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Dichotomy of electron-phonon interactions in the delafossite : From weak bulk to polaronic surface coupling
Phys. Rev. B 112, 085113 – Published 8 August, 2025
DOI: https://doi.org/10.1103/5w81-7jtk
Abstract
The metallic delafossites host ultrahigh-mobility carriers in the bulk, while at their polar surfaces, intrinsic electronic reconstructions stabilize markedly distinct electronic phases, from charge-disproportionated insulators to Rashba-split heavy-hole gases and ferromagnetic metals. The understanding of these phases has been strongly informed by surface spectroscopic measurements, but previous studies have been complicated by the presence of spatially varying terminations of the material surface. Here, we demonstrate the potential of microscopic-area angle-resolved photoemission to overcome these challenges. Our measurements of the model compound yield extremely high quality spectra of the electronic structure, which allows us to place stringent experimental constraints on the weak electron-phonon coupling in the bulk of , while revealing much stronger interactions at its surfaces. While the -terminated surface exhibits a conventional weak-coupling behavior, our measurements reveal surprising spectroscopic signatures of polaron formation at the Pd-terminated surface, despite its pronounced metallicity. Together, our findings reveal how mode- and symmetry-selective couplings can markedly tune the electron-phonon interactions in a single host material, here opening routes to stabilize surprisingly persistent polaronic quasiparticles.
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References (76)
- A. B. Migdal, Interaction between electrons and lattice vibrations in a normal metal, Sov. Phys. JETP 34, 996 (1958) [J. Exptl. Theoret. Phys. (U.S.S.R.) 34, 1438 (1958)].
- G. M. Eliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov. Phys. JETP 11, 696 (1960) [J. Exptl. Theoret. Phys. (U.S.S.R.) 38, 1438 (1960)].
- M. Strongin, O. F. Kammerer, J. E. Crow, R. D. Parks, D. H. Douglass, and M. A. Jensen, Enhanced superconductivity in layered metallic films, Phys. Rev. Lett. 21, 1320 (1968).
- W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
- A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, and Z.-X. Shen, Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors, Nature (London) 412, 510 (2001).
- R. Peierls, Zur Theorie der elektrischen und thermischen Leitfähigkeit von Metallen, Ann. Phys. 396, 121 (1930).
- H. Luo, Q. Gao, H. Liu, Y. Gu, D. Wu, C. Yi, J. Jia, S. Wu, X. Luo, Y. Xu, L. Zhao, Q. Wang, H. Mao, G. Liu, Z. Zhu, Y. Shi, K. Jiang, J. Hu, Z. Xu, and X. J. Zhou, Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor , Nat. Commun. 13, 273 (2022).
- Y. Xie, Y. Li, P. Bourges, A. Ivanov, Z. Ye, J.-X. Yin, M. Z. Hasan, A. Luo, Y. Yao, Z. Wang, G. Xu, and P. Dai, Electron-phonon coupling in the charge density wave state of , Phys. Rev. B 105, L140501 (2022).
- M. I. Dykman and E. I. Rashba, The roots of polaron theory, Phys. Today 68(4), 10 (2015).
- C. Franchini, M. Reticcioli, M. Setvin, and U. Diebold, Polarons in materials, Nat. Rev. Mater. 6, 560 (2021).
- A. S. Alexandrov and J. T. Devreese, Advances in Polaron Physics, Springer Series in Solid State Sciences Vol. 159 (Springer, Berlin, 2010).
- J. L. Bredas and G. B. Street, Polarons, bipolarons, and solitons in conducting polymers, Acc. Chem. Res. 18, 309 (1985).
- C. W. Hicks, A. S. Gibbs, A. P. Mackenzie, H. Takatsu, Y. Maeno, and E. A. Yelland, Quantum oscillations and high carrier mobility in the delafossite , Phys. Rev. Lett. 109, 116401 (2012).
