- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Nonlinear thermoelectric probes of anomalous electron lifetimes in topological Fermi liquids

Johannes Hofmann1,2,* and Habib Rostami3,†

  • *Contact author: johannes.hofmann@physics.gu.se
  • †Contact author: hr745@bath.ac.uk
PDF

Phys. Rev. Research 6, L042042 – Published 14 November, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042042

Abstract

In two-dimensional Fermi liquids (FLs), odd-parity Fermi surface deformations have anomalously slow relaxation rates that are suppressed as T4 with temperature T, distinct from the standard FL T2 scaling. We demonstrate here that these long-lived modes, which are often hidden in linear response, have a significant impact on nonlinear transport by establishing a direct proportionality of nonlinear thermoelectric currents to the anomalously large relaxation time. These currents exist in topological time-reversal invariant FLs, and their magnitude is characterized by topological heat capacitance terms that we refer to as the Berry curvature capacity and the velocity-curvature capacity. We quantify the effect in bismuth telluride, which is an efficient thermoelectric and a topological insulator with a hexagonal Fermi surface. The proposed field-induced thermoelectric currents are well within the range of current experiments. Our findings demonstrate the potential to explore topological and many-body effects in FLs through the nonlinear thermoelectric response, urging further experimental studies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (83)

  1. M. J. M. de Jong and L. W. Molenkamp, Hydrodynamic electron flow in high-mobility wires, Phys. Rev. B 51, 13389 (1995).
  2. H. Buhmann and L. Molenkamp, 1D diffusion: A novel transport regime in narrow 2DEG channels, Physica E 12, 715 (2002).
  3. D. A. Bandurin, I. Torre, R. K. Kumar, M. B. Shalom, A. Tomadin, A. Principi, G. H. Auton, E. Khestanova, K. S. Novoselov, I. V. Grigorieva et al., Negative local resistance caused by viscous electron backflow in graphene, Science 351, 1055 (2016).
  4. J. Crossno, J. K. Shi, K. Wang, X. Liu, A. Harzheim, A. Lucas, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe et al., Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene, Science 351, 1058 (2016).
  5. P. J. W. Moll, P. Kushwaha, N. Nandi, B. Schmidt, and A. P. Mackenzie, Evidence for hydrodynamic electron flow in PdCoO2, Science 351, 1061 (2016).
  6. Y. Nam, D.-K. Ki, D. Soler-Delgado, and A. F. Morpurgo, Electron-hole collision limited transport in charge-neutral bilayer graphene, Nat. Phys. 13, 1207 (2017).
  7. R. Krishna Kumar, D. A. Bandurin, F. M. D. Pellegrino, Y. Cao, A. Principi, H. Guo, G. H. Auton, M. Ben Shalom, L. A. Ponomarenko, G. Falkovich et al., Superballistic flow of viscous electron fluid through graphene constrictions, Nat. Phys. 13, 1182 (2017).
  8. J. Gooth, F. Menges, N. Kumar, V. Süß, C. Shekhar, Y. Sun, U. Drechsler, R. Zierold, C. Felser, and B. Gotsmann, Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide, Nat. Commun. 9, 4093 (2018).
  9. G. M. Gusev, A. D. Levin, E. V. Levinson, and A. K. Bakarov, Viscous transport and Hall viscosity in a two-dimensional electron system, Phys. Rev. B 98, 161303(R) (2018).
  10. D. A. Bandurin, A. V. Shytov, L. S. Levitov, R. K. Kumar, A. I. Berdyugin, M. Ben Shalom, I. V. Grigorieva, A. K. Geim, and G. Falkovich, Fluidity onset in graphene, Nat. Commun. 9, 4533 (2018).
