Evidence for superconductivity in Li-decorated monolayer graphene
Bart Ludbrook, Giorgio Levy, Pascal Nigge, Marta Zonno, Michael Schneider, David Dvorak, Christian Veenstra, Sergey Zhdanovich, Douglas Wong, Pinder Dosanjh, Carola Straßer, Alexander Stohr, Stiven Forti, Christian Ast, Ulrich Starke, Andrea Damascelli
EEvidence for superconductivity in Li-decorated monolayer graphene
B.M. Ludbrook,
1, 2
G. Levy,
1, 2
P. Nigge,
1, 2
M. Zonno,
1, 2
M. Schneider,
1, 2
D.J. Dvorak,
1, 2
C.N. Veenstra,
1, 2
S. Zhdanovich,
2, 3
D. Wong,
1, 2
P. Dosanjh,
1, 2
C. Straßer, A. St¨ohr, S. Forti, C.R. Ast, U. Starke, and A. Damascelli
1, 2, ∗ Department of Physics & Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
Monolayer graphene exhibits many spectacu-lar electronic properties, with superconductiv-ity being arguably the most notable exception.It was theoretically proposed that supercon-ductivity might be induced by enhancing theelectron-phonon coupling through the decora-tion of graphene with an alkali adatom super-lattice [Profeta et al. Nat. Phys.
8, 131-134(2012)]. While experiments have indeed demon-strated an adatom-induced enhancement of theelectron-phonon coupling, superconductivity hasnever been observed. Using angle-resolved pho-toemission spectroscopy (ARPES) we show thatlithium deposited on graphene at low temper-ature strongly modifies the phonon density ofstates, leading to an enhancement of the electron-phonon coupling of up to λ (cid:39) . . On partof the graphene-derived π ∗ -band Fermi surface,we then observe the opening of a ∆ (cid:39) . meVtemperature-dependent pairing gap. This resultsuggests for the first time, to our knowledge, thatLi-decorated monolayer graphene is indeed super-conducting with T c (cid:39) . K . While not observed in pure bulk graphite, supercon-ductivity occurs in certain graphite intercalated com-pounds (GICs), with T c of up to 11.5 K in the case ofCaC [1, 2]. The origin of superconductivity in thesematerials has been identified in the enhancement ofelectron-phonon coupling induced by the intercalant lay-ers [3, 4]. The observation of a superconducting gap onthe graphitic π ∗ bands in bulk CaC [5] suggests that re-alizing superconductivity in monolayer graphene mightbe a real possibility. This has indeed attracted intensetheoretical and experimental efforts [6–12]. In partic-ular, recent density-functional theory calculations havesuggested that, analogous to the case of intercalated bulkgraphite, superconductivity can be induced in monolayergraphene through the adsorption of certain alkali metals[8].Although the Li-based GIC – bulk LiC – is not knownto be superconducting, Li decorated graphene emerges asa particularly interesting case with a predicted supercon-ducting T c of up to 8 . T c is the removal of the confin-ing potential of the graphite C layers, which changes both the occupancy of the Li 2 s band (or the ionizationof the Li) and its position with respect to the graphenelayer. This ultimately leads to an increase of the electron-phonon coupling constant from λ = 0 .
