Abstract Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful tool to reveal transport properties of quantum materials. A systematic study of the thermal Hall effect in a Chern insulator is still lacking. Here, using the Landauer-Büttiker formula, we investigated the thermal Hall transport of the Harper-Hofstadter model with flux =1/2 and its generalizations. We demonstrated that the Wiedemann-Franz law, which states that the thermal Hall conductivity is linearly proportional to the quantum Hall conductivity in the low temperature limit, is still valid in this Chern insulator, and that the thermal Hall conductivity can be used to characterize the topological properties of quantum materials.
(Electronic transport in nanoscale materials and structures)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. U2032164 and 12174394) and the Start-up Fund from Anhui University in China.
Corresponding Authors:
Tao Qin
E-mail: taoqin@ahu.edu.cn
Cite this article:
Anxin Wang(王安新) and Tao Qin(秦涛) Thermal Hall effect and the Wiedemann-Franz law in Chern insulator 2023 Chin. Phys. B 32 107301
[1] Kane C L and Fisher M P A 2005 Phys. Rev. B55 15832 [2] Qin T, Niu Q and Shi J 2011 Phys. Rev. Lett.107 236601 [3] Onose Y, Shiomi Y and Tokura Y 2008 Phys. Rev. Lett.100 016601 [4] Nagaosa N, Sinova J, Onoda S, MacDonald A H and Ong N P 2010 Rev. Mod. Phys.82 1539 [5] Long W, Zhang H and Sun Q F 2011 Phys. Rev. B84 075416 [6] Wakeham N, Bangura A F, Xu X, Mercure J F, Greenblatt M and Hussey N E 2011 Nat. Commun.2 396 [7] Grissonnanche G, Legros A, Badoux S, Lefrançois E, Zatko V, Lizaire M, Laliberté F, Gourgout A, Zhou J S, Pyon S, et al. 2019 Nature571 376 [8] Grissonnanche G, Thériault S, Gourgout A, Boulanger M E, Lefrançois E, Ataei A, Laliberté F, Dion M, Zhou J S, Pyon S, et al. 2020 Nat. Phys.16 1108 [9] Haldane F D M 1988 Phys. Rev. Lett.61 2015 [10] Harper P G 1955 Proc. Phys. Soc. A68 874 [11] Hofstadter D R 1976 Phys. Rev. B14 2239 [12] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 Nature515 237 [13] Fläschner N, Rem B S, Tarnowski M, Vogel D, Lühmann D S, Sengstock K and Weitenberg C 2016 Science352 1091 [14] Miyake H, Siviloglou G A, Kennedy C J, Burton W C and Ketterle W 2013 Phys. Rev. Lett.111 185302 [15] Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B and Bloch I 2013 Phys. Rev. Lett.111 185301 [16] Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, et al. 2013 Nature497 598 [17] Hunt B, Sanchez-Yamagishi J D, Young A F, Yankowitz M, LeRoy B J, Watanabe K, Taniguchi T, Moon P, Koshino M, Jarillo-Herrero P, et al. 2013 Science340 1427 [18] Hatsugai Y and Kohmoto M 1990 Phys. Rev. B42 8282 [19] Delplace P and Montambaux G 2010 Phys. Rev. B82 035438 [20] Loring T A and Hastings M B 2010 Europhys. Lett.92 67004 [21] Kuno Y 2019 Phys. Rev. B100 054108 [22] Zheng J H, Qin T and Hofstetter W 2019 Phys. Rev. B99 125138 [23] Chen J C, Wang J and Sun Q F 2012 Phys. Rev. B85 125401 [24] Harper F, Simon S H and Roy R 2014 Phys. Rev. B90 075104 [25] Thonhauser T and Vanderbilt D 2006 Phys. Rev. B74 235111 [26] Smrcka L and Streda P 1977 J. Phys. C: Solid State Physics10 2153 [27] Cheng S G, Xing Y, Sun Q F and Xie X C 2008 Phys. Rev. B78 045302 [28] Jiang H, Cheng S, Sun Q F and Xie X C 2009 Phys. Rev. Lett.103 036803 [29] Hasan M Z and Kane C L 2010 Rev. Mod. Phys.82 3045 [30] Qi X L and Zhang S C 2011 Rev. Mod. Phys.83 1057 [31] Chauwin M, Siu Z B and Jalil M B A 2022 Phys. Rev. Appl.17 024035 [32] Oka T and Aoki H 2009 Phys. Rev. B79 081406 [33] Lee C H, Imhof S, Berger C, Bayer F, Brehm J, Molenkamp L W, Kiessling T and Thomale R 2018 Commun. Phys.1 39 [34] Yatsugi K, Yoshida T, Mizoguchi T, Kuno Y, Iizuka H, Tadokoro Y and Hatsugai Y 2022 Commun. Phys.5 180 [35] Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett.49 405
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
