Superconducting FeSe monolayer with milli-electron volt Fermi energy
Wantong Huang, Haicheng Lin, Cheng Zheng, Yuguo Yin, Xi Chen, Shuai-Hua Ji
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b Superconducting FeSe monolayer with milli-electron volt Fermi energy
Wantong Huang,
1, 2
Haicheng Lin, Cheng Zheng, Yuguo Yin, Xi Chen,
1, 3, ∗ and Shuai-Hua Ji
1, 3, 4, † State Key Laboratory of Low-Dimensional Quantum Physics,Department of Physics, Tsinghua University, Beijing 100084, China. Institute of Flexible Electronics Technology of THU, Zhejiang Frontier Science Center for Quantum Information, Beijing, China RIKEN Center for Emergent Matter Science (CEMS) - Wako, Saitama 351-0198, Japan (Dated: February 22, 2021)Iron selenide (FeSe) is an iron-based superconductor which shows unique properties, includingstrongly anisotropic superconducting gap, paramagnetism in undoped compound and extremelysmall Fermi pocket size. In this work, we demonstrate that the sizes of electron and hole pockets inFeSe monolayer become much smaller than those in bulk. The Fermi energy is in the order of a fewmeV and can be fine-tuned by the thickness of graphene layers underneath. Despite the low carrierdensity, the FeSe monolayers grown on trilayer or multi-layer graphene are superconducting. Thesuperconducting gap size is sensitive to the Fermi energy of the hole band. Remarkably, the FeSemonolayer provides the opportunity to study the physics in the crossover regime where the Fermienergy and superconducting gap are comparable to each other.
I. INTRODUCTION
New physics often emerges when two energy scalesbecomes comparable. It is highly desirable to discovermaterials in such a crossover regime. Here we showthat monolayer iron selenide (FeSe) is an eligible can-didate. FeSe is a compensated semimetal and ownsthe simplest crystalline structure [1] among the iron-based superconductors while exhibiting the characteris-tic tetragonal-orthorhombic structure transition [2] andnematicity [3, 4] in common. In the tetragonal phase,the Fermi surface of bulk FeSe consists of ellipsoidalhole pockets around Γ=(0,0) point and electron pocketsaround X=( π / a F e ,0) points [Fig. 1(a)]. The hole andelectron pockets are predominately contributed by the d xz and d yz orbitals, respectively. It has been demon-strated by angle-resolved photon-electron spectroscopy[4–7], scanning tunneling spectroscopy (STS) [8–10], andtransport measurements [7, 8, 11, 12] that the pocketsare rather shallow with Fermi energy ǫ F around 10 meV.Furthermore, the Fermi energy can be tuned via chem-ical doping, such as S[13]- and Te-substitutions [14–16].In Fe y Se x Te − x , the Fermi energy of the hole bandis reduced from 19 to 6 meV with decreasing excess Feconcentration y [16]. The Seebeck coefficient [17] setsthe upper limit of the Fermi energy of electron band inFe y Se . Te . to be ∼
10 meV. Conceivably, the pocketscan become even smaller in monolayer FeSe because theabsence of inter-layer coupling tends to narrow the energyband and decrease the overlap between electron and holepockets in energy. In light of this expectation, we havebeen able to achieve a Fermi energy of a couple of meV inmonolayer FeSe, which is almost one order of magnitudelower than that in bulk and comparable to the supercon-ducting gap. In term of the Uemura plot [18], the T c /T F ∗ [email protected] † [email protected] ratio of FeSe monolayer is higher than most of the uncon-ventional superconductors. Moreover, the in-depth studyof monolayer FeSe has it own importance. The transi-tion temperature of monolayer FeSe grown on SrTiO isgreatly enhanced as manifested by various investigations[19–22]. The enhancement is mainly interpreted by thestrong coupling between FeSe and SrTiO . To elucidatethe mechanism, it is desirable to reveal the intrinsic prop-erties of an almost free-standing FeSe monolayer, whichleads us to grow the film on van der Waals substrate. Wealso show that the charge transfer from the substrate canfine-tune the Fermi energy of the FeSe monolayer. II. EXPERIMENTAL DETAILS