33 to 0.61, in goingfrom bulk to monolayer LiC . It has been argued thatthe LiC monolayer should exhibit the largest values ofboth λ and T c among all alkali-metal-C superlattices[8]. Nevertheless, while there is thorough experimentalevidence for adatom-enhanced electron-phonon couplingin graphene [7, 11, 13], superconductivity has not yetbeen observed in decorated monolayer graphene.ARPES measurements of the electronic dispersion ofpristine and Li-decorated graphene at 8 K, character-ized by the distinctive Dirac cones at the corners ofthe hexagonal Brillouin zone [Fig. 1(e)], are shown inFig. 1(a) and (b). Li adatoms electron-dope the graphenesheet via charge-transfer doping, leading to a shift of theDirac point to higher binding energies. As evidencedby the evolution of the graphene sheet carrier densityin Fig. 1(f), this trend begins to saturate after severalminutes of Li deposition. Concomitantly, we observethe emergence of new spectral weight at the Brillouinzone centre [see Fig. 1(e) and the comparison of the Γ-point ARPES dispersion for pristine and 10 minute Li-decorated graphene in Fig. 1(c,d)]. The origin of thisspectral weight is probably the Li-2 s band expected forthis system [8], superimposed with the folded graphenebands due to a Li superstructure, as observed in Li andCa bulk GIC systems [5, 14]. This spectral weight, whichdisappears above ∼
50 K and is not recovered on subse-quent cooling (see SI Appendix), is associated with thestrong enhancement of electron-phonon coupling to bediscussed later.Next we use high-resolution, low-temperature ARPESto search for the opening of a temperature-dependentpairing gap along the π ∗ -band Fermi surface, as a directspectroscopic signature of the realization of a supercon-ducting state in monolayer LiC . To increase our experi-mental sensitivity, as illustrated in Fig. 2(a) and followingthe approach introduced for FeAs [17] and cuprate [18]superconductors, we perform an analysis of ARPES en-ergy distribution curves (EDC) integrated in dk along aone-dimensional momentum-space cut perpendicular tothe Fermi surface. This also provides the added benefitthat the integrated EDCs can be modelled in terms of a r X i v : . [ c ond - m a t . s up r- c on ] A ug K 0 min Lia . . . KRelative Momentum, k-K ( ˚A ) E ne r g y ( e V ) . . K 0 min Lic . . E ne r g y ( e V )
10 min Lid . . . .
50
Momentum ( ˚A ) E ne r g y ( e V ) Spectral weightat pointf Li deposition time (min) n D ( ⇥ c m )
10 min Lie
FIG. 1.
Charge-transfer doping of graphene by lithium adatoms. (a) Dirac-cone dispersion measured by ARPES at 8 Kon pristine graphene and (b) after 3 minutes of Li evaporation, along the K -point momentum cut indicated by the white linein the Fermi surface plot in (e). The Dirac cone Fermi surface was measured at this specific K point, and then replicated at theother K points by symmetry (note that high-symmetry points are here defined for the Brillouin zone of pristine graphene andnot of √ × √ R ◦ reconstructed Li-graphene, which is instead the notation in Ref. 8). The point at which the spectroscopicgap is studied is indicated by the shaded white circle. The Dirac point, already located below E F on pristine graphene dueto the charge-transfer from the SiC substrate (a), further shifts to higher energies with Li evaporation (b). The presence ofa single well-defined Dirac cone indicates a macroscopically uniform Li-induced doping. While no bands are present at theΓ-point on pristine graphene (c), spectral weight is detected on 10-minute Li-decorated graphene in (d) and (e). As illustratedin the 8 K sheet carrier density plot versus Li deposition time in (f), which accounts for the filling of the π ∗ Fermi surface, thespectral weight at Γ is observed for charge densities n D (cid:38) × cm − (but completely disappears if the sample temperatureis raised above ∼
50 K, and is not recovered on subsequent cooling; see also SI Appendix). a simple Dynes gap function [19] multiplied by a linearbackground and the Fermi-Dirac distribution, all con-volved with a Gaussian resolution function (see Methodsand in particular Eq. 4). As shown in Fig. 2(a) and espe-cially 2(b) for data from the k-space location indicatedby the white circle in Figs. 1(e) and 3(e), a temperaturedependence characteristic of the opening of a pairing gapcan be observed near E F . The leading edge midpoint ofthe Li-graphene spectra moves away from E F [Fig. 2(b)]in cooling from 15 to 3.5 K, at variance with the caseof Au spectra crossing precisely at E F according to theFermi-Dirac distribution [Fig. 2(d)]. When fit to Eq. 4,this returns a gap value ∆ = 0 . ± . (cid:39) .