- P. Kushwaha, V. Sunko, P. J. W. Moll, L. Bawden, J. M. Riley, N. Nandi, H. Rosner, M. P. Schmidt, F. Arnold, E. Hassinger, T. K. Kim, M. Hoesch, A. P. Mackenzie, and P. D. C. King, Nearly free electrons in a delafossite oxide metal, Sci. Adv. 1, e1500692 (2015).
- A. P. Mackenzie, The properties of ultrapure delafossite metals, Rep. Prog. Phys. 80, 032501 (2017).
- R. D. Shannon, D. B. Rogers, C. T. Prewitt, and J. L. Gillson, Chemistry of noble metal oxides. III. Electrical transport properties and crystal chemistry of compounds with the delafossite structure, Inorg. Chem. 10, 723 (1971).
- K. Kim, H. C. Choi, and B. I. Min, Fermi surface and surface electronic structure of delafossite , Phys. Rev. B 80, 035116 (2009).
- H.-J. Noh, J. Jeong, J. Jeong, E.-J. Cho, S. B. Kim, K. Kim, B. I. Min, and H.-D. Kim, Anisotropic electric conductivity of delafossite studied by angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 102, 256404 (2009).
- V. Sunko, H. Rosner, P. Kushwaha, S. Khim, F. Mazzola, L. Bawden, O. J. Clark, J. M. Riley, D. Kasinathan, M. W. Haverkort, T. K. Kim, M. Hoesch, J. Fujii, I. Vobornik, A. P. Mackenzie, and P. D. C. King, Maximal Rashba-like spin splitting via kinetic-energy-coupled inversion-symmetry breaking, Nature (London) 549, 492 (2017).
- C. M. Yim, D. Chakraborti, L. C. Rhodes, S. Khim, A. P. Mackenzie, and P. Wahl, Quasiparticle interference and quantum confinement in a correlated Rashba spin-split 2D electron liquid, Sci. Adv. 7, eabd7361 (2021).
- F. Mazzola, V. Sunko, S. Khim, H. Rosner, P. Kushwaha, O. J. Clark, L. Bawden, I. Marković, T. K. Kim, M. Hoesch, A. P. Mackenzie, and P. D. C. King, Itinerant ferromagnetism of the Pd-terminated polar surface of , Proc. Natl. Acad. Sci. USA 115, 12956 (2018).
- C. M. Yim, G.-R. Siemann, S. Stavrić, S. Khim, I. Benedičič, P. A. Murgatroyd, T. Antonelli, M. D. Watson, A. P. Mackenzie, S. Picozzi et al., Avoided metallicity in a hole-doped Mott insulator on a triangular lattice, Nat. Commun. 15, 8098 (2024).
- K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
- I. Opahle, K. Koepernik, and H. Eschrig, Full-potential band-structure calculation of iron pyrite, Phys. Rev. B 60, 14035 (1999).
- http://www.fplo.de.
- J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- H. Eschrig, M. Richter, and I. Opahle, Relativistic solid state calculations, in Relativistic Electronic Structure Theory, edited by P. Schwerdtfeger, Theoretical and Computational Chemistry Vol. 14 (Elsevier, 2004), Chap. 12, pp. 723–776.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/5w81-7jtk for additional figures related to spatial mapping, self-energy analysis, and sample ageing.
- P. Hofmann, I. Y. Sklyadneva, E. D. L. Rienks, and E. V. Chulkov, Electron-phonon coupling at surfaces and interfaces, New J. Phys. 11, 125005 (2009).
- B. Hellsing, A. Eiguren, and E. V. Chulkov, Electron-phonon coupling at metal surfaces, J. Phys.: Condens. Matter 14, 5959 (2002).
- C. Kirkegaard, T. K. Kim, and P. Hofmann, Self-energy determination and electron-phonon coupling on Bi(110), New J. Phys. 7, 99 (2005).
- G. L. Goodvin, M. Berciu, and G. A. Sawatzky, Green's function of the Holstein polaron, Phys. Rev. B 74, 245104 (2006).
- C. N. Veenstra, G. L. Goodvin, M. Berciu, and A. Damascelli, Spectral function tour of electron-phonon coupling outside the Migdal limit, Phys. Rev. B 84, 085126 (2011).
- F. Mazzola, C. M. Yim, V. Sunko, S. Khim, P. Kushwaha, O. J. Clark, L. Bawden, I. Marković, D. Chakraborti, T. K. Kim, M. Hoesch, A. P. Mackenzie, P. Wahl, and P. D. C. King, Tuneable electron–magnon coupling of ferromagnetic surface states in , npj Quantum Mater. 7, 20 (2022).
- G.-R. Siemann, S.-J. Kim, E. A. Morales, P. A. E. Murgatroyd, A. Zivanovic, B. Edwards, I. Marković, F. Mazzola, L. Trzaska, O. J. Clark, C. Bigi, H. Zhang, B. Achinuq, T. Hesjedal, M. D. Watson, T. K. Kim, P. Bencok, G. van der Laan, C. M. Polley, M. Leandersson et al., Spin-orbit coupled spin-polarised hole gas at the -terminated surface of , npj Quantum Mater. 8, 61 (2023).
- X. Yao, Y. Xun, Z. Zhu, S. Zhao, and W. Li, Origin of the high electrical conductivity of the delafossite metal , Phys. Rev. B 109, 075110 (2024).
- H. Usui, M. Ochi, S. Kitamura, T. Oka, D. Ogura, H. Rosner, M. W. Haverkort, V. Sunko, P. D. C. King, A. P. Mackenzie, and K. Kuroki, Hidden kagome-lattice picture and origin of high conductivity in delafossite , Phys. Rev. Mater. 3, 045002 (2019).
- C. W. Hicks, A. S. Gibbs, L. Zhao, P. Kushwaha, H. Borrmann, A. P. Mackenzie, H. Takatsu, S. Yonezawa, Y. Maeno, and E. A. Yelland, Quantum oscillations and magnetic reconstruction in the delafossite , Phys. Rev. B 92, 014425 (2015).
- P. B. Allen, Empirical electron-phonon values from resistivity of cubic metallic elements, Phys. Rev. B 36, 2920 (1987).
- V. Sunko, P. H. McGuinness, C. S. Chang, E. Zhakina, S. Khim, C. E. Dreyer, M. Konczykowski, H. Borrmann, P. J. W. Moll, M. König, D. A. Muller, and A. P. Mackenzie, Controlled introduction of defects to delafossite metals by electron irradiation, Phys. Rev. X 10, 021018 (2020).
- C. C. Homes, S. Khim, and A. P. Mackenzie, Perfect separation of intraband and interband excitations in , Phys. Rev. B 99, 195127 (2019).
- L. Cheng, Q.-B. Yan, and M. Hu, The role of phonon-phonon and electron-phonon scattering in thermal transport in , Phys. Chem. Chem. Phys. 19, 21714 (2017).
- S. Kumar, H. Gupta, and Karandeep, First principles study of structural, bonding and vibrational properties of , and metallic delafossites, J. Phys. Chem. Solids 74, 305 (2013).
- H. Takatsu, S. Yonezawa, S. Mouri, S. Nakatsuji, K. Tanaka, and Y. Maeno, Roles of high-frequency optical phonons in the physical properties of the conductive delafossite , J. Phys. Soc. Jpn. 76, 104701 (2007).
- T. Holstein, Studies of polaron motion: Part I. The molecular-crystal model, Ann. Phys. 8, 325 (1959).
- T. Holstein, Studies of polaron motion: Part II. The “small” polaron, Ann. Phys. 8, 343 (1959).
- M. Kang, S. W. Jung, W. J. Shin, Y. Sohn, S. H. Ryu, T. K. Kim, M. Hoesch, and K. S. Kim, Holstein polaron in a valley-degenerate two-dimensional semiconductor, Nat. Mater. 17, 676 (2018).
- S. W. Jung, M. D. Watson, S. Mukherjee, D. V. Evtushinsky, C. Cacho, E. Martino, H. Berger, and T. K. Kim, Holstein polarons, Rashba-like spin splitting, and Ising superconductivity in electron-doped , ACS Nano 18, 33359 (2024).
- L. Kang, X. Du, J. S. Zhou, X. Gu, Y. J. Chen, R. Z. Xu, Q. Q. Zhang, S. C. Sun, Z. X. Yin, Y. W. Li, D. Pei, J. Zhang, R. K. Gu, Z. G. Wang, Z. K. Liu, R. Xiong, J. Shi, Y. Zhang, Y. L. Chen, and L. X. Yang, Band-selective Holstein polaron in Luttinger liquid material ( = K, Rb), Nat. Commun. 12, 6183 (2021).
- C. A. Perroni, G. De Filippis, and V. Cataudella, Ground-state features and spectral properties of large polaron liquids from low to high charge densities, Phys. Rev. B 103, 245130 (2021).
- D. H. Dickey, E. J. Johnson, and D. M. Larsen, Polaron effects in the cyclotron-resonance absorption of InSb, Phys. Rev. Lett. 18, 599 (1967).
- J. Scott, T. Damen, W. Silfvast, R. Leite, and L. Cheesman, Resonant Raman scattering in ZnS and ZnSe with the cadmium laser, Opt. Commun. 1, 397 (1970).
- S. Moser, L. Moreschini, J. Jaćimović, O. S. Barišić, H. Berger, A. Magrez, Y. J. Chang, K. S. Kim, A. Bostwick, E. Rotenberg, L. Forró, and M. Grioni, Tunable polaronic conduction in anatase , Phys. Rev. Lett. 110, 196403 (2013).
- Z. Wang, S. McKeown Walker, A. Tamai, Y. Wang, Z. Ristic, F. Y. Bruno, A. De La Torre, S. Riccò, N. C. Plumb, M. Shi, P. Hlawenka, J. Sánchez-Barriga, A. Varykhalov, T. K. Kim, M. Hoesch, P. D. C. King, W. Meevasana, U. Diebold, J. Mesot, B. Moritz et al., Tailoring the nature and strength of electron-phonon interactions in the (001) 2D electron liquid, Nat. Mater. 15, 835 (2016).
- A. G. Swartz, H. Inoue, T. A. Merz, Y. Hikita, S. Raghu, T. P. Devereaux, S. Johnston, and H. Y. Hwang, Polaronic behavior in a weak-coupling superconductor, Proc. Natl. Acad. Sci. USA 115, 1475 (2018).
- M. Reticcioli, Z. Wang, M. Schmid, D. Wrana, L. A. Boatner, U. Diebold, M. Setvin, and C. Franchini, Competing electronic states emerging on polar surfaces, Nat. Commun. 13, 4311 (2022).
- C. Chen, J. Avila, E. Frantzeskakis, A. Levy, and M. C. Asensio, Observation of a two-dimensional liquid of Fröhlich polarons at the bare surface, Nat. Commun. 6, 8585 (2015).
- Z. Wang, M. Reticcioli, Z. Jakub, I. Sokolović, M. Meier, L. A. Boatner, M. Schmid, G. S. Parkinson, U. Diebold, C. Franchini, and M. Setvin, Surface chemistry on a polarizable surface: Coupling of CO with (001), Sci. Adv. 8, eabq1433 (2022).
- J. M. Riley, F. Caruso, C. Verdi, L. B. Duffy, M. D. Watson, L. Bawden, K. Volckaert, G. van der Laan, T. Hesjedal, M. Hoesch, F. Giustino, and P. D. C. King, Crossover from lattice to plasmonic polarons of a spin-polarised electron gas in ferromagnetic EuO, Nat. Commun. 9, 2305 (2018).
- C. Cancellieri, A. S. Mishchenko, U. Aschauer, A. Filippetti, C. Faber, O. S. Barišić, V. A. Rogalev, T. Schmitt, N. Nagaosa, and V. N. Strocov, Polaronic metal state at the / interface, Nat. Commun. 7, 10386 (2016).
- R. Yukawa, K. Ozawa, S. Yamamoto, H. Iwasawa, K. Shimada, E. F. Schwier, K. Yoshimatsu, H. Kumigashira, H. Namatame, M. Taniguchi, and I. Matsuda, Phonon-dressed two-dimensional carriers on the ZnO surface, Phys. Rev. B 94, 165313 (2016).