The experiments were performed on a low temperatureultra-high vacuum (UHV, 1 × − torr) scanning tun-neling microscope (STM) equipped with molecular beamepitaxy (MBE). The lowest temperature of STM headcould reach base temperature of 60 mK with relativehigh effective electronic temperature of 260 mK in sam-ples [23]. To prepare the FeSe monolayer, which has beengrown on SrTiO [19] and other substrates [24, 25], high-purity Fe (99.995%) and Se (99.999%) were co-depositedonto the n-type 6H-SiC(0001) substrate (nitrogen-doped,resistivity 0.02-0.2 Ω · cm) held at 400 ◦ C. To reduce thecoupling between FeSe and the substrate to the van derWaals type [26], the surface of SiC was graphitized in ad-vance by thermal desorption of Si from the topmost lay-ers. Both bi-layer (BLG) and tri-layer graphene (TLG)can be formed and their relative coverage depends onthe heating temperature (1400 ◦ C ∼ ◦ C) and durationtime. The growth of FeSe was carried out under Se-rich condition and monitored by in situ reflection high-energy electron diffraction. The growth rate was abouttwo monolayers per hour.The electronic structure of FeSe monolayer was stud-ied by STM and STS. To avoid any contamination, we (e) (b) (d)
LOHI
FeSe SiC
95 pm H e i gh t ( p m ) (c)1-Fe2-Fek y k x Xq e q h Γ(a)
FIG. 1. (a) Schematic of the Brillouin zone and the Fermi surface. In the nematic phase, the electronic structure should bemore properly viewed in the two-Fe Brillouin zone. (b) Topographic image (350 nm ×
315 nm) of FeSe islands acquired by usingsample bias of V =3 V and tunneling current of I =20 pA. 1 UC (unit cell) and 2 UC are the areas for monolayer and bilayerFeSe. (c) Atomically resolved STM topography (10 nm ×
10 nm, 0.1 V, 0.1 nA) of the area marked by the white square in (b).(d) Side view of the monolayer FeSe across the step between BLG and TLG on adjacent SiC terraces. (e) Topographic profilealong the black dashed line in (b). performed the STM experiments on the films in the sameUHV system as MBE. Throughout the experiments, theSTM remained at the base temperature. Before imaging,the polycrystalline Pt-Ir alloy tip was modified and cali-brated on a clean Ag(111) surface. In the measurement,the d I /d V spectra on FeSe films were acquired by thestandard lock-in technique with a modulation frequency f = 887 Hz. III. RESULTS
Figure 1(b) shows the topographic image of FeSe filmson the substrate covered with both BLG and TLG whoseboundary is indicated by white dotted line. The lateralsize of a film is usually a few hundred nanometers. Atom-ically resolved STM image reveals the top Se atoms withSe-Se distance of 3.75 ˚A [Fig. 1(c)]. In the nematic phasebelow ∼
90 K, FeSe unit cell has two inequivalent Fe-Fe distances: a F e =2.665 ˚A and b F e =2.655 ˚A[27]. Sucha tiny difference is beyond the resolution of STM andcould not be resolved. The lattice of FeSe monolayer iscontinuous across the border between BLG and TLG. Asillustrated in Fig. 1(d), TLG is about 0.9 ˚A higher thanBLG because one more layer of SiC needs to be depletedto form TLG. The 0.9 ˚A difference also presents in theapparent height of FeSe monolayer (see the profile in Fig.1(e)).High quality of the FeSe monolayer film enables usto estimate the Fermi energies of the hole and electronbands via the quasi-particle interference (QPI) imag-ing. QPI visualizes the elastic scattering of electronson the constant-energy contour by mapping the energy-dependent normalized differential tunneling conductance(Supplementary Fig. S1[28]) on the surface. Therebythe Fourier transform of QPI provides information ofthe energy-momentum dispersion. Such spectroscopic
