper–Schrieffer gap equation, $\mathrm{\Delta }=3.5\hspace{0.17em}{k}_b\hspace{0.17em}{T}_c$, we estimate a superconducting transition temperature $T_c\simeq 5.9$ K, remarkably close to the value of 8.1 K found in density functional theory calculations (8). This work constitutes the first, to our knowledge, experimental realization of superconductivity in graphene—the most prominent electronic phenomenon still missing among the remarkable properties of this single layer of carbon atoms.

Methods

Sample Preparation.

Epitaxial graphene monolayers with a carbon buffer layer were grown under argon atmosphere on hydrogen-etched 6H-SiC(0001) substrates as described in ref. 35. The samples were annealed at 500 °C and 8 × 10^-10 torr for 1 h immediately before the ARPES measurements. Lithium adatoms were deposited from a commercial SAES alkali metal source, with the graphene samples held at a temperature of 8 K. Bulk Nb polycrystalline samples, with $T_c=9.2$ K, were cleaved in the ARPES chamber before the experiments.

ARPES Experiments.

The measurements were performed at the University of British Columbia with s-polarized 21.2-eV photons on an ARPES spectrometer equipped with a SPECS Phoibos 150 Hemispherical Analyzer, a SPECS UVS300 Monochromatized Gas Discharge Lamp, and a six-axes cryogenic manipulator that allows for controlling the sample temperature between 300 and 3.5 K, with accuracy $\pm 0.1$ K. Band and Fermi surface mapping as well as the study of electron–phonon coupling were performed at 8 K, with energy and angular resolution set to 15 meV and 0.01 Å^-1, respectively. For the measurements of the superconducting gaps, energy and angular resolution were set to 6 meV and 0.01 Å^-1, and the sample temperature was varied between 3.5 and 15 K. During the ARPES measurement, the chamber pressure was better than 4 × 10^-11 torr.

Electron–Phonon Coupling Analysis.

The spectral function $A\left(\mathbf{k},\omega \right)$ measured by ARPES (36) provides information on both the single-particle electronic dispersion ${\epsilon }_{\mathbf{k}}^b$ (the so-called “bare band”) and the quasiparticle self-energy $\Sigma \left(\mathbf{k},\omega \right)=\Sigma \prime \left(\mathbf{k},\omega \right)+i\Sigma ″\left(\mathbf{k},\omega \right)$, which have real and imaginary parts that account for the renormalization of electron energy and lifetime caused by many-body interactions, including electron–phonon coupling. By fitting with a Lorentzian and a constant background, the ARPES intensity profiles at constant energy $\omega =\tilde{\omega }$ known as MDCs, one obtains the MDC dispersion defined by the peak maximum $k_m$ (plotted in Fig. 3 A–D) as well as the corresponding half-width half-maximum $\mathrm{\Delta }{k}_m$. The real and imaginary parts of the self-energy can then be defined as

$$\begin{array}{l}{\displaystyle {\Sigma }_{\tilde{\omega }}^{\prime }=}\tilde{\omega }-{\epsilon }_{k_m}^b\\ {\displaystyle {\Sigma }_{\tilde{\omega }}^{″}=}-\mathrm{\Delta }{k}_m{v}_{k_m}^b,\end{array}$$ [1]

where $v_{k_m}^b$ is the bare-band velocity. To extract the self-energy and dispersion without any a priori knowledge of the bare band, we use the self-consistent Kramers–Kronig bare-band fitting routine from refs. 20 and 21 (SI Appendix). As for the dimensionless k-resolved electron–phonon coupling constant discussed in the paper and particularly, Fig. 3 F–I, this quantity is formally defined as (37)

$${\lambda }_{\mathbf{k}}\left(\omega \right)=\hspace{0.17em}2{\displaystyle {\int }_0^{\omega }d\omega \prime \hspace{0.17em}\frac{{\alpha }^{2}F\left(\mathbf{k},\omega \prime \right)}{\omega \prime }},$$ [2]

where ${\alpha }^{2}F\left(\mathbf{k},\omega \right)$ is the Eliashberg function [i.e., the phonon density of states weighted by the electron–phonon coupling strength (37)]. The latter is related to the real part of the self-energy $\Sigma \prime \left(\mathbf{k},\omega \right)$ through the integral relation

$$\Sigma \prime \left(\mathbf{k},\omega \right)={\displaystyle \underset{0}{\overset{\infty }{\int }}d\omega \prime {\alpha }^{2}F\left(\mathbf{k},\omega \prime \right)\hspace{0.17em}K\left(\frac{\omega }{kT},\frac{\omega \prime }{kT}\right)}\hspace{0.17em},$$ [3]

where $K\left(y,y\prime \right)={\displaystyle {\int }_{-\infty }^{+\infty }dx\hspace{0.17em}f\left(x-y\right)\hspace{0.17em}2y\prime /\left(x^2-y\prime \hspace{0.17em}2\right)}$ and $f\left(x-y\right)$ is the Fermi–Dirac distribution. The momentum resolved ${\alpha }^{2}F\left(\mathbf{k},\omega \right)$ function plotted in Fig. 3 F–H can then be extracted from the real part of the self-energy $\Sigma \prime \left(\mathbf{k},\omega \right)$ probed by ARPES by the integral inversion procedure described in ref. 22. Ultimately, by means of Eq. 2, this approach also allows the calculation of the electron–phonon coupling constant shown in Fig. 3 (SI Appendix).

Superconducting Gap Fitting.

As discussed in detail for the cases of FeAs and cuprate superconductors in refs. 17 and 18, respectively, when evaluating the opening of a superconducting gap based on the EDCs integrated in $dk$ along a 1D momentum–space cut perpendicular to the Fermi surface (such as those presented in Fig. 2), one can make use of the following formula:

$$I_{\int dk}\left(\omega \right)=\left[f\left(\omega ,T\right)\hspace{0.17em}\left(a+b\hspace{0.17em}\omega \right)\left|\text{Re}\frac{\omega -i\mathrm{\Gamma }}{\sqrt{{\left(\omega -i\mathrm{\Gamma }\right)}^2-{\mathrm{\Delta }}^2}}\right|\right]\otimes R_{\omega }.$$ [4]

This equation corresponds to the Dynes gap function [i.e., the Bardeen–Cooper–Schrieffer density of states with a superconducting gap $\mathrm{\Delta }$ broadened by the pair-breaking scattering rate $\mathrm{\Gamma }$ (19)] multiplied by a linear background (with parameters a and b) and the Fermi–Dirac distribution $f\left(\omega ,T\right)$ all convolved with a Gaussian function $R_{\omega }$ accounting for the experimental energy resolution [owing to the integration of the ARPES intensity in $dk$, this analysis is unaffected by momentum resolution (17)]. The high- and low-temperature ARPES data in Fig. 2 are fitted simultaneously using the above equation according to the following additional considerations. Because the integrated EDCs were observed not to change outside of the gap region, the linear background is constrained to be the same for the above and below $T_c$ measurements. The temperatures are fixed to the known measured values (with accuracy $\pm 0.1$ K). The Fermi energy $E_F$ and energy resolution are determined from fitting the high-temperature data from either Nb or Li-graphene during each measurement and independently verified from measurements on polycrystalline gold.