- F. Ellinger, M. Shafiq, I. Ahmad, M. Reticcioli, and C. Franchini, Small polaron formation on the Nb-doped (001) surface, Phys. Rev. Mater. 7, 064602 (2023).
- C. Verdi, F. Caruso, and F. Giustino, Origin of the crossover from polarons to Fermi liquids in transition metal oxides, Nat. Commun. 8, 15769 (2017).
- D. Seo, G. Ahn, G. Rimal, S. Khim, S. B. Chung, A. P. Mackenzie, S. Oh, S. J. Moon, and E. Choi, Interaction of in-plane Drude carrier with -axis phonon in , npj Quantum Mater. 8, 74 (2023).
- M. Reticcioli, I. Sokolović, M. Schmid, U. Diebold, M. Setvin, and C. Franchini, Interplay between adsorbates and polarons: CO on rutile (110), Phys. Rev. Lett. 122, 016805 (2019).
- C. Cheng, Y. Zhu, W.-H. Fang, R. Long, and O. V. Prezhdo, CO adsorbate promotes polaron photoactivity on the reduced rutile (110) surface, JACS Au 2, 234 (2022).
- G. Li, H. Kobayashi, J. M. Taylor, R. Ikeda, Y. Kubota, K. Kato, M. Takata, T. Yamamoto, S. Toh, S. Matsumura, and H. Kitagawa, Hydrogen storage in Pd nanocrystals covered with a metal-organic framework, Nat. Mater. 13, 802 (2014).
- Hydrogen in Metals I, edited by G. Alefeld and J. Völkl, Topics in Applied Physics Vol. 28 (Springer, Berlin, 1978).
- T. Kawae, Y. Inagaki, S. Wen, S. Hirota, D. Itou, and T. Kimura, Superconductivity in palladium hydride systems, J. Phys. Soc. Jpn. 89, 051004 (2020).
- S. Hong, T. S. Rahman, R. Heid, and K. P. Bohnen, First-principles calculations of the phonon dispersion curves of H on Pt(111), Phys. Rev. B 71, 245409 (2005).
- G. Li, S. Khim, C. S. Chang, C. Fu, N. Nandi, F. Li, Q. Yang, G. R. Blake, S. Parkin, G. Auffermann, Y. Sun, D. A. Muller, A. P. Mackenzie, and C. Felser, In situ modification of a delafossite-type bulk single crystal for reversible hydrogen sorption and fast hydrogen evolution, ACS Energy Lett. 4, 2185 (2019).
- F. Podjaski, D. Weber, S. Zhang, L. Diehl, R. Eger, V. Duppel, E. Alarcón-Lladó, G. Richter, F. Haase, A. Fontcuberta I Morral, C. Scheu, and B. V. Lotsch, Rational strain engineering in delafossite oxides for highly efficient hydrogen evolution catalysis in acidic media, Nat. Catal. 3, 55 (2019).
- C. M. Yim, Y. Zheng, O. R. Armitage, D. Chakraborti, C. J. Wells, S. Khim, A. P. Mackenzie, and P. Wahl, Adsorbate-induced formation of a surface-polarity-driven nonperiodic superstructure, Commun. Mater. 6, 128 (2025).
- Z. Ren, Z. Shi, H. Feng, Z. Xu, and W. Hao, Recent progresses of polarons: Fundamentals and roles in photocatalysis and photoelectrocatalysis, Adv. Sci. 11, 2305139 (2024).
- G.-R. Siemann, P. A. E. Murgatroyd, T. Antonelli, E. A. Morales, S. Khim, H. Rosner, M. D. Watson, A. P. Mackenzie, and P. D. C. King, Dichotomy of electron-phonon interactions in the delafossite : From weak bulk to polaronic surface coupling, Dataset, University of St Andrews Research Portal, https://doi.org/10.17630/1d055932-4ea7-4bc2-ac03-cdc120a9bac9.