09 meV [20]). Given its small value compared tothe experimental resolution, the gap opening is best vi-sualized in the symmetrized data in Fig. 2(c), which min-imizes the effects of the Fermi function. Finally, we notethat the gap appears to be anisotropic, and is either ab-sent or below our detection limit along the K − M direc-tion (see Fig. 4 in SI Appendix).The detection of a temperature-dependent anisotropicgap at the Fermi level with a leading-edge profile de-scribed by the Dynes function – with its asymmetryabout E F and associated transfer of spectral weight tojust below the gap edge – is suggestive of a supercon- ducting pairing gap . The phenomenology would in factbe very different in the case of a Coulomb gap, typi-cally observed in disordered semiconductors [24–26], dueto the combination of disorder with long-range Coulombinteractions. This would lead to a rigid shift of the spec-tra leading edge, isotropic in momentum, and result in avanishing of the momentum-integrated density of statesat E F .Similarly, the observed gap is unlikely to have a chargedensity wave origin, since the gap is tied to the Fermi en-ergy as opposed to a particular high-symmetry wavevec-tor (the latter might occur at the M points, whengraphene is doped all the way to the Van Hove singulari-ties resulting in a highly-nested hexagonal Fermi surface,or at the K points in the case of a √ × √ R ◦ recon-struction leading to a Dirac-point gap). Finally, we notethat these measurements do not allow us to speculate onthe precise symmetry of the gap along a single Dirac-coneFermi surface, nor on the relative phases of the gap onthe six disconnected Fermi pockets. As such, our resultsdo not rule out any of the recent proposals for a possibleunconventional superconducting order parameter (see forexample Refs. 9, 27, and 28).To further explore the nature of the gap observed on Li-decorated graphene (and also demonstrate our ability to Li-GrapheneT=15 KT=3.5 K =0.9 meVb . Energy (meV) I n t en s i t y ( a . u . ) Li-GrapheneT=15 KT=3.5 K . I n t en s i t y ( a . u . ) a
10 0 10
Energy (meV) k NiobiumT=12 KT=4.5 K =1.4 meVe . Energy (meV) I n t en s i t y ( a . u . ) Li-G15 K3.5 Kc . . . Energy (meV)Nb12 K4.5 Kf . . . Energy (meV)GoldT=15 KT=3.5 Kd . Energy (meV) I n t en s i t y ( a . u . ) FIG. 2.
Spectroscopic observation of a pairing gap in Li-decorated graphene. (a) Dirac dispersion from 10-minuteLi-decorated graphene measured at 15 and 3.5 K, at the k-space location indicated by the white circle in Figs. 1(e) and 3(e);the temperature dependence is here evaluated for EDCs integrated in the 0.1 ˚A − momentum region about k F shown by thewhite box (bottom), with the only changes occurring near E F (top). While Au spectra (d) cross at E f as described by theFermi-Dirac distribution, the crossing point of the Li-graphene spectra (b) is shifted away from E F (cyan dashed line), due tothe pull-back of the leading edge at 3.5 K. A fit to the Dynes gap equation (see Methods) yields a gap ∆ (cid:39) . I ( ω )+ I ( − ω )which minimizes the effects of the Fermi function even in the case of finite energy and momentum resolutions [15, 16] [blue andred symbols in (c) represent the smoothed data, while the light shading gives the root-mean-square deviation of the raw data].The qualitatively similar behaviour observed on polycrystalline niobium – and returning a superconducting gap ∆ (cid:39) . resolve a gap of the order of 1 meV), in Fig. 2(e,f) we showas a bench-mark comparison the analogous results froma bulk, polycrystalline niobium sample – a known BCSsuperconductor with T c (cid:39) . K . The Dynes fit of theintegrated EDCs Fermi edge in Fig. 2(e) determines thegap to be ∆ = 1 . ± . (cid:39) .
14 meV [20]), inexcellent agreement with reported values [29]. Althoughthe leading edge shift [Fig. 2(e)] and the dip in the sym-metrized spectra [Fig. 2(f)] are more pronounced than forLi-graphene owing to the larger gap, the behaviour isqualitatively very similar. This provides additional sup-port to the superconducting origin of the temperature-dependent gap observed in Li-decorated graphene.If this is indeed a superconducting gap, the responsi-ble mechanism may likely be electron-phonon coupling,as predicted by theory for monolayer Li-graphene [8] and also seen experimentally for bulk GIC CaC [5]. In directsupport of this scenario, we present a detailed analysis ofthe graphene π ∗ bands in Fig. 3, demonstrating that theLi-induced enhancement of the electron-phonon couplingis indeed sufficient to stabilize a low-temperature super-conducting state. Graphene doped with alkali adatomsalways shows a strong kink in the π ∗ band dispersionat a binding energy of about 160 meV [11]. For the Li-graphene studied here, this is seen in the momentum-distribution curve (MDC) dispersions and correspond-ing real part of the self-energy Σ (cid:48) in Fig. 3(b-d). Thisstructure stems from the coupling to carbon in-plane(C xy ) phonons [4, 8]. Despite the apparent strength ofthis kink, the interaction with these phonon modes con-tributes little to the overall coupling parameter due totheir high energy (note that ω appears as a weighting . k k F ( ˚A ) E ne r g y ( m e V ) . k k F ( ˚A ) E ne r g y ( m e V ) ⌃
25 50 (meV)3 min LiExpt Theory ↵ F ( ! ) ( ! ) f . . . Energy (meV) ↵ F ( ! ) , ( ! ) . k k F ( ˚A ) ⌃
25 50 (meV)6 min Lig . . . Energy (meV) 10 min Lid . k k F ( ˚A ) ⌃
25 50 (meV)10 min Lih . . . Energy (meV) 10 min Liei Experiment . . . Li deposition time (min) FIG. 3.
Analysis of electron-phonon coupling in Li-decorated graphene. (a) Dirac dispersion from 3-minuteLi-decorated graphene, along the k -space cut indicated in the Fermi surface plot in (e), exhibiting kink anomalies due toelectron-phonon coupling (white line: MDC dispersion). (b-d) MDC dispersion and bare-band obtained from the self-consistentKramers-Kronig bare-band fitting (KKBF) routine [21, 22], for several Li coverages (see Methods and SI Appendix); the realpart of the self-energy Σ (cid:48) is shown in the side panels (orange: Σ (cid:48) from KKBF routine analysis; black: Σ (cid:48) corresponding to theEliashberg function presented below). (f-h) Eliashberg function α F ( ω ) from the integral inversion of Σ (cid:48) ( ω ) [23], and electron-phonon coupling constant λ = 2 (cid:82) dω α F ( ω ) /ω (see Methods and SI Appendix); in (h) the theoretical result from Ref. 8 fora LiC monolayer are also shown (gray shading). (i) Experimentally-determined contribution to the total electron-phononcoupling (black symbols) from: phonon modes in the energy range 100-250 meV (blue shading, white symbols), and 0-100 meV(orange shading); the coupling of low-energy modes strongly increases with Li coverage. factor in the integral calculation of λ - see Methods). Asillustrated by the white symbols in Fig. 3(i), the contri-bution to λ from these high-energy (100-200 meV) modesis determined to be 0 . ± .
05, and it remains approxi-mately constant for all Li coverages studied here. Thisvalue is, however, too small to stabilize a superconduct-ing state in this system [8, 11].With increasing Li coverage and the appearance of thespectral weight at Γ, significant modifications to the low-energy part of the dispersion ( (cid:46)
100 meV) become ap-parent [Fig. 3(b-d)]. With 10 minutes of Li deposition[Fig. 3(d)], an additional kink is visible at a binding en-ergy of approximately 30 meV, along with the associatedpeak in the real part of the self-energy Σ (cid:48) . The extracted(see Methods) Eliashberg functions and energy-resolved λ ( ω ) in Fig. 3(f-h) show that, at high Li coverage, phononmodes at energies below 60 meV are coupling strongly tothe graphene electronic excitations. The phonon modesin this energy range are of Li in-plane (Li xy ) and C out-of-plane (C z ) character [4, 8]. This is in agreement withpredictions [8], as shown by the direct comparison be-tween theory and experiment in Fig. 3(h) [30]. As for thetotal electron-phonon coupling λ for each coverage [blacksymbols in Fig. 3(i)], our values measured on the π ∗ -bandFermi surface at an intermediate location between Γ − K and K − M directions [Fig. 3(e)] provide an effective esti-mate for the momentum-averaged coupling strength [31]. Remarkably, the value λ = 0 . ± .
05 observed at thehighest Li coverage [Fig. 3(i)] is comparable with λ = 0 . [8] as well as λ (cid:39) .
58 ob-served for bulk CaC [32] – it is thus large enough forinducing superconductivity in Li-decorated graphene. Itis also significantly larger than the momentum-averagedresults previously reported for both Li and Ca depositionon monolayer graphene ( λ (cid:39) .
22 and 0.28, respectively[11]). We note that achieving such a large λ value is crit-ically dependent on the presence of the spectral weightobserved at Γ when Li is deposited on graphene at lowtemperatures, presumably forming an ordered structureon the surface and not intercalating. As shown in the SIAppendix, we find λ = 0 . ± .
05 after the same sampleis annealed at 60 K for several minutes, destroying the Liorder and associated Γ spectral weight.Taken together, our ARPES study of Li-decoratedmonolayer graphene provides the first evidence for thepresence of a temperature-dependent pairing gap on partof the graphene-derived π ∗ Fermi surface. The detailedevolution of the density of states at the gap edge, as wellas the phenomenology analogous to the one of known su-perconductors such as Nb – as well as CaC and NbSe ,which also show a similarly anisotropic gap around the K point [33–37] – indicate that the pairing gap observed at3.5 K in graphene is most likely associated with supercon-ductivity. Based on the BCS gap equation, ∆ = 3 . k b T c ,this suggests that Li-decorated graphene is superconduct-ing with T c (cid:39) . ACKNOWLEDGEMENTS
We gratefully acknowledge D.A. Bonn, S.A. Burke, M.Calandra, A. Chubukov, E.H. da Silva Neto, J.A. Folk,M. Franz, P. Hofmann, A.F. Morpurgo, G. Profeta, G.A.Sawatzky, and S. Ulstrup for valuable discussions, andP. Trochtchanovitch and M. O’Keane for technical assis-tance. This work was supported by the Max Planck -UBC Centre for Quantum Materials, the Killam, AlfredP. Sloan, Alexander von Humboldt, and NSERC’s SteacieMemorial Fellowship Programs (A.D.), the Canada Re-search Chairs Program (A.D.), the NSERC PDF Schol-arship (S.Z.), NSERC, CFI, and CIFAR Quantum Ma-terials.
METHODS
Sample preparation.
Epitaxial graphene monolayerswith a carbon buffer layer were grown under argon at-mosphere on hydrogen-etched 6H-SiC(0001) substrates,as described in Ref. 38. The samples were annealed at500 ◦ C and 8 × − Torr for 1 hour, immediately priorto the ARPES measurements. Lithium adatoms weredeposited 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 . ARPES experiments.
The measurements were per-formed at UBC with s -polarized 21.2 eV photons on anARPES spectrometer equipped with a SPECS Phoibos150 hemispherical analyzer, a SPECS UVS300 monochro-matized gas discharge lamp, and a 6-axes cryogenic ma-nipulator that allows controlling the sample temperaturebetween 300 and 3.5 K, with accuracy ± . − , respec-tively. For the measurements of the superconductinggaps, energy and angular resolution were set to 6 meVand 0.01 ˚A − , while the sample temperature was variedbetween 3.5 and 15 K. During the ARPES measurementthe chamber pressure was better than 4 × − Torr.
Electron-phonon coupling analysis.
The spectralfunction A ( k , ω ) measured by ARPES [39] provides infor-mation on both the single-particle electronic dispersion ε b k (the so-called ‘bare-band’) as well as the quasiparticle self-energy Σ( k , ω ) = Σ (cid:48) ( k , ω )+ i Σ (cid:48)(cid:48) ( k , ω ), whose real andimaginary parts account for the renormalization of elec-tron energy and lifetime due to many-body interactions,including electron-phonon coupling. By fitting with aLorentzian and a constant background the ARPES inten-sity profiles at constant energy ω = ˜ ω , known as momen-tum distribution curves (MDCs), one obtains the MDCdispersion defined by the peak maximum k m [plotted inFig. 3(a-d)], as well as the corresponding half-width half-maximum (HWHM) ∆ k m . The real and imaginary partsof the self-energy can then be defined as:Σ (cid:48) ˜ ω = ˜ ω − ε bk m , Σ (cid:48)(cid:48) ˜ ω = − ∆ k m v bk m , (1)(where v bk m is the bare-band velocity). To extract theself-energy and dispersion without any a priori knowledgeof the bare-band, we use the self-consistent Kramers-Kronig bare-band fitting (KKBF) routine from Ref. 21and 22 (see also SI Appendix).As for the dimensionless k -resolved electron-phononcoupling constant discussed in the paper and in particu-lar in Fig. 3(f-i), this is formally defined as [40]: λ k ( ω ) = 2 (cid:90) ω dω (cid:48) α F ( k , ω (cid:48) ) ω (cid:48) , (2)where α F ( k , ω ) is the Eliashberg function, i.e. thephonon density of states weighted by the electron-phononcoupling strength [40]. The latter is related to the realpart of the self-energy Σ (cid:48) ( k , ω ) via the integral relation:Σ (cid:48) ( k , ω ) = (cid:90) ∞ dω (cid:48) α F ( k , ω (cid:48) ) K (cid:18) ωkT , ω (cid:48) kT (cid:19) , (3)where K ( y, y (cid:48) ) = (cid:82) + ∞−∞ dx f ( x − y ) 2 y (cid:48) / ( x − y (cid:48) ) and f ( x − y ) is the Fermi-Dirac distribution. The momen-tum resolved α F ( k , ω ) function plotted in Fig. 3(f-h)can then be extracted from the real part of the self-energy Σ (cid:48) ( k , ω ) probed by ARPES via the integral in-version procedure described in Ref. 23. Ultimately, bymeans of Eq. 2, this also allows the calculation of theelectron-phonon coupling constant shown in Fig. 3 (seealso SI Appendix). Superconducting gap fitting.
As discussed in detailfor the case of FeAs and cuprate superconductors inRef. 17 and 18, respectively, when evaluating the openingof a superconducting gap based on the EDCs integratedin dk along a one-dimensional momentum-space cut per-pendicular to the Fermi surface (such as those presentedin Fig. 2), one can make use of the following formula: I (cid:82) dk ( ω ) = (cid:34) f ( ω, T ) ( a + b ω ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) Re ω − i Γ (cid:112) ( ω − i Γ) − ∆ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:35) ⊗ R ω . (4)This corresponds to the Dynes gap function (i.e., theBardeen-Cooper-Schrieffer density of states with a su-perconducting gap ∆, broadened by the pair-breakingscattering rate Γ [19]), multiplied by a linear background(with parameters a and b ) and by the Fermi-Dirac distri-bution f ( ω, T ), all convolved with a Gaussian function R ω 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 arefitted simultaneously using the above equation, accord-ing to the following additional considerations: since theintegrated EDCs were observed not to change outside ofthe gap region, the linear background is constrained tobe the same for the above and below T c measurements;the temperatures are fixed to the known measured values(with accuracy ± . E F and energyresolution are determined from fitting the high temper-ature data from either Nb and Li-graphene during eachmeasurement, and independently verified from measure-ments on polycrystalline gold. ∗ [email protected][1] Emery, N. et al. Superconductivity of Bulk CaC . Phys.Rev. Lett. , 087003 (2005).[2] Weller, T. E., Ellerby, M., Saxena, S. S., Smith, R. P.& Skipper, N. T. Superconductivity in the intercalatedgraphite compounds C Yb and C Ca.
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