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
  • Open Access

Room-temperature disorder-driven nonlinear transport in topological materials

Rhonald Burgos Atencia1,2,3, Shanshan Liu4, Kian Ping Loh4, and Dimitrie Culcer1,2

Phys. Rev. B 113, 205429 – Published 26 May, 2026

DOI: https://doi.org/10.1103/58gz-d7zc

Abstract

Recent experiments have reported nonlinear signals in topological materials up to room temperature. Here we show that this response stems from extrinsic spin-orbit contributions to both impurity and phonon scattering. While skew scattering dominates at low temperatures, the side jump contribution ∝τ/τβ, where τ, τβ are the momentum and skew scattering times, respectively. Consequently side jump exhibits a weak temperature dependence and remains sizable at room temperature. Our results provide a roadmap for engineering nonlinear transport at ambient conditions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (93)

  1. Z. He and H. Weng, Giant nonlinear Hall effect in twisted bilayer WTe2, npj Quantum Mater. 6, 101 (2021).
  2. M. Huang, Z. Wu, J. Hu, X. Cai, E. Li, L. An, X. Feng, Z. Ye, N. Lin, K. T. Law, and N. Wang, Giant nonlinear Hall effect in twisted bilayer WSe2, Natl. Sci. Rev. 10, nwac232 (2023).
  3. J. Duan, Y. Jian, Y. Gao, H. Peng, J. Zhong, Q. Feng, J. Mao, and Y. Yao, Giant second-order nonlinear Hall effect in twisted bilayer graphene, Phys. Rev. Lett. 129, 186801 (2022).
  4. H.-J. Tien, H. Lin, L. Fu, and T.-R. Chang, Quantum metric non-linear Hall effect in an antiferromagnetic topological insulator thin-film EuSn2As2, Mater. Today Quantum 5, 100027 (2025).
  5. M. S. Okyay, M. Choi, Q. Xu, A. P. Diéguez, M. Del Ben, K. Z. Ibrahim, and B. M. Wong, Unconventional nonlinear Hall effects in twisted multilayer 2D materials, npj 2D Mater. Appl. 9, 1 (2025).
  6. D. Kaplan, T. Holder, and B. Yan, Unification of nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in metals by the quantum geometry, Phys. Rev. Lett. 132, 026301 (2024).
  7. M. T. Mercaldo, M. Cuoco, and C. Ortix, Nonlinear planar magnetotransport as a probe of the topology of surface states, Phys. Rev. B 111, 155442 (2025).
  8. R. B. Atencia, D. Xiao, and D. Culcer, Disorder in the nonlinear anomalous Hall effect of PT-symmetric Dirac fermions, Phys. Rev. B 108, L201115 (2023).
  9. 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).
  10. S. Nandy and I. Sodemann, Symmetry and quantum kinetics of the nonlinear Hall effect, Phys. Rev. B 100, 195117 (2019).
  11. P. Makushko, S. Kovalev, Y. Zabila, I. Ilyakov, A. Ponomaryov, A. Arshad, G. L. Prajapati, T. V. A. G. de Oliveira, J.-C. Deinert, P. Chekhonin, I. Veremchuk, T. Kosub, Y. Skourski, F. Ganss, D. Makarov, and C. Ortix, A tunable room-temperature nonlinear Hall effect in elemental bismuth thin films, Nature Electron. 7, 207 (2024).
  12. L. Min, H. Tan, Z. Xie, L. Miao, R. Zhang, S. H. Lee, V. Gopalan, C.-X. Liu, N. Alem, B. Yan, and Z. Mao, Strong room-temperature bulk nonlinear Hall effect in a spin-valley locked Dirac material, Nature Commun. 14, 364 (2023).
  13. S. Wang, X. Li, H. Zhang, B. Chen, H. Xie, C. Li, F. Fei, S. Zhang, and F. Song, Nonlinear Hall effect and scaling law in Sb-doped topological insulator MnBi4Te7, Appl. Phys. Lett. 124, 153102 (2024).