LOHI E ( m e V ) -10-50510-15-20 E ( m e V ) -10-50510 E ( k ) k Γ X (d)(c) -0.2 -0.1 0.1 0.20 q y ( Å -1 ) (b)(a) -0.2 -0.1 0.1 0.20 q x ( Å -1 ) -10 -5 10 Bias (mV) d I/ d V ( a . u . ) FeSe/BLG -4.6 meV
FIG. 2. (a-b) QPI dispersions of the non-superconductingarea of FeSe monolayer grown on BLG, obtained by taking linecuts from the Fourier transform of energy-dependent normal-ized conductance images (Supplementary Fig. S2[28]) along q x and q y , respectively. The dispersions are fitted by thedashed curves. The tunneling spectra of the mappings weretaken on a grid of 128 ×
128 pixels for a 85 nm ×
85 nm fieldof view. Sample bias voltage V =20 mV, tunneling current I =100 pA, modulation amplitude for the lock-in detection V mod =0.2 mV. (c) Schematic of the band dispersion aroundΓ=(0,0) point and X=( π /a F e ,0) point. (d) The d I /d V spec-trum ( V =10 mV, I =0.1 nA, V mod =0.1 mV) of monolayer onBLG. The arrow marks the top of hole pocket. The peaks arecaused by the quantum confinement in the lateral direction. mapping was performed on the FeSe monolayer grownon BLG. The Fourier transform (Supplementary Fig.S2[28]) exhibits strong in-plane anisotropy because of theorbital selective coherence [9]. The intra-pocket scatter-ing wave vectors q e and q h in Fig. 1(a) for the electronand hole pockets can be identified in the Fourier trans-form pattern. The band dispersions are extracted [Figs.2(a-b)] and then fitted with parabolic curves. The fittinggives the effective mass of holes (electrons) of 1.5 ± m (2.9 ± m ) along the corresponding directions k x ( k y )in the momentum space, where m is the free electronmass. Notably, the top of the hole band is at 2.7 ± ± E ( m e V ) -10-50510-15-20 (d) -0.2 -0.1 0.1 0.20 q y ( Å -1 ) E ( m e V ) -10-50510 (e)(b) Graphene (c) d I/ d V ( a . u . ) -4 -2 Bias (mV)
Bias (mV) d I/ d V ( a . u . ) (a) - - - - -- - - - - - - - - + + + + + + + ++ + + + + + + + FeSeSiC - - E~ se FeSe/TLG -0.2 -0.1 0.1 0.20 q x ( Å -1 ) LOHI
FIG. 3. (a) The dipole layer formed between SiC and FeSesurface. (b) The d I /d V spectrum ( V =10 mV, I =0.1 nA, V mod =0.1 mV) in the superconducting area. (c) A series ofd I /d V spectra ( V =5 mV, I =0.1 nA, V mod =0.05 mV) mea-sured along the arrow of 50 nm long in Fig. 1(b). (d-e) QPIdispersions of the superconducting area of FeSe monolayergrown on TLG (Supplementary Fig. S3[28]). FeSe monolayer on graphene can become supercon-ducting by hole doping from substrate as shown in Fig.3(a). In thermal equilibrium, the chemical potentials ofSiC, graphene and FeSe should be aligned as a result ofcharge transfer. The alignment leads to the formation ofa dipole-layer of a few nanometer thick below the surface [Fig. 3(a)]. The charge distribution inside the dipole-layer depends on the detailed structure at the atomiclevel. For FeSe/graphene/SiC structure, the carrier den-sity and Fermi energy of FeSe are closely related to thethickness of the graphene layers underneath. In this case,the characteristic energy and length scales are 0.1 eV(Supplementary Fig. S4[28]) and 1 nm, respectively. Thecorresponding carrier density induced by electric field( ∼ energy/length) is estimated to be 10 electrons / cm [Fig. 3(a)]. Given the density of states for FeSe mono-layer as 10 electrons / (eV · cm ) (Supplementary sectionV[28]), the change in the carrier density of FeSe on differ-ent thickness of graphene layers can bring about a shiftof Fermi energy in the order of