- Letter
- Open Access
Electronic correlations and universal long-range scaling in kagome metals
Phys. Rev. Research 5, L012008 – Published 19 January, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L012008
Abstract
We investigate the real-space profile of effective Coulomb interactions in correlated kagome materials. By particularizing to , , FeSn, and , we analyze representative cases that exhibit a large span of correlation-mediated phenomena, and contrast them to prototypical perovskite transition metal oxides. From our constrained random phase approximation studies we find that the on-site interaction strength in kagome metals not only depends on the screening processes at high energy, but also on the low-energy hybridization profile of the electronic density of states. Our results indicate that rescaled by the on-site interaction amplitude, all kagome metals exhibit a universal long-range Coulomb behavior.
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References (64)
- M. R. Norman, Colloquium: Herbertsmithite and the search for the quantum spin liquid, Rev. Mod. Phys. 88, 041002 (2016).
- A. Mielke, Ferromagnetic ground states for the Hubbard model on line graphs, J. Phys. A: Math. Gen. 24, L73 (1991).
- S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional quantum Hall physics in topological flat bands, C. R. Phys. 14, 816 (2013).
- C. H. Lee, D. P. Arovas, and R. Thomale, Band flatness optimization through complex analysis, Phys. Rev. B 93, 155155 (2016).
- D.-S. Ma, Y. Xu, C. S. Chiu, N. Regnault, A. A. Houck, Z. Song, and B. A. Bernevig, Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices, Phys. Rev. Lett. 125, 266403 (2020).
- I. I. Mazin, H. O. Jeschke, F. Lechermann, H. Lee, M. Fink, R. Thomale, and R. Valentí, Theoretical prediction of a strongly correlated Dirac metal, Nat. Commun. 5, 4261 (2014).
- M. Fuchs, P. Liu, T. Schwemmer, G. Sangiovanni, R. Thomale, C. Franchini, and D. Di Sante, Kagome metal-organic frameworks as a platform for strongly correlated electrons, J. Phys. Mater. 3, 025001 (2020).
- D. Di Sante, J. Erdmenger, M. Greiter, I. Matthaiakakis, R. Meyer, D. R. Fernández, R. Thomale, E. van Loon, and T. Wehling, Turbulent hydrodynamics in strongly correlated kagome metals, Nat. Commun. 11, 3997 (2020).
- M. L. Kiesel and R. Thomale, Sublattice interference in the kagome Hubbard model, Phys. Rev. B 86, 121105(R) (2012).
- M. L. Kiesel, C. Platt, and R. Thomale, Unconventional Fermi Surface Instabilities in the Kagome Hubbard Model, Phys. Rev. Lett. 110, 126405 (2013).
- S. K. Blau, A string-theory calculation of viscosity could have surprising applications, Phys. Today 58(5), 23 (2005).
- M. Polini and A. K. Geim, Viscous electron fluids, Phys. Today 73(6), 28 (2020).
- B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson, E. Ertekin, T. M. McQueen, and E. S. Toberer, New kagome prototype materials: Discovery of , and , Phys. Rev. Mater. 3, 094407 (2019).
- X. Wu, T. Schwemmer, T. Müller, A. Consiglio, G. Sangiovanni, D. Di Sante, Y. Iqbal, W. Hanke, A. P. Schnyder, M. M. Denner, M. H. Fischer, T. Neupert, and R. Thomale, Nature of Unconventional Pairing in the Kagome Superconductors (), Phys. Rev. Lett. 127, 177001 (2021).
- M. Kang, S. Fang, J.-K. Kim, B. R. Ortiz, S. H. Ryu, J. Kim, J. Yoo, G. Sangiovanni, D. Di Sante, B.-G. Park, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, S. D. Wilson, J.-H. Park, and R. Comin, Twofold van Hove singularity and origin of charge order in topological kagome superconductor , Nat. Phys. 18, 301 (2022).
- Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wilson, A. P. Schnyder, and M. Shi, Rich nature of van Hove singularities in kagome superconductor , Nat. Commun. 13, 2220 (2022).
- Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu, J. Ruff, L. Kautzsch, S. S. Zhang, G. Chang, I. Belopolski, Q. Zhang, T. A. Cochran, D. Multer, M. Litskevich, Z.-J. Cheng, X. P. Yang, Z. Wang, R. Thomale, T. Neupert, S. D. Wilson, and M. Z. Hasan, Unconventional chiral charge order in kagome superconductor , Nat. Mater. 20, 1353 (2021).
- B. R. Ortiz, P. M. Sarte, E. M. Kenney, M. J. Graf, S. M. L. Teicher, R. Seshadri, and S. D. Wilson, Superconductivity in the kagome metal , Phys. Rev. Mater. 5, 034801 (2021).
- H. Li, T. T. Zhang, T. Yilmaz, Y. Y. Pai, C. E. Marvinney, A. Said, Q. W. Yin, C. S. Gong, Z. J. Tu, E. Vescovo, C. S. Nelson, R. G. Moore, S. Murakami, H. C. Lei, H. N. Lee, B. J. Lawrie, and H. Miao, Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors (, Cs), Phys. Rev. X 11, 031050 (2021).
- C. C. Zhao, L. S. Wang, W. Xia, Q. W. Yin, J. M. Ni, Y. Y. Huang, C. P. Tu, Z. C. Tao, Z. J. Tu, C. S. Gong, H. C. Lei, Y. F. Guo, X. F. Yang, and S. Y. Li, Nodal superconductivity and superconducting domes in the topological kagome metal , arXiv:2102.08356.
- H. Chen, H. Yang, B. Hu, Z. Zhao, J. Yuan, Y. Xing, G. Qian, Z. Huang, G. Li, Y. Ye, S. Ma, S. Ni, H. Zhang, Q. Yin, C. Gong, Z. Tu, H. Lei, H. Tan, S. Zhou, C. Shen, X. Dong, B. Yan, Z. Wang, and H.-J. Gao, Roton pair density wave in a strong-coupling kagome superconductor, Nature (London) 599, 222 (2021).
- T. Neupert, M. M. Denner, J.-X. Yin, R. Thomale, and M. Z. Hasan, Charge order and superconductivity in kagome materials, Nat. Phys. 18, 137 (2022).
- Q. Xu, E. Liu, W. Shi, L. Muechler, J. Gayles, C. Felser, and Y. Sun, Topological surface Fermi arcs in the magnetic Weyl semimetal , Phys. Rev. B 97, 235416 (2018).
- E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu, J. Kroder, V. Süß, H. Borrmann, C. Shekhar, Z. Wang, C. Xi, W. Wang, W. Schnelle, S. Wirth, Y. Chen, S. T. B. Goennenwein, and C. Felser, Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal, Nat. Phys. 14, 1125 (2018).
- Q. Wang, Y. Xu, R. Lou, Z. Liu, M. Li, Y. Huang, D. Shen, H. Weng, S. Wang, and H. Lei, Large intrinsic anomalous Hall effect in half-metallic ferromagnet with magnetic Weyl fermions, Nat. Commun. 9, 3681 (2018).
- D. F. Liu, A. J. Liang, E. K. Liu, Q. N. Xu, Y. W. Li, C. Chen, D. Pei, W. J. Shi, S. K. Mo, P. Dudin, T. Kim, C. Cacho, G. Li, Y. Sun, L. X. Yang, Z. K. Liu, S. S. P. Parkin, C. Felser, and Y. L. Chen, Magnetic Weyl semimetal phase in a kagome crystal, Science 365, 1282 (2019).
- N. Morali, R. Batabyal, P. K. Nag, E. Liu, Q. Xu, Y. Sun, B. Yan, C. Felser, N. Avraham, and H. Beidenkopf, Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal , Science 365, 1286 (2019).
- L. Ye, M. Kang, J. Liu, F. von Cube, C. R. Wicker, T. Suzuki, C. Jozwiak, A. Bostwick, E. Rotenberg, D. C. Bell, L. Fu, R. Comin, and J. G. Checkelsky, Massive Dirac fermions in a ferromagnetic kagome metal, Nature (London) 555, 638 (2018).
- J.-X. Yin, S. S. Zhang, H. Li, K. Jiang, G. Chang, B. Zhang, B. Lian, C. Xiang, I. Belopolski, H. Zheng, T. A. Cochran, S.-Y. Xu, G. Bian, K. Liu, T.-R. Chang, H. Lin, Z.-Y. Lu, Z. Wang, S. Jia, W. Wang, and M. Z. Hasan, Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet, Nature (London) 562, 91 (2018).
- L. Ye, M. K. Chan, R. D. McDonald, D. Graf, M. Kang, J. Liu, T. Suzuki, R. Comin, L. Fu, and J. G. Checkelsky, de –van Alphen effect of correlated Dirac states in kagome metal , Nat. Commun. 10, 4870 (2019).
- N. J. Ghimire and I. I. Mazin, Topology and correlations on the kagome lattice, Nat. Mater. 19, 137 (2020).
- M. Kang, L. Ye, S. Fang, J.-S. You, A. Levitan, M. Han, J. I. Facio, C. Jozwiak, A. Bostwick, E. Rotenberg, M. K. Chan, R. D. McDonald, D. Graf, K. Kaznatcheev, E. Vescovo, D. C. Bell, E. Kaxiras, J. van den Brink, M. Richter, M. Prasad Ghimire, J. G. Checkelsky, and R. Comin, Dirac fermions and flat bands in the ideal kagome metal FeSn, Nat. Mater. 19, 163 (2020).
- Z. Liu, M. Li, Q. Wang, G. Wang, C. Wen, K. Jiang, X. Lu, S. Yan, Y. Huang, D. Shen, J.-X. Yin, Z. Wang, Z. Yin, H. Lei, and S. Wang, Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn, Nat. Commun. 11, 4002 (2020).
- L. Ye, S. Fang, M. G. Kang, J. Kaufmann, Y. Lee, J. Denlinger, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, D. C. Bell, O. Janson, R. Comin, and J. G. Checkelsky, A flat band-induced correlated kagome metal, arXiv:2106.10824.
- F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70, 195104 (2004).
- T. Miyake, F. Aryasetiawan, and M. Imada, Ab initio procedure for constructing effective models of correlated materials with entangled band structure, Phys. Rev. B 80, 155134 (2009).
- J. M. Tomczak, T. Miyake, R. Sakuma, and F. Aryasetiawan, Effective Coulomb interactions in solids under pressure, Phys. Rev. B 79, 235133 (2009).
- L. Vaugier, H. Jiang, and S. Biermann, Hubbard and Hund exchange in transition metal oxides: Screening versus localization trends from constrained random phase approximation, Phys. Rev. B 86, 165105 (2012).
- P. Werner, M. Casula, T. Miyake, F. Aryasetiawan, A. J. Millis, and S. Biermann, Satellites and large doping and temperature dependence of electronic properties in hole-doped , Nat. Phys. 8, 331 (2012).
- P. Werner, R. Sakuma, F. Nilsson, and F. Aryasetiawan, Dynamical screening in , Phys. Rev. B 91, 125142 (2015).
- P. Hansmann, T. Ayral, L. Vaugier, P. Werner, and S. Biermann, Long-Range Coulomb Interactions in Surface Systems: A First-Principles Description within Self-Consistently Combined and Dynamical Mean-Field Theory, Phys. Rev. Lett. 110, 166401 (2013).
- T. Miyake and F. Aryasetiawan, Screened Coulomb interaction in the maximally localized Wannier basis, Phys. Rev. B 77, 085122 (2008).
- E. Şaşıoğlu, C. Friedrich, and S. Blügel, Effective Coulomb interaction in transition metals from constrained random-phase approximation, Phys. Rev. B 83, 121101(R) (2011).
- M. Kaltak, Merging GW with DMFT, Ph.D. thesis, University of Vienna, 2015.
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178, 685 (2008).
- C. Franchini, R. Kováčik, M. Marsman, S. S. Murthy, J. He, C. Ederer, and G. Kresse, Maximally localized wannier functions in LaMnO within PBE+U, hybrid functionals and partially self-consistent GW: an efficient route to construct ab initio tight-binding parameters for perovskites, J. Phys.: Condens. Matter 24, 235602 (2012).
- We included around 200 unoccupied bands, a mesh ( only for due to its rhombohedral lattice structure with the space group ), and a 600 eV cutoff to calculate the dielectric function and properly include local-field effects. The Perdew-Burke-Ernzerhof functional revised for solid is used in all calculations [63]. Partial occupancies in Eq. (1) are computed by the method of Methfessel-Paxton with a smearing of 0.2 eV. In the construction of Wannier functions, and orbitals are always considered, and the following energy windows for the disentanglement are set: eV for , eV for , eV for FeSn, and eV for In. No optimization of Wannier functions spread is performed after the disentanglement.
- D. Di Sante, B. Kim, W. Hanke, T. Wehling, C. Franchini, R. Thomale, and G. Sangiovanni, Zenodo (2022), doi:10.5281/zenodo.7312039.
- E. G. C. P. van Loon, M. Rösner, M. I. Katsnelson, and T. O. Wehling, Random phase approximation for gapped systems: Role of vertex corrections and applicability of the constrained random phase approximation, Phys. Rev. B 104, 045134 (2021).
- C. Honerkamp, H. Shinaoka, F. F. Assaad, and P. Werner, Limitations of constrained random phase approximation downfolding, Phys. Rev. B 98, 235151 (2018).
- X.-J. Han, P. Werner, and C. Honerkamp, Investigation of the effective interactions for the Emery model by the constrained random-phase approximation and constrained functional renormalization group, Phys. Rev. B 103, 125130 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L012008 for a table of on-site Coulomb interaction parameters, which includes Refs. [14, 64].
- B. Kim, P. Liu, J. M. Tomczak, and C. Franchini, Strain-induced tuning of the electronic Coulomb interaction in transition metal oxide perovskites, Phys. Rev. B 98, 075130 (2018).
- K. Ohno, Some remarks on the Pariser-Parr-Pople method, Theoret. Chim. Acta 2, 219 (1964).
- M. J. S. Dewar and W. Thiel, A semiempirical model for the two-center repulsion integrals in the NDDO approximation, Theoret. Chim. Acta 46, 89 (1977).
- R. Resta, Thomas-Fermi dielectric screening in semiconductors, Phys. Rev. B 16, 2717 (1977).
- L. Huang and H. Lu, Signatures of Hundness in kagome metals, Phys. Rev. B 102, 125130 (2020).
- M. Li, Q. Wang, G. Wang, Z. Yuan, W. Song, R. Lou, Z. Liu, Y. Huang, Z. Liu, H. Lei, Z. Yin, and S. Wang, Dirac cone, flat band and saddle point in kagome magnet , Nat. Commun. 12, 3129 (2021).
- J. Zhao, W. Wu, Y. Wang, and S. A. Yang, Electronic correlations in the normal state of the kagome superconductor , Phys. Rev. B 103, L241117 (2021).
- Y. Xie, L. Chen, T. Chen, Q. Wang, Q. Yin, J. R. Stewart, M. B. Stone, L. L. Daemen, E. Feng, H. Cao, H. Lei, Z. Yin, A. H. MacDonald, and P. Dai, Spin excitations in metallic kagome lattice FeSn and CoSn, Commun. Phys. 4, 240 (2021).
- X. Cao, T. Ayral, Z. Zhong, O. Parcollet, D. Manske, and P. Hansmann, Chiral -wave superconductivity in a triangular surface lattice mediated by long-range interaction, Phys. Rev. B 97, 155145 (2018).
- J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Phys. Rev. Lett. 100, 136406 (2008).
- M. Y. Jeong, H.-J. Yang, H. S. Kim, Y. B. Kim, S. B. Lee, and M. J. Han, Crucial role of out-of-plane Sb orbitals in Van Hove singularity formation and electronic correlations in the superconducting kagome metal , Phys. Rev. B 105, 235145 (2022).