  14. T. Nishijima, T. Watanabe, H. Sekiguchi, Y. Ando, E. Shigematsu, R. Ohshima, S. Kuroda, and M. Shiraishi, Ferroic Berry curvature dipole in a topological crystalline insulator at room temperature, Nano Lett. 23, 2247 (2023).
  15. J. Han, T. Uchimura, Y. Araki, J.-Y. Yoon, Y. Takeuchi, Y. Yamane, S. Kanai, J. Ieda, H. Ohno, and S. Fukami, Room-temperature flexible manipulation of the quantum-metric structure in a topological chiral antiferromagnet, Nature Phys. 20, 1110 (2024).
  16. L. Min, Y. Zhang, Z. Xie, S. V. G. Ayyagari, L. Miao, Y. Onishi, S. H. Lee, Y. Wang, N. Alem, L. Fu, and Z. Mao, Colossal room-temperature non-reciprocal Hall effect, Nature Mater. 23, 1671 (2024).
  17. Y. Zhang and L. Fu, Terahertz detection based on nonlinear Hall effect without magnetic field, Proc. Natl. Acad. Sci. USA 118, e2100736118 (2021).
  18. C. Guo, Z. Chen, X. Yu, L. Zhang, X. Wang, X. Chen, and L. Wang, Ultrasensitive anisotropic room-temperature terahertz photodetector based on an intrinsic magnetic topological insulator MnBi2Te4, Nano Lett. 22, 7492 (2022).
  19. Z. Hu, L. Zhang, A. Chakraborty, G. D'Olimpio, J. Fujii, A. Ge, Y. Zhou, C. Liu, A. Agarwal, I. Vobornik, D. Farias, C.-N. Kuo, C. S. Lue, A. Politano, S.-W. Wang, W. Hu, X. Chen, W. Lu, and L. Wang, Terahertz nonlinear Hall rectifiers based on spin-polarized topological electronic states in 1T-CoTe2, Adv. Mater. 35, 2209557 (2023).
  20. Y. Li, W. Yu, K. Zhang, N. Cui, T. Yun, X. Xia, Y. Jiang, G. Zhang, H. Mu, and S. Lin, Two-dimensional topological semimetals: An emerging candidate for terahertz detectors and on-chip integration, Mater. Horiz. 11, 2572 (2024).
  21. E. Mönch, M. D. Moldavskaya, L. E. Golub, V. V. Bel'kov, J. Wunderlich, D. Weiss, J. V. Gumenjuk-Sichevska, C. Niu, P. D. Ye, and S. D. Ganichev, Terahertz radiation driven nonlinear transport phenomena in two-dimensional tellurene, Nano Lett. 25, 476 (2025).
  22. H. Wang and X. Qian, Electrically and magnetically switchable nonlinear photocurrent in PT-symmetric magnetic topological quantum materials, npj Comput. Mater. 6, 199 (2020).
  23. Y. Shen, L. Primeau, J. Li, T.-D. Nguyen, D. Mandrus, Y. C. Lin, and Y. Zhang, Nonlinear photocurrent in quantum materials for broadband photodetection, Prog. Quantum Electron. 97, 100535 (2024).
  24. J. Xiao, Y. Wang, H. Wang, C. D. Pemmaraju, S. Wang, P. Muscher, E. J. Sie, C. M. Nyby, T. P. Devereaux, X. Qian, X. Zhang, and A. M. Lindenberg, Berry curvature memory through electrically driven stacking transitions, Nature Phys. 16, 1028 (2020).
  25. D. Kumar, C.-H. Hsu, R. Sharma, T.-R. Chang, P. Yu, J. Wang, G. Eda, G. Liang, and H. Yang, Room-temperature nonlinear Hall effect and wireless radiofrequency rectification in Weyl semimetal TaIrTe4, Nature Nanotechnol. 16, 421 (2021).