meV. Such a shift is sig-nificant in manipulating the electronic properties if theFermi energy is also in the similar range.More specifically, the charge neutral point of TLGmoves upward in energy by about 0.1 eV compared toBLG (Supplementary Fig. S4[28]). Therefore, the FeSefilm on TLG should be considerably hole doped. As aresult, the FeSe film on TLG in Fig. 1(b) becomes super-conducting. The spectrum in Fig. 3(b) shows a typicalgap of ∆=0.60 meV at the base temperature. The linespectra [Fig. 3(c)] taken along the arrow in Fig. 1(b)exhibit certain inhomogeneity in spatial distribution. (b) (c) HILO-2 -1
Bias (mV)
Bias (mV) (d) ɛ F =3.4meV-0.2 -0.1 0.1 0.20 q x ( Å -1 ) (e) ɛ F =3.9meV-0.2 -0.1 0.1 0.20 q x ( Å -1 ) (f) ɛ F =4.8meV-0.2 -0.1 0.1 0.20 q x ( Å -1 ) E ( m e V ) -10-50510-15-20 (a) -2 -1 Bias (mV) d I/ d V ( a . u . ) FIG. 4. (a-c) The average d I /d V spectra of FeSe monolayeron TLG. The spectrum in (a) is the average of a line cuttaken along a 60 nm long line (64 points evenly distributedalong this line). Set point: V =2 mV, I =100 pA, V mod =0.02mV. The spectrum in (b) is the average of a line cut takenalong a 50 nm long line (32 points evenly distributed alongthis line). Set point: V =-4 mV, I =100 pA, V mod =0.04 mV.The spectrum in (c) is the average of a line cut taken along a48 nm long line (32 points evenly distributed along this line).Set point: V =10 mV, I =100 pA, V mod =0.1 mV. (d-f) Thecorresponding QPI dispersions acquired in the same areas asthe upper panel (Supplementary Fig. S6[28]). The hole doping is confirmed by QPI measurementon FeSe monolayer on TLG. Figures 3(d) and 3(e) showthe band dispersions extracted from QPI. The top of the (a)(b) B i as ( m V ) Distance (nm) (c)
HI LO(d) B i as ( m V ) Distance (nm)
Bias (mV) d I/ d V ( a . u . ) (e)(f) d I/ d V ( a . u . ) Distance (nm) -0.28 meV+0.28 meV
FIG. 5. (a-b) d I /d V ( r , E ) mapping measured on a 50 nm ×
50 nm area of FeSe monolayer films. Standing waves are clearlyvisible. Set point: V =-21 mV, I =0.1 nA, V mod =0.21 mV. Lock-in oscillation amplitude 0.21 mV. (c) A series of d I /d V spectraalong a black arrow of 50 nm long in (a)(32 points evenly distributed along this line). The averaged gap size is 0.28 meV.Set point: V =-5 mV, I =100 pA, V mod =0.05 mV. (d) d I /d V at 0.28 mV and -0.28 mV along the line. (e) A series of d I /d V spectra along a yellow arrow of 50 nm long in (a)(64 points evenly distributed along this line). Set point: V =-10 mV, I =100pA, V mod =0.1 mV. (f) The blue and red curves are the averaged d I /d V spectra of (c) and (e) respectively. The gap size ofblue (red) curve is 0.28 meV (0.35 meV). hole band for FeSe monolayer on TLG [Fig. 3(d)] is at ∼ ± ± × cm − and 1.5 × cm − , respectively. Such a low car-rier density for a superconductor is rare except in sometransition metal dichalcogenide monolayers[29, 30] andrecently discovered twisted bilayer graphene[31].A series of FeSe monolayer films have been preparedon TLG. Depending on the locations of graphene on SiC,the doping level varies. On each film, a relatively largeuniform area was chosen for STS and QPI measurement.Figures 4(a-c) display the averaged d I /d V spectra ofFeSe monolayer all on TLG but with different dopinglevels. The gap sizes of the three areas are 0.31 meV,0.45 meV, and 0.75 meV, respectively. The correspond-ing Fermi energy ǫ F of the hole band in each case canbe obtained by fitting the QPI dispersions [Figs. 4(d-f)]and found to be 3.4 meV, 3.9 meV and 4.8 meV, respec-tively. It is evident that the superconducting gap size∆ is sensitive to and increases monotonically with the Fermi energy of the hole band [see also Fig. S5]. The in-creased hole density in the FeSe monolayer enhances thescreening effect and hence the superconductivity. Thisobservation may also indicate that the superconductiv-ity of FeSe monolayer is dominated by a single hole band.All the dispersions in Figs. 3 and 4 were obtainedin carefully selected areas to make sure that the Fermienergy of each area is highly uniform. The Fourier trans-form of the standing wave generated by the interfer-ence of quantum states scattered off point defects andstep edges in an area leads to the dispersion. The spa-tial uniformity of the dispersion in each area is demon-strated by the clearly-defined Fourier transform pattern[Fig. S6]. Inside a superconducting area, all the spec-tra showing the superconducting gaps in Figs. 3 and 4were obtained along lines away from the defects. In thevicinity of defects, on the other hand, the spectra reveallarge variation. For example, the Bogoliubov quasiparti-cles around the coherence peaks can present the standingwave pattern [Figs. 5(c-e)] due to the scattering of de-fects. The coherence peaks locate at ± ǫ F can be pusheddown to the meV range and thus becomes comparable tothe superconducting gap ∆. As a result, it is possible torealize novel quantum states in FeSe monolayer, such asBCS-BEC crossover [8], which need further investigation.The extremely low Fermi energy is inherent only to themonolayer. For those areas in Fig. 1(b) with bilayerFeSe, the dispersion of the hole pocket corresponds to aFermi energy of 15 ∼
20 meV [Fig. 6(a)], which is closeto the bulk counterpart and much larger than that of theFeSe monolayer. The inter-layer coupling gives rise toone more hole band crossing the Fermi level. Usually thebilayer FeSe is superconducting [Fig. 6(b)]. -0.4 -0.2 0 0.2 0.4-30-20-100102030 E ( m e V ) (a) (b) LOHI -4 -2
Bias (mV) d I/ d V ( a . u . ) q x (Å -1 ) FIG. 6. (a) QPI dispersion of FeSe bilayer. (b) d I /d V ofsuperconducting FeSe bilayer. Set point: V =5 mV, I =100pA, V mod =0.05 mV. The superconducting gap is 1.24 meV. IV. SUMMARY
We performed detailed STM/STS and QPI in-vestigations of FeSe monolayer films grown on graphene/SiC(0001) substrate. The Fermi energyof FeSe monolayer is reduced to only a few milli-electronvolts and can be tuned by graphene layers. Superconduc-tor with ultra small Fermi pockets is a unique platformto study the exotic electron correlation effects[32]. Thelow Fermi energy implicates unconventional pairingmechanism. The retardation condition ( ω D ≪ ǫ F , where ω D is the characteristic frequency of phonons) is crucialfor the applicability of the conventional BCS theory. Theviolation of retardation condition in superconductingmonolayer FeSe suggests pairing mechanism beyondBCS theory [33]. In general, the thin monolayer filmsof high temperature superconductors, both cuprates[34, 35] and iron-based superconductors [19], have greatpotential to achieve deeper understanding of high T C superconductivity.Another attractive property of FeSe monolayer is thatits exceedingly low Fermi energy is comparable to the su-perconducting gap. The competition and cooperation ofthese energies may lead to new physics in the crossoverregime. We propose FeSe monolayer as a distinctive sys-tem to study novel quantum states, such as BCS-BECcrossover. In the current experiments, the BCS-BECcrossover hasn’t been realized yet. Further fine-tuningof the carrier density and correlation effect may lead tosuch many body states.This work is supported by the National Natural Sci-ence Foundation of China (Grants No. 11934001 andNo. 12074211) and the Ministry of Science and Tech-nology of China (Grants No. 2016YFA0301002 and No.2018YFA0305603). [1] J. Paglione and R. L. Greene, Nat. 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