  11. B. A. Braem, F. M. D. Pellegrino, A. Principi, M. Röösli, C. Gold, S. Hennel, J. V. Koski, M. Berl, W. Dietsche, W. Wegscheider et al., Scanning gate microscopy in a viscous electron fluid, Phys. Rev. B 98, 241304(R) (2018).
  12. A. I. Berdyugin, S. G. Xu, F. M. D. Pellegrino, R. K. Kumar, A. Principi, I. Torre, M. B. Shalom, T. Taniguchi, K. Watanabe, I. V. Grigorieva et al., Measuring Hall viscosity of graphene's electron fluid, Science 364, 162 (2019).
  13. P. Gallagher, C.-S. Yang, T. Lyu, F. Tian, R. Kou, H. Zhang, K. Watanabe, T. Taniguchi, and F. Wang, Quantum-critical conductivity of the Dirac fluid in graphene, Science 364, 158 (2019).
  14. J. A. Sulpizio, L. Ella, A. Rozen, J. Birkbeck, D. J. Perello, D. Dutta, M. Ben-Shalom, T. Taniguchi, K. Watanabe, T. Holder et al., Visualizing Poiseuille flow of hydrodynamic electrons, Nature (London) 576, 75 (2019).
  15. G. Baym and C. Pethick, Landau Fermi-Liquid Theory (Wiley-VCH Verlag, Weinheim, 2004).
  16. G. F. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005).
  17. D. Pines and P. Nozières, The Theory of Quantum Liquids (CRC Press, Boca Raton, 2018).
  18. G. F. Giuliani and J. J. Quinn, Lifetime of a quasiparticle in a two-dimensional electron gas, Phys. Rev. B 26, 4421 (1982).
  19. L. Zheng and S. Das Sarma, Coulomb scattering lifetime of a two-dimensional electron gas, Phys. Rev. B 53, 9964 (1996).
  20. Q. Li and S. Das Sarma, Finite temperature inelastic mean free path and quasiparticle lifetime in graphene, Phys. Rev. B 87, 085406 (2013).
  21. S. Das Sarma and Y. Liao, Know the enemy: 2D Fermi liquids, Ann. Phys. 435, 168495 (2021).
  22. U. Gran, E. Nilsson, and J. Hofmann, Shear viscosity in interacting two-dimensional Fermi liquids, arXiv:2312.09977.
  23. B. Laikhtman, Electron-electron angular relaxation in a two-dimensional electron gas, Phys. Rev. B 45, 1259 (1992).
  24. J. Nilsson and A. H. Castro Neto, Heat bath approach to Landau damping and Pomeranchuk quantum critical points, Phys. Rev. B 72, 195104 (2005).
  25. R. N. Gurzhi, A. N. Kalinenko, and A. I. Kopeliovich, Electron-electron momentum relaxation in a two-dimensional electron gas, Phys. Rev. B 52, 4744 (1995).
  26. P. Ledwith, H. Guo, and L. Levitov, Angular superdiffusion and directional memory in two-dimensional electron fluids, arXiv:1708.01915.
  27. P. J. Ledwith, H. Guo, and L. Levitov, The hierarchy of excitation lifetimes in two-dimensional Fermi gases, Ann. Phys. 411, 167913 (2019).
  28. J. Hofmann and U. Gran, Anomalously long lifetimes in two-dimensional Fermi liquids, Phys. Rev. B 108, L121401 (2023).
  29. E. Nilsson, U. Gran, and J. Hofmann, Nonequilibrium relaxation and odd-even effect in finite-temperature electron gases, arXiv:2405.03635.
  30. J. Hofmann and S. Das Sarma, Collective modes in interacting two-dimensional tomographic Fermi liquids, Phys. Rev. B 106, 205412 (2022).
  31. P. Ledwith, H. Guo, A. Shytov, and L. Levitov, Tomographic dynamics and scale-dependent viscosity in 2D electron systems, Phys. Rev. Lett. 123, 116601 (2019).
  32. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  33. S. M. Girvin and K. Yang, Modern Condensed Matter Physics (Cambridge University Press, Cambridge, 2019).
  34. G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59, 14915 (1999).
  35. V. I. Belinicher, Space-oscillating photocurrent in crystals without symmetry center, Phys. Lett. A 66, 213 (1978).
  36. E. Ivchenko and G. Pikus, New photogalvanic effect in gyrotropic crystals, Pis'ma Zh. Eksp. Teor. Fiz. 27, 640 (1978) [JETP Lett. 27, 604 (1978)].
  37. V. I. Belinicher and B. I. Sturman, The photogalvanic effect in media lacking a center of symmetry, Sov. Phys. Usp. 23, 199 (1980).
  38. J. E. Sipe and A. I. Shkrebtii, Second-order optical response in semiconductors, Phys. Rev. B 61, 5337 (2000).
  39. T. Morimoto and N. Nagaosa, Topological nature of nonlinear optical effects in solids, Sci. Adv. 2, e1501524 (2016).
  40. I. Sodemann and L. Fu, Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials, Phys. Rev. Lett. 115, 216806 (2015).
  41. H. Rostami and M. Polini, Nonlinear anomalous photocurrents in Weyl semimetals, Phys. Rev. B 97, 195151 (2018).
  42. A. Principi, D. Bandurin, H. Rostami, and M. Polini, Pseudo-Euler equations from nonlinear optics: Plasmon-assisted photodetection beyond hydrodynamics, Phys. Rev. B 99, 075410 (2019).
  43. H. Watanabe and Y. Yanase, Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet, Phys. Rev. X 11, 011001 (2021).
  44. Y. Zhang and L. Fu, Terahertz detection based on nonlinear Hall effect without magnetic field, Proc. Natl. Acad. Sci. USA 118, e2100736118 (2021).
  45. H. Rostami and V. Juričić, Probing quantum criticality using nonlinear Hall effect in a metallic Dirac system, Phys. Rev. Res. 2, 013069 (2020).
  46. Z. Dai and A. M. Rappe, Recent progress in the theory of bulk photovoltaic effect, Chem. Phys. Rev. 4, 011303 (2023).
  47. Q. Ma, R. Krishna Kumar, S.-Y. Xu, F. H. L. Koppens, and J. C. W. Song, Photocurrent as a multiphysics diagnostic of quantum materials, Nat. Rev. Phys. 5, 170 (2023).
  48. Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nat. Rev. Phys. 3, 744 (2021).
  49. R. Toshio, K. Takasan, and N. Kawakami, Anomalous hydrodynamic transport in interacting noncentrosymmetric metals, Phys. Rev. Res. 2, 032021(R) (2020).
  50. T. Yamaguchi, K. Nakazawa, and A. Yamakage, Microscopic theory of nonlinear Hall effect induced by electric field and temperature gradient, Phys. Rev. B 109, 205117 (2024).
  51. K. Nakazawa, T. Yamaguchi, and A. Yamakage, Nonlinear charge transport properties in chiral tellurium, Phys. Rev. Mater. 8, L091601 (2024).
  52. F. de Juan, A. G. Grushin, T. Morimoto, and J. E. Moore, Quantized circular photogalvanic effect in Weyl semimetals, Nat. Commun. 8, 15995 (2017).
  53. S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, Q. D. Gibson et al., Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2, Nat. Phys. 14, 900 (2018).
  54. K. Kang, T. Li, E. Sohn, J. Shan, and K. F. Mak, Nonlinear anomalous Hall effect in few-layer WTe2, Nat. Mater. 18, 324 (2019).
  55. Q. Ma, S.-Y. Xu, H. Shen, D. MacNeill, V. Fatemi, T.-R. Chang, A. M. Mier Valdivia, S. Wu, Z. Du, C.-H. Hsu et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature (London) 565, 337 (2019).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042042 for details on the nonlinear Fermi surface deformation, the computation of the nonlinear thermoelectric current in terms of the topological heat capacities, and the topological insulator model.
  57. J. M. Luttinger, Theory of thermal transport coefficients, Phys. Rev. 135, A1505 (1964).
  58. G. Tatara, Thermal vector potential theory of transport induced by a temperature gradient, Phys. Rev. Lett. 114, 196601 (2015).
  59. A. Sekine and N. Nagaosa, Quantum kinetic theory of thermoelectric and thermal transport in a magnetic field, Phys. Rev. B 101, 155204 (2020).
  60. D. T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87, 085016 (2013).
  61. D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88, 104412 (2013).
  62. D. Xiao, J. Shi, and Q. Niu, Berry phase correction to electron density of states in solids, Phys. Rev. Lett. 95, 137204 (2005).
  63. J.-W. Chen, T. Ishii, S. Pu, and N. Yamamoto, Nonlinear chiral transport phenomena, Phys. Rev. D 93, 125023 (2016).
  64. J.-Y. Chen and D. T. Son, Berry Fermi liquid theory, Ann. Phys. 377, 345 (2017).
  65. C. Zeng, S. Nandy, A. Taraphder, and S. Tewari, Nonlinear Nernst effect in bilayer WTe2, Phys. Rev. B 100, 245102 (2019).
  66. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1976).
  67. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5, 438 (2009).
  68. D. A. Wright, Thermoelectric properties of bismuth telluride and its alloys, Nature (London) 181, 834 (1958).
  69. K. Pal, S. Anand, and U. V. Waghmare, Thermoelectric properties of materials with nontrivial electronic topology, J. Mater. Chem. C 3, 12130 (2015).
  70. I. T. Witting, T. C. Chasapis, F. Ricci, M. Peters, N. A. Heinz, G. Hautier, and G. J. Snyder, The thermoelectric properties of Bismuth telluride, Adv. Electron. Mater. 5, 1800904 (2019).
  71. C. Fu, Y. Sun, and C. Felser, Topological thermoelectrics, APL Mater. 8, 040913 (2020).
  72. J. Wei, L. Yang, Z. Ma, P. Song, M. Zhang, J. Ma, F. Yang, and X. Wang, Review of current high-ZT thermoelectric materials, J. Mater. Sci. 55, 12642 (2020).
  73. D. Teweldebrhan, V. Goyal, and A. A. Balandin, Exfoliation and characterization of bismuth telluride atomic quintuples and quasi-two-dimensional crystals, Nano Lett. 10, 1209 (2010).
  74. M. Z. Hossain, S. L. Rumyantsev, K. M. F. Shahil, D. Teweldebrhan, M. Shur, and A. A. Balandin, Low-frequency current fluctuations in “graphene-like”exfoliated thin-films of bismuth selenide topological insulators, ACS Nano 5, 2657 (2011).
  75. P. He, H. Isobe, D. Zhu, C.-H. Hsu, L. Fu, and H. Yang, Quantum frequency doubling in the topological insulator Bi2Se3, Nat. Commun. 12, 698 (2021).
  76. P. Makushko, S. Kovalev, Y. Zabila, I. Ilyakov, A. Ponomaryov, A. Arshad, G. L. Prajapati, T. V. de Oliveira, J.-C. Deinert, P. Chekhonin et al., Tunable room temperature nonlinear Hall effect from the surfaces of elementary bismuth thin films, arXiv:2310.15225.
  77. I. Bejenari, V. Kantser, and A. A. Balandin, Thermoelectric properties of electrically gated Bismuth telluride nanowires, Phys. Rev. B 81, 075316 (2010).
  78. N. Xu, Y. Xu, and J. Zhu, Topological insulators for thermoelectrics, npj Quantum Mater. 2, 51 (2017).
  79. Y. Xu, Z. Gan, and S.-C. Zhang, Enhanced thermoelectric performance and anomalous seebeck effects in topological insulators, Phys. Rev. Lett. 112, 226801 (2014).
  80. D. Baldomir and D. Faílde, On behind the physics of the thermoelectricity of topological insulators, Sci. Rep. 9, 6324 (2019).
  81. L. Fu, Hexagonal warping effects in the surface states of the topological insulator Bi2Te3, Phys. Rev. Lett. 103, 266801 (2009).
  82. Z. B. Siu, M. B. A. Jalil, and S. G. Tan, Effective Hamiltonian for surface states of Bi2Te3 nanocylinders with hexagonal warping, J. Phys. D 49, 225304 (2016).
  83. J.-S. You, S. Fang, S.-Y. Xu, E. Kaxiras, and T. Low, Berry curvature dipole current in the transition metal dichalcogenides family, Phys. Rev. B 98, 121109(R) (2018).

Outline

Information

Phys. Rev. Research 6, L042042– Published 14 November, 2024
  • Received 5 January 2024
  • Revised 10 May 2024
  • Accepted 15 October 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation