Interfacial Electron-Phonon Coupling Constants Extracted from Intrinsic Replica Bands in Monolayer FeSe/SrTiO_3
Brendan D. Faeth, Saien Xie, Shuolong Yang, Jason K. Kawasaki, Jocienne N. Nelson, Shuyuan Zhang, Pramita Mishra, Chen Li, Christopher Jozwiak, Aaron Bostwick, Eli Rotenberg, Darrell G. Schlom, Kyle M. Shen
IInterfacial Electron-Phonon Coupling Constants Extracted from Intrinsic ReplicaBands in Monolayer FeSe/SrTiO Brendan D. Faeth, ∗ Saien Xie, Shuolong Yang,
1, 2, 3, † Jason K. Kawasaki,
1, 2, ‡ Jocienne N. Nelson, Shuyuan Zhang, Pramita Mishra, § Chen Li, ChristopherJozwiak, Aaron Bostwick, Eli Rotenberg, Darrell G. Schlom,
3, 2 and Kyle M. Shen
1, 2, ¶ Department of Physics, Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA Advanced Light Source, E.O. Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
The observation of replica bands by angle-resolved photoemission spectroscopy has ignited in-terest in the study of electron-phonon coupling at low carrier densities, particularly in monolayerFeSe/SrTiO , where the appearance of replica bands has motivated theoretical work suggesting thatthe interfacial coupling of electrons in the FeSe layer to optical phonons in the SrTiO substratemight contribute to the enhanced superconducting pairing temperature. Alternatively, it has alsobeen recently proposed that such replica bands might instead originate from extrinsic final statelosses associated with the photoemission process. Here, we perform a quantitative examination ofreplica bands in monolayer FeSe/SrTiO , where we are able to conclusively demonstrate that thereplica bands are indeed signatures of intrinsic electron-boson coupling, and not associated withfinal state effects. A detailed analysis of the energy splittings between the higher-order replicas, aswell as other self-energy effects, allow us to determine that the interfacial electron-phonon couplingin the system corresponds to a value of λ = 0 . ± . One of the most powerful attributes of angle-resolvedphotoemission spectroscopy (ARPES) is its ability to re-veal many-body interactions through its lineshape, ow-ing to its close relationship to the single-particle spectralfunction A ( k , ω ). ARPES has revealed the presence ofstrong electron-boson coupling in a variety of quantummaterials, including high-temperature cuprate supercon-ductors [1, 2], colossal magnetoresistive manganites [3],and titanates [4]. At high carrier densities, electron-boson coupling is manifested as an abrupt kink in thequasiparticle dispersion occurring at the boson energy.At low carrier densities, where screening is weaker andthe Fermi energy, E F , can be comparable to the rele-vant phonon frequency, Ω , the electron-phonon couplingcan give rise to polaronic quasiparticles and the presenceof satellite “replica bands”, which occur at near-integermultiples of Ω . Such features have been recently re-ported in a variety of systems, including at the surfaceof SrTiO [4–6], anatase TiO [7, 8], and most notablyin monolayer FeSe films grown on SrTiO [9–12], whereit has been argued that the interfacial coupling of elec-trons in the FeSe monolayer to optical phonons in theSrTiO substrate could potentially be responsible for itsenhanced superconducting properties [9]. Furthermore, ∗ Corresponding author: [email protected] † Current Address: Pritzker School of Molecular Engineering, TheUniversity of Chicago, Chicago, IL 60637, USA ‡ Current Address: Department of Materials Science and Engi-neering, University of Wisconsin, Madison, Wisconsin 53706,USA. § Current Address: Department of Physics, Indian Institute of Sci-ence, Bangalore 560012, India ¶ Corresponding author: [email protected] it may be possible to extract more extensive quantitativeinformation about the nature of interactions through adetailed analysis of the replica bands, including their in-tensities and energy separations. On the other hand,it has also been recently suggested that these replicabands observed by ARPES are not signatures of intrin-sic electron-phonon interactions, but rather could arisefrom extrinsic electron energy losses in the photoemis-sion process, whereby ejected photoelectrons lose energyto surface phonons [13]. Such extrinsic “final-state ef-fects” produced by photoelectron energy loss processeswould appear very similar to intrinsic satellites. Fur-ther complicating the situation, such loss features shouldbe prevalent in systems where the carrier density is lowand screening effects are weak, precisely where pola-ronic quasiparticles and intrinsic replica bands in ARPESwould also be expected.Therefore, a detailed investigation of photoemissionreplica bands is imperative to distinguish whether theyare indeed intrinsic features in the spectral function ofquantum materials versus extrinsic final-state loss effects.Given the importance of ARPES as the premier tool forinvestigating electronic many-body interactions, this iscritical not only for the understanding of ARPES as atechnique, but also for the general study of quantum ma-terials and their many-body interactions. To achieve this,we investigate MBE-grown, single layer FeSe/SrTiO thin films, where such replica bands have been observed,but also where it has been suggested as potentially arisingfrom extrinsic loss effects from Fuchs-Kliewer phonons inthe SrTiO substrate [14]. By employing a wide rangeof photon energies, we are able to conclusively deter-mine that the replica bands indeed arise from intrin-sic electron-phonon coupling between the FeSe film andSrTiO substrate, and not from extrinsic losses. Fur- a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b thermore, a quantitative analysis of the spectra in com-parison to prior theoretical calculations also allows us todetermine the coupling constant, λ = 0 . ± .
02, byextracting the blue shift of the first satellite feature, aswell as accurately measuring the ratio of the main bandto replica bands [15]. This work not only demonstratesthat replica bands in FeSe/SrTiO arise from intrinsicelectron-phonon coupling, but also suggests a general-ized approach for evaluating whether features in the pho-toemission spectrum indeed arise from intrinsic many-body interactions in other quantum materials. Further-more, this work introduces a new experimental procedurefor extracting quantitative electron-phonon coupling con-stants in polaronic systems from observed replica bands,for instance, allowing us to estimate the likely enhance-ment of T c in monolayer FeSe/SrTiO due to coupling tothe interfacial SrTiO phonons.Monolayer FeSe films were grown by molecular beamepitaxy (MBE) on undoped SrTiO substrates and mea-sured immediately by in situ ARPES (He-I photons, hν = 21.2 eV) as well as in situ resistivity measure-ments (Fig. S1). Having verified their quality andsuperconducting properties, samples were then cappedwith ≈
100 nm amorphous Se for transport to the Ad-vanced Light Source MAESTRO beamline (7.0.2) in asealed, inert environment. Films were then decappedat the endstation at 420 ◦ C, in a vacuum better than5 × − Torr immediately prior to ARPES measure-ments. ARPES measurements were then performed at15 K at photon energies ranging between 21-75 eV, witha total energy resolution of 10-20 meV (depending on theincident photon energy).In Figure 1 we present ARPES measurements of mono-layer FeSe/SrTiO after decapping, taken at hν = 24 eVwith p -polarized light. Consistent with previous reports,the Fermi surface is comprised of nearly degenerate ellip-tical electron pockets at M which arise from the glide-mirror symmetry of the iron-selenium plane [16]. Due tomatrix element effects, the electron pocket at M appearswith lobes of increased intensity in a three-fold patternabout the pocket. In Figure 1(b,c), we show raw andsecond-derivative spectra taken along the Γ- M directionas indicated by the blue line in Fig. 1(a). The mainband closest to E F , which we denote as γ , exhibits awell-defined gap and back-bending at 15 K, indicative ofthe expected superconductivity. The first replica band,( γ (cid:48) , red) is visible in the raw ARPES spectra 98 meVbelow the main band. Two additional, weaker featuresare also visible in the second-derivative spectra shownin Fig. 1(c), including a faint replica at ≈
60 meV (de-noted as ( γ ∗ , shown in orange), and also an additionalreplica band separated by 192 meV from the main band( γ (cid:48)(cid:48) , denoted in green). Their characteristic energiesassociate them with two distinct Fuchs-Kliewer (F-K)phonons of the SrTiO substrate, which arise from out-of-plane vibration modes of the oppositely charged Tiand O ions [17]; γ ∗ corresponds to FK , and γ (cid:48) and γ (cid:48)(cid:48) are the first and second-order satellites from FK [18]. Figure 1. Fermi surface and replica band topology in single-layer FeSe/SrTiO . ( a ) Fermi surface map of single-layerFeSe/SrTiO taken with p -polarized light at hν = 24eV.( b ) High-statistics spectra along the cut shown at M (blue).( c ) Second-derivative of the spectra in (b). An additional60 meV replica (labelled γ ∗ in the figure) is clearly visible, aswell as a second-order replica (labelled γ (cid:48)(cid:48) ) after saturatingthe color scale over the higher binding energy region. If the replica bands indeed arise from extrinsic final-state energy losses, as suggested in Ref. [13], then it ispredicted that the ratio of the intensity of the first replicaband, γ (cid:48) , relative to the intensity of the main band, γ , I γ (cid:48) /I γ , should depend strongly on the kinetic energy anddirection of the outgoing photoelectron. Conversely, ifthe replica bands arise from electron-phonon coupling inthe initial state, they should be intrinsic features of thesingle-particle spectral function and hence, the intensityratio I γ (cid:48) /I γ should be insensitive to the photoelectron ki-netic energy. In Figure 2(a), we plot energy distributioncurves (EDCs) around M between 21 eV < hν <
75 eV(corresponding to photoelectron kinetic energies between ≈
17 to 71 eV). To improve statistics, the EDCs havebeen generated by integrating over the entire band, off-setting each individual EDC by the peak position of themain band (cid:15) k (Fig. S2), then fitted to a smooth splinebackground with the integrated weight of the main bandpeak ( I γ ) and replica band peak ( I γ (cid:48) ) shown after sub- Figure 2. Photon energy dependence of the replica band in-tensity. ( a ) Integrated EDC’s collected from hν = 21 to 75 eV.Grey lines indicate the spline background, while blue and redshaded regions indicate the integrated signal of the γ and γ (cid:48) bands, respectively. ( b ) Relative intensity of γ (cid:48) to γ as a func-tion of incident photon energy (red markers) compared to thetheoretical prediction for a photoelectron loss effect from Ref.[13] (black dashed line). traction in Figure S3. In Figure 2(b), we plot the ratioof I γ (cid:48) /I γ as a function of photon energy, which is clearlyindependent of photon energy, with an extracted value of I γ (cid:48) /I γ = 0 . ± .
02, together with a comparison of theprediction for the extrinsic photoelectron energy loss sce-nario, where a ≈
60% reduction in I γ (cid:48) /I γ would have beenexpected. This is despite the fact that the overall abso-lute intensity of both I γ and I γ (cid:48) drop by a factor of 10 ingoing to higher photon energies (hence the larger errorbars for hν >
40 eV), thus definitively ruling out extrinsicphotoelectron loss effects as the origin of the replica bandin FeSe/SrTiO . We have confirmed that this behavioris robust against details of the fitting procedure, for ex-ample, whether a single EDC at M is used as opposed toband-averaged spectra, or whether a Shirley backgroundis used in place of a spline fit.Performing this extensive photon energy dependencestudy provides the opportunity to extract more detailedinformation about the electron-phonon coupling constantthan had previously been possible. For one, this analysisallows us to reliably determine the absolute intensity of I γ (cid:48) /I γ = 0.21 ± hν = 24 eV with p -polarization where the intensity of features is strongest,so as to enable a more detailed, quantitative lineshapeanalysis of the spectral function and replica bands. InFigure 3(a,b), we show a series of EDCs around M at 24 Figure 3. Observation of second-order replica bands in single-layer FeSe/SrTiO . ( a,b ) EDC’s across the spectra at M shown as a waterfall plot. Blue, red, yellow, and green mark-ers track the main band ( γ ), 98 meV replica ( γ (cid:48) ), and 60meV replica ( γ ∗ ), and 190 meV second order replica ( γ (cid:48)(cid:48) re-spectively. ( c ) Band positions based on fits to the EDC peakpositions. ( d,e ) Determination of the electron-phonon cou-pling constant λ based on the γ (cid:48) blue shift (d) and replicaband intensity (e). Theoretical behavior based on Ref. [15].Grey regions indicate the experimental uncertainty. eV, with the band positions for γ , γ ∗ , γ (cid:48) , and γ (cid:48)(cid:48) indicatedby markers. This data allows us to accurately determinethe separation between γ and γ (cid:48) as ω = 98 ± γ (cid:48) and γ (cid:48)(cid:48) , ω = 94 ± ω . Theenergy of the FK phonon in undoped SrTiO substratehas previously been determined to be 94 meV [10, 19], al-though this value is highly doping dependent [20]. There-fore, the separation between γ and γ (cid:48) is blue-shifted by δ λ = 4 meV, relative to the bare FK phonon energy,as shown in Fig. 3(c). This is in contrast to the sepa-ration between γ (cid:48) and γ (cid:48)(cid:48) , which closely matches Ω KF1 to within experimental error (94 ± Figure 4. Quasiparticle lifetime broadening in the replicaband. ( a ) Background-subtracted EDC’s spanning the elec-tron pocket dispersion, from the band bottom ( k M ) to k F , fordata taken at hν = 24 eV. The γ (cid:48) feature has been multipliedby 3 for visual clarity. ( b ) Quasiparticle lifetimes based onspectral function fits for γ (blue) and γ (cid:48) (red). The solid blackline indicate the anticipated replica band behavior under theextrinsic photoelectron energy loss scenario. has been clearly identified experimentally. As has beendiscussed theoretically, reliably extracting both the blueshift, δ λ , as well as the intensity ratio between the mainand first replica bands, I γ (cid:48) /I γ , allows us to more accu-rately infer the precise value of the interfacial electron-phonon coupling constant, λ . This is of particular impor-tance to the FeSe/SrTiO system, since the possible en-hancement of T c due to coupling to interfacial substratephonons has been shown to vary strongly as a functionof λ in certain models [15, 22]. Here, we compare ourmeasurements to prior calculations based on solutions ofthe Migdal-Eliashberg equations of FeSe/SrTiO in thepresence of strong forward-scattering [21]. The calcu-lations by Li et al. provide theoretical estimates in thelimit of small momentum transfer for both I γ (cid:48) /I γ and δ λ ,which are reproduced as dashed lines in Figures 3(d,e),together with our experimentally determined values forboth quantities (shown as shaded bars, which denote ourexperimental uncertainty). Both I γ (cid:48) /I γ = 0 . ± .
02, aswell as δ λ = 4 ± . λ = 0 . ± .
02. With this value of λ =0.19, the work by Li et al. would suggest an interfacialenhancement of ∆ of ≈
11 %. While considerable, thiscannot entirely account for gap closing temperature of60 K compared to bulk electron-doped FeSe compounds(T c ≈
40 K). In addition, recent combined in situ re-sistivity and ARPES measurements suggest the presenceof a pseudogap above 40 K and the possible additionalrole of the enhanced two-dimensionality of the electronicstructure in the monolayer limit [23]. In addition to the blue-shift and intensity ratios, a de-tailed analysis of the spectral function also reveals evi-dence for electron-phonon coupling in the lifetime broad-ening of the first replica band, Γ γ (cid:48) relative to that of themain band, Γ γ (the second replica, γ (cid:48)(cid:48) , is too weak to al-low a reliable analysis of its lineshape). In Figure 4(a), weshow the extracted spectral function after fitting to thebackgrounds used in Figure 2 (as before, our conclusionshere are independent of the specific background that isemployed, Fig. S4). The expected sharpening of themain band peak, Γ γ , as it approaches E F can be clearlyobserved in Figure 4(b), where we plot Γ as a function ofbinding energy E B . Likewise, the scattering rate of thefirst replica band, Γ γ (cid:48) , exhibits similar behavior, but withthe minimum value of Γ γ (cid:48) (at k F ) approximately equalto the maximum value of Γ γ (taken at the band bot-tom, M ), as would be expected if both features naturallyarise from a single, intrinsic spectral function. For com-parison, we also plot the simulated linewidth of the firstreplica, Γ γ (cid:48) in the extrinsic photoelectron loss scenario,where the width would correspond to that of the mainband γ convoluted with the lifetime of the FK phonon,Γ FK1 [20]. As can be seen in Fig. 4(b), the experimen-tally determined value of Γ γ (cid:48) is substantially larger thanwould be expected in a photoelectron loss scenario, onceagain pointing towards its intrinsic character.In summary, we have performed an extensive quantita-tive analysis of replica bands in the ARPES lineshape ofsingle-layer FeSe/SrTiO , which allows us to reliably ex-tract both the blue-shift of the first replica band, δ λ , andthe intensity ratio I γ (cid:48) /I γ between the replica and mainbands. A comparison with theoretical calculations in thelimit of strong forward-scattering allows us to accuratelydetermine the strength of the coupling between elec-trons in the FeSe layer and Fuchs-Kliewer phonons in theSrTiO substrate as λ = 0 . ± .
02, suggesting that suchinterfacial coupling may play an important role in theelectronic properties of monolayer FeSe/SrTiO includ-ing its superconductivity, and could also be a promisingfuture approach for investigating the influence of phononsat heterointerfaces. More generally, our approach alsoprovides a clear and unambiguous methodology for dis-tinguishing whether replica bands observed in ARPESspectra of quantum materials with low carrier densitiesarise from intrinsic electron-phonon coupling or from ex-trinsic losses associated with the photoemission process. ACKNOWLEDGMENTS
This work was supported through the Air Force Officeof Scientific Research Grant No. FA9550-15-1-0474, andthe National Science Foundation [Platform for the Accel-erated Realization, Analysis, and Discovery of InterfaceMaterials (PARADIM)] under Cooperative AgreementNo. DMR-1539918, NSF DMR-1709255. This research isfunded in part by the Gordon and Betty Moore Founda-tion’s EPiQS Initiative through Grant No. GBMF3850to Cornell University. B.D.F. and J.N.N. acknowledgesupport from the NSF Graduate Research Fellowship un-der Grant No. DGE-1650441. P.M. acknowledges sup-port from the Indo US Science and Technology Forum(IUSSTF). This work made use of the Cornell Centerfor Materials Research (CCMR) Shared Facilities, which are supported through the NSF MRSEC Program (No.DMR-1719875). Substrate preparation was performedin part at the Cornell NanoScale Facility, a memberof the National Nanotechnology Coordinated Infrastruc-ture (NNCI), which is supported by the NSF (Grant No.ECCS-1542081). [1] A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar,D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fuji-mori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida,Z. Hussain, and Z.-X. Shen, Nature , 510 (2001).[2] X. J. Zhou, T. Yoshida, A. Lanzara, P. V. Bogdanov,S. A. Kellar, K. M. Shen, W. L. Yang, F. Ron-ning, T. Sasagawa, T. Kakeshita, T. Noda, H. Eisaki,S. Uchida, C. T. Lin, F. Zhou, J. W. Xiong, W. X. Ti,Z. X. Zhao, A. Fujimori, Z. Hussain, and Z.-X. Shen,Nature , 398 (2003).[3] N. Mannella, W. L. Yang, X. J. Zhou, H. Zheng, J. F.Mitchell, J. Zaanen, T. P. Devereaux, N. Nagaosa,Z. Hussain, and Z.-X. Shen, Nature , 474 (2005).[4] Z. Wang, S. McKeown Walker, A. Tamai, Y. Wang,Z. Ristic, F. Y. Bruno, A. de la Torre, S. Ricc`o,N. C. Plumb, M. Shi, P. Hlawenka, J. S´anchez-Barriga,A. Varykhalov, T. K. Kim, M. Hoesch, P. D. C. King,W. Meevasana, U. Diebold, J. Mesot, B. Moritz, T. P.Devereaux, M. Radovic, and F. Baumberger, Nature Ma-terials , 835 (2016).[5] C. Chen, J. Avila, E. Frantzeskakis, A. Levy, and M. C.Asensio, Nature Communications , 8585 (2015).[6] C. Zhang, Z. Liu, Z. Chen, Y. Xie, R. He, S. Tang,J. He, W. Li, T. Jia, S. N. Rebec, E. Y. Ma, H. Yan,M. Hashimoto, D. Lu, S.-K. Mo, Y. Hikita, R. G. Moore,H. Y. Hwang, D. Lee, and Z. Shen, Nature Communica-tions , 14468 (2017).[7] S. Moser, L. Moreschini, J. Ja´cimovi´c, O. S. Bariˇsi´c,H. Berger, A. Magrez, Y. J. Chang, K. S. Kim, A. Bost-wick, E. Rotenberg, L. Forr´o, and M. Grioni, Phys. Rev.Lett. , 196403 (2013).[8] C. Verdi, F. Caruso, and F. Giustino, Nature Commu-nications , 15769 (2017).[9] J. J. Lee, F. T. Schmitt, R. G. Moore, S. Johnston, Y.-T.Cui, W. Li, M. Yi, Z. K. Liu, M. Hashimoto, Y. Zhang,D. H. Lu, T. P. Devereaux, D.-H. Lee, and Z.-X. Shen,Nature , 245 (2014). [10] Q. Song, T. L. Yu, X. Lou, B. P. Xie, H. C. Xu, C. H. P.Wen, Q. Yao, S. Y. Zhang, X. T. Zhu, J. D. Guo, R. Peng,and D. L. Feng, Nature Communications , 758 (2019).[11] X. Shi, Z.-Q. Han, X.-L. Peng, P. Richard, T. Qian, X.-X. Wu, M.-W. Qiu, S. C. Wang, J. P. Hu, Y.-J. Sun,and H. Ding, Nature Communications , 14988 (2017),article.[12] M. Yang, C. Yan, Y. Ma, L. Li, and C. Cen, NatureCommunications , 85 (2019).[13] F. Li and G. A. Sawatzky, Phys. Rev. Lett. , 237001(2018).[14] R. Fuchs and K. L. Kliewer, Phys. Rev. , A2076(1965).[15] Z.-X. Li, T. P. Devereaux, and D.-H. Lee, Phys. Rev. B , 241101 (2019).[16] Y. Zhang, J. J. Lee, R. G. Moore, W. Li, M. Yi,M. Hashimoto, D. H. Lu, T. P. Devereaux, D.-H. Lee,and Z.-X. Shen, Phys. Rev. Lett. , 117001 (2016).[17] H. Vogt, Phys. Rev. B , 5699 (1988).[18] S. Zhang, J. Guan, X. Jia, B. Liu, W. Wang, F. Li,L. Wang, X. Ma, Q. Xue, J. Zhang, E. W. Plummer,X. Zhu, and J. Guo, Phys. Rev. B , 081116 (2016).[19] T. Conard, L. Philippe, P. Thiry, P. Lambin, andR. Caudano, Surface Science , 382 (1993).[20] S. Zhang, J. Guan, Y. Wang, T. Berlijn, S. Johnston,X. Jia, B. Liu, Q. Zhu, Q. An, S. Xue, Y. Cao, F. Yang,W. Wang, J. Zhang, E. W. Plummer, X. Zhu, andJ. Guo, Phys. Rev. B , 035408 (2018).[21] F. Schrodi, A. Aperis, and P. M. Oppeneer, Phys. Rev.B , 094509 (2018).[22] L. Rademaker, Y. Wang, T. Berlijn, and S. Johnston,New Journal of Physics18