Enhanced superconductivity and evidence for novel pairing in single-layer FeSe on SrTiO3 thin film under large tensile strain
R. Peng, X. P. Shen, X. Xie, H. C. Xu, S. Y. Tan, M. Xia, T. Zhang, H. Y. Cao, X. G. Gong, J. P. Hu, B. P. Xie, D. L. Feng
aa r X i v : . [ c ond - m a t . s up r- c on ] O c t Enhanced superconductivity and evidence for novel pairing in single-layer FeSe on SrTiO thin filmunder large tensile strain R. Peng,
1, 2
X. P. Shen,
1, 2
X. Xie,
1, 2
H. C. Xu,
1, 2
S. Y. Tan,
1, 2
M. Xia,
1, 2
T.Zhang,
1, 2
H. Y. Cao,
1, 3
X. G. Gong,
J. P. Hu,
4, 5
B. P. Xie,
1, 2, ∗ and D. L. Feng
1, 2, † State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China Advanced Materials Laboratory, Fudan University, Shanghai 200433, People’s Republic of China Key Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200433, China Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Sciences, Beijing 100080, People’s Republic of China Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA (Dated: July 18, 2018)Single-layer FeSe films with extremely expanded in-plane lattice constant of 3.99 ± / Nb:SrTiO / KTaO heterostructures, and studied by in situ angle-resolved photoe-mission spectroscopy. Two elliptical electron pockets at the Brillion zone corner are resolved with negligiblehybridization between them, indicating the symmetry of the low energy electronic structure remains intact as afree-standing single-layer FeSe, although it is on a substrate. The superconducting gap closes at a record hightemperature of 70 K for the iron based superconductors. Intriguingly, the superconducting gap distribution isanisotropic but nodeless around the electron pockets, with minima at the crossings of the two pockets. Ourresults put strong constraints on the current theories, and support the coexistence of both even and odd parityspin-singlet pairing channels as classified by the lattice symmetry. PACS numbers: 74.20.Rp,81.15.Hi,74.25.Jb,74.70.Xa
After five years of intensive studies on iron-based high tem-perature superconductors (FeHTSs), a universal picture of thepairing symmetry has not been achieved so far. The once pre-vailing s ± pairing [1], with the sign reversal between elec-tron and hole Fermi surfaces, was seriously challenged byFeHTSs with only electron Fermi surfaces (called e-FeHTSshereafter), including A x Fe − y Se (A = K, Cs, Rb, etc. ) [2] andsingle-layer FeSe on SrTiO (STO) [3–5]. For these systems,weak coupling theories based on spin-fluctuations predict a d -wave pairing symmetry [6, 7]. However, it is inconsistent withthe isotropic superconducting gap observed by angle resolvedphotoemission spectroscopy (ARPES) [2, 3, 8, 9], togetherwith evidences for nodeless superconducting gap from spe-cific heat [10], nuclear magnetic resonance [11], etc. On theother hand, the sign preserving s -wave pairing symmetry [12–15] could not account for the spin-resonance mode found inRb x Fe − y Se by inelastic neutron scattering [16], which sug-gests the sign change of the superconducting order parameteron di ff erent Fermi surface sections [17].To explain the sign changing isotropic gap in e-FeHTSs,several novel pairing scenarios were proposed. For example,it is argued in the bonding-antibonding s ± pairing scenariothat with strong hybridization between electron pockets, thetwo reconstructed electron pockets can have di ff erent signs[18]. A further study suggested that this pairing likely co-exists with the d -wave to form an s + id -wave pairing sym-metry [19]. More recently, the importance of the parity ofthe 2-Fe unit cell has been emphasized [20], and it has beenproposed that there are even and odd parity s -wave spin sin-glet pairing states, and the coexistence of both states gives afully gapped state with varied signs in di ff erent Fermi surfacesections [21, 22]. The hybridization between the two elec- tron pockets is not necessary in this scenario. So far, thesescenarios could not be convincingly tested, since the detailedstructure of the two electron pockets could not be resolved inall known e-FeHTSs.Two recent ARPES studies have found a gap in single-layer FeSe / STO, which closes at 65 K and suggests a pos-sible record high superconducting transition temperature ( T c )of 65 K for FeHTSs [4, 5]; or at least, it is the pair-formationtemperature record, if the superconducting transition thereis a two dimensional Berezinskii-Kosterlitz-Thouless (BKT)type. Particularly, our previous ARPES study has found thatthe high T c in single-layer FeSe / STO is induced by suppress-ing the otherwise strong spin density wave (SDW) with elec-trons transferred from the oxygen-vacancy induced states inthe substrate, and the SDW in undoped FeSe is enhanced withexpanded in-plane lattice constant [5]. Consistently, the den-sity functional theory (DFT) calculations show that it is dueto the increased superexchange interactions in films under en-hanced tensile strain [23]. We explicitly suggested that higher T c might be obtained by doping films with further enlargedlattice [5], assuming the underlying spin fluctuations and su-perexchange interactions are important for the superconduc-tivity.In this paper, we have fabricated a new kind of e-FeHTS,the single-layer FeSe on top of the Nb:SrTiO epitaxial thinfilm grown on a KTaO substrate, by successfully expandingthe in-plane lattice of FeSe to 3.99 ± (a) (d)(b) LowLow HighHigh k y ( Å - ) KTaO (103)Nb:STO(103) Q ( Å - ) Q // (Å -1 ) (c) KTaO substrate35u.c. 5% Nb:STO5u.c. 0.5% Nb:STOFeSe filmsilver paste k x (Å -1 ) (e) a ( Å ) moderately expandedextremelyexpanded .5.0.5 .5.0.5 .5.0.5 .5.0.5 .5.0.5 FIG. 1: (color online). (a) Schematic illustration of the heterostruc-ture. (b) Cubic unit cell of KTaO substrate. (c) X-ray di ff rac-tion reciprocal space map of the grown heterostructure around the(103) Bragg reflections. (d) Thickness-dependent photoemission in-tensity maps at the Fermi energy (E F ) for FeSe / Nb:SrTiO / KTaO .The intensity was integrated over a window of [E F -10 meV, E F + / Nb:SrTiO is reproduced from ref. 5. zone (BZ) corner and minimal at the crossings of the twopockets. The anisotropic but nodeless superconducting gaptogether with the intact electronic structure strongly supportsthe co-existence of the intra-pocket and inter-pocket pairingchannels of the two electron pockets. Our experiments pro-vide important information for solving the pairing symmetrypuzzle in e-FeHTSs, and also elucidate a new way to manip-ulate the electronic structure and enhance T c for FeSe withartificial interface.The heterostructure is designed to further enhance the ten-sile strain on FeSe while preserving a FeSe / Nb:SrTiO inter-face (Fig. 1(a)). KTaO (KTO) serves as the substrate, withcubic structure and lattice constant of 3.989Å (Fig. 1(b)), 2%larger than that of bulk STO (3.905Å). To eliminate the pho-toemission charging e ff ect of KTO, silver paste was attachedon the substrate edge, and 35 unit cells (u.c.) of highly con-ductive 5% Nb doped STO films [24] were grown layer-by-layer on KTO substrate with ozone-assisted molecular beamepitaxy (MBE) [25, 26]. Afterwards, 5 u.c. of 0.5% Nb dopedSTO were epitaxially grown, with similar chemical composi-tion as the Nb:SrTiO substrate in the previous works [3–5].The grown Nb:SrTiO films were directly transferred to an-other MBE chamber, where FeSe thin films were grown andpost-annealed following the method in ref. 5. Details are de-scribed in the Supplementary Material [26]. ARPES data weretaken in situ under ultra-high vacuum of 1 . × − mbar , with a SPECS UVLS discharge lamp (21.2eV He-I α light)and a Scienta R4000 electron analyzer. The energy resolutionis 6 meV and angular resolution is 0.3 ◦ . Data were taken at25 K if not specified otherwise.To check the actual strain on FeSe film, x-ray di ff raction re-ciprocal lattice map was performed on the grown heterostruc-ture around the (103) Bragg reflections. The in-plane recip-rocal vector (Q // ) of the Nb:SrTiO film equals that of KTOsubstrate (Fig. 1(c)). Moreover, as shown in Fig. 1(d), basedon the high symmetry points of the photoemission intensitymaps, a clear expansion of the BZ size with increasing FeSethickness can be identified. The in-plane lattice constants ofFeSe films were calculated by inversing the BZ size and plot-ted in Fig. 1(e), demonstrating a rapid relaxation of the in-plane lattice in multilayer FeSe [5]. Indeed, the lattice con-stant of single-layer FeSe is 3.99 ± / Nb:SrTiO (Fig. 1(e)), and the cross-shape Fermi surface at the BZ cor-ner in films with more than 2 monolayers (ML) thick is ahallmark of the SDW (Fig. 1(d)), as shown in our previousstudies [5]. Hereafter, we refer FeSe X to the extremely tensilestrained 1ML FeSe studied in this paper, while refer FeSe M tothe moderately expanded 1ML FeSe on Nb:SrTiO substrate.Detailed electronic structure of FeSe X is studied. As shownby the photoemission intensity maps (Fig. 2(a)), the Fermi sur-face of FeSe X also consists of only electron pockets, similarto A x Fe − y Se and FeSe M . However, instead of the nearlycircular and highly degenerate pockets in FeSe M , two ellipti-cal Fermi-surfaces perpendicular to each other are observedin Fig. 2(a), and sketched in Fig. 2(b). Based on the Fermisurface volume, the estimated carrier concentration is 0.12 e − per Fe for FeSe X , similar to that of FeSe M . This indicates thatstrain modifies the Fermi-surface shape without much changeof the charge transfer from the substrate. DFT calculationswere performed on free-standing monolayer FeSe with extra0.12 e − per Fe for the two lattice constants (Fig. 2(c)), show-ing that the expanded lattice increases the ellipticity of the theelectron pockets at M, which is qualitatively consistent withour experimental findings.As shown in Fig. 2(d1)-(d2), a parabolic band (assigned as α ) below E F can be identified around the zone center, withband top at about -72 meV. The ω band is clearly resolvedaround 0.21 eV below E F near Γ , which is often observed iniron pnictides with d z orbital character. Around the zone cor-ner (Fig. 2(e1),(f1)), the γ band in FeSe M [3] splits into γ and γ bands in FeSe X , due to the lifted degeneracy of γ and γ pockets. In this 2-Fe BZ, the γ ( γ ) band is intensearound M1 (M2), while its folded band around the neighbor-ing BZ corner M2 (M1) is weak in intensity but can still betracked in MDCs (momentum distribution curves) as shown inFigs. 2(f2) (Figs. 2(e2)). By fitting the MDC at E F with fourLorentzian peaks (Fig. 2(e3),(f3)), the Fermi wave-vector ( k F )is resolved, which is 0.51 Å − for the major axis and 0.37 Å − for the minor axis of the elliptical pocket. The deduced k F ’sfrom cut β β Μ2Γ
High HighLow Low α ω γ γ γ γ /γ γ -0.3 0.0 I n t en s i t y ( a r b . un i t s ) E-E F (eV) (a) (d1)(d2) (e2) Μ1 -0.4 0.4 Μ1 -0.4 0.4 I n t en s i t y ( a r b . un i t s ) k // (Å -1 ) (e3) (f2) (g2) Μ2 -0.4 0.4 k // (Å -1 ) k // (Å -1 ) (f3) (g3)(e1) (f1) (g1)(h)(b) -0.3-0.2-0.10.0 -0.4 -0.2 0.0 0.2 0.4 αω E - E F ( e V ) k // (Å -1 ) γ γ E - E F ( e V ) Μ1 Μ1 γ -0.20-0.100.00 -0.4 -0.2 0.0 0.2 0.4 βγ γ F -25meV (c) (i)(j) Γ ΓΜ1 ΓΜ1 .5.0.5 ΓΜ1 Μ2
Γ ΓΓΜΜ XX ΓΜ1Μ1
E-E F (meV) -100 -50 0 50 100 I n t en s i t y ( a r b . un i t s ) γ γ γ γ / γ γ / γ γ X a=3.989Åa=3.905Å Temperature(K) G ap ( m e V ) M Γ X M0-1-2 E ne r g y ( e V ) FeSe X FeSe M FIG. 2: (color online). (a) Photoemission intensity map of FeSe X , compared with that of FeSe M which is reproduced from ref. 5. The intensitywas integrated over a window of [E F -10 meV, E F +
10 meV]. The the measured Fermi surface sheets are shown by the dashed curves. (b)Four-fold symmetrized sketch of the Fermi surface sheets observed in panel (a) for FeSe X . Cuts X and FeSe M , respectively. The extra 0.12 e − per Fe are included by shifting the chemical potential [23]. (d1) Photoemission intensityalong cut Γ as indicated in panel (b), and the corresponding (d2) energy distribution curves (EDCs). (e1) Photoemission intensityalong cut F fitted by Lorentzian peaks. (f1)-(f3) are the same as (e1)-(e3), but alongcut γ band along cut X . The gap isobtained following the standard fitting procedure described in ref. 28. The original data, the fitted results and gap positions are shown in blackdots, red curves, and red arrows, respectively. (j) The superconducting gap vs. temperature for FeSe X , compared with that of FeSe M which isreproduced from ref. 5. photoemission intensity along cut γ and γ pock-ets intersect. Remarkably, the MDCs (Fig 2(g2)-(g3)) showa single-Lorentzian-peak behavior for both sides, without anyhybridization-induced band anti-crossing. Normally, this isonly expected for a free-standing single-layer FeSe, as illus-trated by our DFT calculations in Fig 2(h), when there is nointerlayer hopping and the S symmetry is preserved. Thenegligible hybridization here thus suggests that the low energyelectronic structure of the FeSe layer remains intact withoutmuch influence from the substrate. The screening from thesubstrate phonon on the Cooper pairing in FeSe thus shouldbe unlikely [27]. Upon post-annealing under vacuum and Seflux [26], the superconducting gap size and sample quality aretuned. As shown in Fig. 2(i), one could still observe the signa-ture of gap in the 65 K data and in the corresponding fit [28].The temperature dependence of the gap can be well-fitted bythe BCS gap temperature dependence function in Fig. 2(j).These suggest that this film has a possible T c of 70 K, as-suming the gap is not due to Cooper pair pre-formation inthe normal state. The T c is slightly enhanced in this film com-pared with FeSe M (Fig. 2(j)), probably due to the enhanced su-perexchange interactions with increased lattice constant here[5, 23].The momentum dependence of the superconducting gap isfurther investigated. Figures 3(b) and 3(c) show the EDCs (energy distribution curves) along the two cuts indicated inFig. 3(a). The EDCs are symmetrized with respect to E F toremove the influence of Fermi-Dirac cut-o ff . Due to the lowintensity of the folded Fermi surface, the superconducting gapof γ band can be deduced without interference from the γ band. At the k F , the spectra lose half intensity and the EDCsbend back. The vertical green and brown dashed lines indicatethe coherence peak positions at two k F ’s (274 ◦ and 224 ◦ inthe polar coordinates) respectively, and they unambiguouslydi ff er from each other. The symmetrized spectra in the su-perconducting state at various k F ’s of γ pocket are shown inFig. 3(d). The peak positions of the coherence peaks di ff erat di ff erent momenta, indicating an anisotropy in supercon-ducting gaps. To quantify the anisotropy, the superconductinggap size are fitted [28], and plotted in a polar coordinate inFig. 4(a). Beyond the finite error bars, a clear anisotropy ofsuperconducting gap can be recognized, following four-foldsymmetry. The superconducting gap distribution on anothersample is shown in Fig. 3(e) and Fig. 4(b). Despite of the var-ied superconducting gap size due to di ff erent post-annealingprocess, anisotropic but nodeless superconducting gap distri-bution along the electron Fermi surface is alike in di ff erentsamples.Although the in-plane anisotropic superconducting gap onthe electron Fermi surfaces has not been observed in e- F (meV) I n t en s i t y ( a r b . un i t s ) Sample A (e) Sample B -100 -50 0 50 100 F (meV)Sample A(a) Μ1 ϕ -100 -50 0 50 100 F (meV) ϕ= FIG. 3: (color online). (a) Fermi surface sheets around M1 and thedefinition of cut ϕ . (b),(c) SymmetrizedEDCs for sample A along cut k F ’s of γ are shown by the thicker curves, with the polar angle of 274 ◦ and224 ◦ , respectively. (d) Symmetrized EDCs at k F ’s of γ band forsample A, with the momentums counterclockwise along γ pocketas indicated by the polar angles. (e) is the same as panel (d), butmeasured on sample B. FeHTSs before, it has been reported in several iron pnictides.For example, we recently found that the superconducting gapis anisotropic in NaFe . Co . As due to the coexistenceof SDW and superconductivity, with its minima at ϕ = π/ ϕ = ◦ were reportedfor an electron pocket of LiFeAs, which is attributed to bandhybridization and the mixture of (cos k x + cos k y )-term in thegap function [30]. However, none of these could account forthe over 50% variation of the gap size in the elliptical Fermisurface of FeSe X as neither SDW nor hybridization is present.The observed nodeless superconducting gap poses strongconstraints on theoretical scenarios. Based on the d -wavepairing, if the electron pockets are elliptical with negligiblehybridization, gap nodes would be induced in the folder BZ,which is not observed here. The bonding-antibonding s ± [18]or s + id symmetry [19] also can not explain our observations,since the required sizable hybridization between the electronpockets is absent in the data. We note that our data might beconsistent with the theory with even and odd parity s -wavespin singlet pairing channels [21]. This theory suggests that afull gap with a sign change on the electron pockets can be real-ized without the hybridization by combining the two di ff erent s -wave pairings: the even parity s -wave pairing contributesa d -wave-like momentum dependence of the gap structurearound each electron pocket, ∆ e ∼ cos (2 ϕ ), with nodes around ϕ ∆(ϕ) (a) Sample A (c) Μ +- ϕ (meV) ∆(ϕ) FIG. 4: (color online). (a) Gap distribution of the γ pocket in polarcoordinates for sample A, where the radius represents the gap size,and the polar angle represents ϕ . The gap is estimated through anempirical fit [28], and the error bars come from the standard deviationof the fitting process. Solid black curve shows the fitting by ∆=∆ +∆ | cos(2 ϕ ) | , with ∆ = ∆ = ∆ = ∆ = A g symmetry on the four zone corners around Γ [21, 22]. ϕ = ± π/ , ± π/ ∆ o . The convolution ofthese two momentum-dependent pairing components gener-ally produces an anisotropic gap function [22]. In Figs. 4(a)and 4(b), we show that the experimental gap can be well fittedby ∆=∆ + ∆ | cos(2 ϕ ) | , which agrees with the above theoryif taking ∆ o = ∆ at ϕ = ± π/ , ± π/
4, and ∆ e ≈ ∆ + ∆ at ϕ = , ± π/
2, and π according to the theory [21, 22].To summarize, we have shown that heterostructure providesa novel path for exploring superconductivity in FeHTSs, andrevealed the novel electronic structure and gap distribution inextremely tensile strained single-layer FeSe. The lifted degen-eracy of the electron pockets with negligible hybridization, to-gether with the anisotropic but nodeless superconducting gap,provide important experimental foundations for solving thepairing symmetry puzzle of e-FeHTSs. Acknowledgements:
We gratefully acknowledge the fruit-ful discussions with Prof. Jianxin Li and Prof. Jian Shen, andwe thank Prof. Dawei Shen and Prof. Wei Peng for helpingwith x-ray di ff raction measurements. This work is supportedin part by the National Science Foundation of China, and Na-tional Basic Research Program of China (973 Program) underthe grant No. 2012CB921402. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Rep. Prog.Phys. , 124508 (2011).[2] Y. Zhang, L. X. Yang, M. Xu, etal., Nat. Mater. , 273 (2011).[3] D. F. Liu, etal., Nat. Commun. , 931 (2012).[4] S. L. He, etal., Nat. Mater. , 605 (2013).[5] S. Y. Tan, etal., Nat. Mater. , 634 (2013).[6] T.A. Maier, S. Graser, P.J. Hirschfeld, D.J. Scalapino, Phys. Rev. B , 220504(R) (2012).[9] I. I. Mazin, Physics 4, 26 (2011).[10] B. Zeng, B. Shen, G. F. Chen, J. B. He, D. M. Wang, C. H. Li,and H. H. Wen, Phys. Rev. B , 144511 (2011).[11] L. Ma, J. B. He, D. M. Wang, G. F. Chen, and W. Yu, Phys. Rev.Lett. , 197001 (2011).[12] C. Fang, Y. L. Wu, R. Thomale, B. A. Bernevig and J. P. Hu,Phys. Rev. X , 011009 (2011).[13] J. P. Hu and N. N. Hao, Phys. Rev. X , 021009 (2011).[14] R. Yu, P. Goswami, Q. Si, P. Nikolic, and J.-X. Zhu,arXiv:1103.3259.[15] K. J. Seo, B. A. Bernevig, and J. P. Hu, Phys. Rev. Lett. ,206404 (2008).[16] J. T. Park, G. Friemel, Y. Li, etal., Phys. Rev. Lett. , 024529 (2011).[19] M. Khodas and A. V. Chubukov, Phys. Rev. Lett. , 247003(2012).[20] Chia-Hui Lin, Tom Berlijn, Limin Wang, Chi-Cheng Lee, Wei- Guo Yin, and Wei Ku, Phys. Rev. Lett. , 257001 (2011).[21] J. P. Hu, Phys. Rev. X , 031004 (2013).[22] N. N. Hao and J. P. Hu, arXiv:1305.5034 (2013).[23] First-principle calculations were conducted using the project-augmented-wave pseudopotential implemented in the VASPcode. The generalized-gradient correction of Perdew-Burke-Ernzerhof is employed for the exchange-correlation-potentials.For more details, see Hai-Yuan Cao, Shiyong Tan, Hongjun Xi-ang, Donglai Feng, and Xin-Gao Gong, (preprint).[24] Tong Zhao, Huibin Lu, Fan Chen, Shouyu Dai, Guozhen Yang,Zhenghao Chen, Journal of Crystal Growth
451 (2000).[25] J. H. Haeni, C. D. Theis, and D. G. Schlom, Journal of Electro-ceramics , 385 (2000).[26] A link to the online Supplementary Material of this paper willbe added here.[27] Yuan-Yuan Xiang, Fa Wang, Da Wang, Qiang-Hua Wang, andDung-Hai Lee, Phys. Rev. B , 371 (2012).[29] Q. Q. Ge, Z. R. Ye, M. Xu, et al., Phys. Rev. X.108