  26. B. Cheng, Y. Gao, Z. Zheng, S. Chen, Z. Liu, L. Zhang, Q. Zhu, H. Li, L. Li, and C. Zeng, Giant nonlinear Hall and wireless rectification effects at room temperature in the elemental semiconductor tellurium, Nature Commun. 15, 5513 (2024).
  27. D. Kumar, R. Sharma, F. Wang, Y. Liu, S. Zhao, and H. Yang, Quantum rectification based on room temperature multidirectional nonlinearity in Bi2Te3, Nano Lett. 24, 12545 (2024).
  28. H. Liu, T. Y. Lim, S. Tian, J. Zhai, D. Xiang, T. Liu, T.-R. Chang, P. He, and J. Shen, Giant nonlinear Hall effect induced ultrahigh rectification in a Weyl semiconductor, Adv. Electron. Mater. 11, 2400648 (2025).
  29. Z. Z. Du, C. M. Wang, S. Li, H.-Z. Lu, and X. C. Xie, Disorder-induced nonlinear Hall effect with time-reversal symmetry, Nature Commun. 10, 3047 (2019).
  30. Z. Z. Du, C. M. Wang, H.-P. Sun, H.-Z. Lu, and X. C. Xie, Quantum theory of the nonlinear Hall effect, Nature Commun. 12, 5038 (2021).
  31. Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nature Rev. Phys. 3, 744 (2021).
  32. C. Ortix, Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations, Adv. Quantum Technol. 4, 2100056 (2021).
  33. D. Ma, A. Arora, G. Vignale, and J. C. W. Song, Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in PT-symmetric antiferromagnets, Phys. Rev. Lett. 131, 076601 (2023).
  34. B. T. Zhou, C.-P. Zhang, and K. T. Law, Highly tunable nonlinear Hall effects induced by spin-orbit couplings in strained polar transition-metal dichalcogenides, Phys. Rev. Appl. 13, 024053 (2020).
  35. C.-P. Zhang, J. Xiao, B. T. Zhou, J.-X. Hu, Y.-M. Xie, B. Yan, and K. T. Law, Giant nonlinear Hall effect in strained twisted bilayer graphene, Phys. Rev. B 106, L041111 (2022).
  36. C.-L. Zhang, T. Liang, Y. Kaneko, N. Nagaosa, and Y. Tokura, Giant Berry curvature dipole density in a ferroelectric Weyl semimetal, npj Quantum Mater. 7, 103 (2022).
  37. E. J. König, M. Dzero, A. Levchenko, and D. A. Pesin, Gyrotropic Hall effect in Berry-curved materials, Phys. Rev. B 99, 155404 (2019).
  38. H. Isobe, S.-Y. Xu, and L. Fu, High-frequency rectification via chiral Bloch electrons, Sci. Adv. 6, eaay2497 (2020).
  39. S. Liu, R. Burgos, E. Zhang, N. Wang, X.-B. Qiang, C. Li, Q. Zhang, Z. Z. Du, R. Zheng, J. Chen, Q.-H. Xu, K. Leng, W. Gao, F. Xiu, D. Culcer, and K. P. Loh, Room-temperature nonlinear transport and microwave rectification in antiferromagnetic MnBi2Te4 films, Commun. Phys. 7, 413 (2024).
  40. S. Lai, H. Liu, Z. Zhang, J. Zhao, X. Feng, N. Wang, C. Tang, Y. Liu, K. S. Novoselov, S. A. Yang, and Wei-bo Gao, Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor, Nature Nanotechnol. 16, 869 (2021).
  41. C. Wang, R.-C. Xiao, H. Liu, Z. Zhang, S. Lai, C. Zhu, H. Cai, N. Wang, S. Chen, Y. Deng, Z. Liu, S. A. Yang, and W.-B. Gao, Room-temperature third-order nonlinear Hall effect in Weyl semimetal TaIrTe4, Natl. Sci. Rev. 9, nwac020 (2022).
  42. S. Sankar, R. Liu, C.-P. Zhang, Q.-F. Li, C. Chen, X.-J. Gao, J. Zheng, Y.-H. Lin, K. Qian, R.-P. Yu, X. Zhang, Z. Y. Meng, K. T. Law, Q. Shao, and B. Jäck, Experimental evidence for a Berry curvature quadrupole in an antiferromagnet, Phys. Rev. X 14, 021046 (2024).
  43. T. Nag, S. K. Das, C. Zeng, and S. Nandy, Third-order Hall effect in the surface states of a topological insulator, Phys. Rev. B 107, 245141 (2023).
  44. Y. Gao, Z.-Q. Zhang, and K.-H. Ding, Third-order nonlinear Hall effect in two-dimensional Dirac systems, New J. Phys. 25, 053013 (2023).
  45. P. He, H. Isobe, G. K. W. Koon, J. Y. Tan, J. Hu, J. Li, N. Nagaosa, and J. Shen, Third-order nonlinear Hall effect in a quantum Hall system, Nature Nanotechnol. 19, 1460 (2024).
  46. X. Zhang, K. Sun, and Z. Y. Meng, Third-order anomalous Hall response to the Fermi-surface topology in magnetic materials, Phys. Rev. B 110, 165140 (2024).
  47. S. Li, X. Wang, Z. Yang, L. Zhang, S. L. Teo, M. Lin, R. He, N. Wang, P. Song, W. Tian, X. J. Loh, Q. Zhu, B. Sun, and X. R. Wang, Giant third-order nonlinear Hall effect in misfit layer compound (SnS)1.17(NbS2)3, ACS Appl. Mater. Interfaces 16, 11043 (2024).
  48. D. Mandal, S. Sarkar, K. Das, and A. Agarwal, Quantum geometry induced third-order nonlinear transport responses, Phys. Rev. B 110, 195131 (2024).
  49. W.-C. Lee, C. Wu, D. P. Arovas, and S.-C. Zhang, Quasiparticle interference on the surface of the topological insulator bi2te3, Phys. Rev. B 80, 245439 (2009).
  50. P. Adroguer, W. E. Liu, D. Culcer, and E. M. Hankiewicz, Conductivity corrections for topological insulators with spin-orbit impurities: Hikami-Larkin-Nagaoka formula revisited, Phys. Rev. B 92, 241402(R) (2015).
  51. D. Culcer, A. Sekine, and A. H. MacDonald, Interband coherence response to electric fields in crystals: Berry-phase contributions and disorder effects, Phys. Rev. B 96, 035106 (2017).
  52. R. B. Atencia, Q. Niu, and D. Culcer, Semiclassical response of disordered conductors: Extrinsic carrier velocity and spin and field-corrected collision integral, Phys. Rev. Res. 4, 013001 (2022).
  53. M. Mehraeen, Quantum kinetic theory of quadratic responses, Phys. Rev. B 110, 174423 (2024).
  54. E. H. Hwang and S. Das Sarma, Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene, Phys. Rev. B 77, 115449 (2008).
  55. B.-L. Huang and M. Kaviany, Ab initio and molecular dynamics predictions for electron and phonon transport in bismuth telluride, Phys. Rev. B 77, 125209 (2008).
  56. X. Zhu, L. Santos, R. Sankar, S. Chikara, C. Howard, F. C. Chou, C. Chamon, and M. El-Batanouny, Interaction of phonons and Dirac fermions on the surface of Bi2Se3: A strong Kohn anomaly, Phys. Rev. Lett. 107, 186102 (2011).
  57. K. Kaasbjerg, K. S. Thygesen, and K. W. Jacobsen, Unraveling the acoustic electron-phonon interaction in graphene, Phys. Rev. B 85, 165440 (2012).
  58. V. Parente, A. Tagliacozzo, F. von Oppen, and F. Guinea, Electron-phonon interaction on the surface of a three-dimensional topological insulator, Phys. Rev. B 88, 075432 (2013).
  59. S. Giraud and R. Egger, Electron-phonon scattering in topological insulators, Phys. Rev. B 83, 245322 (2011).
  60. J. Wang and D. Culcer, Suppression of the Kondo resistivity minimum in topological insulators, Phys. Rev. B 88, 125140 (2013).
  61. L. Fu, Hexagonal warping effects in the surface states of the topological insulator bi2te3, Phys. Rev. Lett. 103, 266801 (2009).
  62. G. Naselli, A. G. Moghaddam, S. Di Napoli, V. Vildosola, I. C. Fulga, J. van den Brink, and J. I. Facio, Magnetic warping in topological insulators, Phys. Rev. Res. 4, 033198 (2022).
  63. P. He, H. Isobe, D. Zhu, C.-H. Hsu, L. Fu, and H. Yang, Quantum frequency doubling in the topological insulator Bi2Se3, Nature Commun. 12, 698 (2021).
  64. X. F. Lu, C.-P. Zhang, N. Wang, D. Zhao, X. Zhou, W. Gao, X. H. Chen, K. T. Law, and K. P. Loh, Nonlinear transport and radio frequency rectification in BiTeBr at room temperature, Nature Commun. 15, 245 (2024).
  65. D. Culcer, E. M. Hankiewicz, G. Vignale, and R. Winkler, Side jumps in the spin Hall effect: Construction of the Boltzmann collision integral, Phys. Rev. B 81, 125332 (2010).
  66. N. A. Sinitsyn, Q. Niu, and A. H. MacDonald, Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect, Phys. Rev. B 73, 075318 (2006).
  67. N. A. Sinitsyn, A. H. MacDonald, T. Jungwirth, V. K. Dugaev, and J. Sinova, Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach, Phys. Rev. B 75, 045315 (2007).
  68. N. A. Sinitsyn, Semiclassical theories of the anomalous Hall effect, J. Phys.: Condens. Matter 20, 023201 (2008).
  69. 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, S. Fang, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, E. Kaxiras, H.-Z. Lu, H. Lin, L. Fu, N. Gedik, et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature (London) 565, 337 (2019).
  70. S. Sinha, P. C. Adak, A. Chakraborty, K. Das, K. Debnath, L. D. V. Sangani, K. Watanabe, T. Taniguchi, U. V. Waghmare, A. Agarwal, and M. M. Deshmukh, Berry curvature dipole senses topological transition in a moirésuperlattice, Nature Phys. 18, 765 (2022).
  71. Y. Zhang, J. van den Brink, C. Felser, and B. Yan, Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2, 2D Mater. 5, 044001 (2018).
  72. Z. Z. Du, C. M. Wang, H.-Z. Lu, and X. C. Xie, Band signatures for strong nonlinear Hall effect in bilayer WTe2, Phys. Rev. Lett. 121, 266601 (2018).
  73. J. I. Facio, D. Efremov, K. Koepernik, J.-S. You, I. Sodemann, and J. van den Brink, Strongly enhanced Berry dipole at topological phase transitions in BiTeI, Phys. Rev. Lett. 121, 246403 (2018).
  74. Y. Zhang, Y. Sun, and B. Yan, Berry curvature dipole in Weyl semimetal materials: An ab initio study, Phys. Rev. B 97, 041101(R) (2018).
  75. C. Wang, Y. Gao, and D. Xiao, Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs, Phys. Rev. Lett. 127, 277201 (2021).
  76. H. Liu, J. Zhao, Y.-X. Huang, W. Wu, X.-L. Sheng, C. Xiao, and S. A. Yang, Intrinsic second-order anomalous Hall effect and its application in compensated antiferromagnets, Phys. Rev. Lett. 127, 277202 (2021).
  77. A. Gao, Y.-F. Liu, J.-X. Qiu, B. Ghosh, T. V. Trevisan, Y. Onishi, C. Hu, T. Qian, H.-J. Tien, S.-W. Chen, M. Huang, D. Bérubé, H. Li, C. Tzschaschel, T. Dinh, Z. Sun, S.-C. Ho, S.-W. Lien, B. Singh, K. Watanabe, et al., Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure, Science 381, 181 (2023).
  78. K. Das, S. Lahiri, R. B. Atencia, D. Culcer, and A. Agarwal, Intrinsic nonlinear conductivities induced by the quantum metric, Phys. Rev. B 108, L201405 (2023).
  79. N. Wang, D. Kaplan, Z. Zhang, T. Holder, N. Cao, A. Wang, X. Zhou, F. Zhou, Z. Jiang, C. Zhang, S. Ru, H. Cai, K. Watanabe, T. Taniguchi, B. Yan, and W. Gao, Quantum-metric-induced nonlinear transport in a topological antiferromagnet, Nature (London) 621, 487 (2023).
  80. K. Kang, T. Li, E. Sohn, J. Shan, and K. F. Mak, Nonlinear anomalous Hall effect in few-layer WTe2, Nature Mater. 18, 324 (2019).
  81. A. Tiwari, F. Chen, S. Zhong, E. Drueke, J. Koo, A. Kaczmarek, C. Xiao, J. Gao, X. Luo, Q. Niu, Y. Sun, B. Yan, L. Zhao, and A. W. Tsen, Giant c-axis nonlinear anomalous Hall effect in Td-MoTe2 and WTe2, Nature Commun. 12, 2049 (2021).
  82. P. He, G. K. W. Koon, H. Isobe, J. Y. Tan, J. Hu, A. H. C. Neto, L. Fu, and H. Yang, Graphene moirésuperlattices with giant quantum nonlinearity of chiral Bloch electrons, Nature Nanotechnol. 17, 378 (2022).
  83. J. Kötzler and W. Gil, Anomalous Hall resistivity of cobalt films: Evidence for the intrinsic spin-orbit effect, Phys. Rev. B 72, 060412(R) (2005).
  84. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys. 82, 1539 (2010).
  85. S. Gholizadeh, J. H. Cullen, and D. Culcer, Nonlinear Hall effect of magnetized two-dimensional spin-32 heavy holes, Phys. Rev. B 107, L041301 (2023).
  86. K. Nakazawa, H. F. Legg, J. Klinovaja, and D. Loss, Interband contributions to nonlinear transport in semiconductor nanostructures, Phys. Rev. B 111, 125305 (2025).
  87. M. Suárez-Rodríguez, B. Martín-García, W. Skowroński, F. Calavalle, S. S. Tsirkin, I. Souza, F. De Juan, A. Chuvilin, A. Fert, M. Gobbi, F. Casanova, and L. E. Hueso, Odd nonlinear conductivity under spatial inversion in chiral tellurium, Phys. Rev. Lett. 132, 046303 (2024).
  88. Z.-Y. Cao, A.-Q. Wang, X.-Y. Liu, T.-Y. Zhao, D. Yu, and Z.-M. Liao, Nonlinear Hall effect and scaling law analysis in twisted bilayer WSe2, Phys. Rev. B 111, 125407 (2025).
  89. Y.-X. Huang, C. Xiao, S. A. Yang, and X. Li, Scaling law and extrinsic mechanisms for time-reversal-odd second-order nonlinear transport, Phys. Rev. B 111, 155127 (2025).
  90. 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).
  91. D.-F. Shao, S.-H. Zhang, G. Gurung, W. Yang, and E. Y. Tsymbal, Nonlinear anomalous Hall effect for Néel vector detection, Phys. Rev. Lett. 124, 067203 (2020).
  92. C.-H. Park, N. Bonini, T. Sohier, G. Samsonidze, B. Kozinsky, M. Calandra, F. Mauri, and N. Marzari, Electron–phonon interactions and the intrinsic electrical resistivity of graphene, Nano Lett. 14, 1113 (2014).
  93. T. Sohier, M. Calandra, C.-H. Park, N. Bonini, N. Marzari, and F. Mauri, Phonon-limited resistivity of graphene by first-principles calculations: Electron-phonon interactions, strain-induced gauge field, and Boltzmann equation, Phys. Rev. B 90, 125414 (2014).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation