| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
|
|
|
|
Flat Band and $\eta$-Pairing States in a One-Dimensional Moiré Hubbard Model |
| R. Wang1 and Z. Song2* |
1College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China
2School of Physics, Nankai University, Tianjin 300071, China
|
|
| Cite this article: |
|
R. Wang and Z. Song 2024 Chin. Phys. Lett. 41 047101 |
|
|
|
|
Abstract A Moiré system is formed when two periodic structures have a slightly mismatched period, resulting in unusual strongly correlated states in the presence of particle-particle interactions. The periodic structures can arise from the intrinsic crystalline order and periodic external field. We investigate a one-dimensional Hubbard model with periodic on-site potential of period $n_{0}$, which is commensurate to the lattice constant. For large $n_{0}$, the exact solution demonstrates that there is a midgap flat band with zero energy in the absence of Hubbard interaction. Each Moiré unit cell contributes two zero energy levels to the flat band. In the presence of Hubbard interaction, the midgap physics is demonstrated to be well described by a uniform Hubbard chain in which the effective hopping and on-site interaction strength can be controlled by the amplitude and period of the external field. Numerical simulations are performed to demonstrate the correlated behaviors in the finite-sized Moiré Hubbard system, including the existence of an $\eta $-pairing state and bound pair oscillation. This finding provides a method to enhance the correlated effect by a spatially periodic external field.
|
|
|
Received: 27 October 2023
Published: 25 April 2024
|
|
| PACS: |
71.27.+a
|
(Strongly correlated electron systems; heavy fermions)
|
| |
74.78.Fk
|
(Multilayers, superlattices, heterostructures)
|
| |
02.30.Nw
|
(Fourier analysis)
|
| |
02.60.Cb
|
(Numerical simulation; solution of equations)
|
|
|
|
|
|
| [1] | Bistritzer R and MacDonald A H 2011 Proc. Natl. Acad. Sci. USA 108 12233 |
| [2] | Cao Y, Luo J Y, Fatemi V, Fang S, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, and Jarillo-Herrero P 2016 Phys. Rev. Lett. 117 116804 |
| [3] | Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, and Jarillo-Herrero P 2018 Nature 556 80 |
| [4] | Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, and Jarillo-Herrero P 2018 Nature 556 43 |
| [5] | Kim K, DaSilva A, Huang S Q, Fallahazad B, Larentis S, Taniguchi T, Watanabe K, LeRoy B J, MacDonald A H, and Tutuc E 2017 Proc. Natl. Acad. Sci. USA 114 3364 |
| [6] | Yankowitz M, Chen S W, Polshyn H, Zhang Y X, Watanabe K, Taniguchi T, Graf D, Young A F, and Dean C R 2019 Science 363 1059 |
| [7] | Lu X B, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G Y, Bachtold A, MacDonald A H, and Efetov D K 2019 Nature 574 653 |
| [8] | Shen C, Ying J H, Liu L et al. 2021 Chin. Phys. Lett. 38 047301 |
| [9] | Zhang X, Pan G, Zhang Y, Kang J, and Meng Z Y 2021 Chin. Phys. Lett. 38 077305 |
| [10] | Li X F, Sun R X, Wang S Y, Li X, Liu Z B, and Tian J G 2022 Chin. Phys. Lett. 39 037301 |
| [11] | Ma J J, Wang Z Y, Xu S G, Gao Y X, Zhang Y Y, Dai Q, Lin X, Du S X, Ren J, and Gao H J 2022 Chin. Phys. Lett. 39 047403 |
| [12] | Wang Y, Liu Y X, Hao Z Y et al. 2023 Chin. Phys. Lett. 40 049901 |
| [13] | Chen X T, Liu C H, Xu D H, and Chen C Z 2023 Chin. Phys. Lett. 40 097403 |
| [14] | Dong S J, Zhang H, Wang C, Zhang M, Han Y J, and He L X 2023 Chin. Phys. Lett. 40 126403 |
| [15] | Wu H C, Xu H S, Xie L C, and Jin L 2024 Phys. Rev. Lett. 132 083801 |
| [16] | Xie L C, Jin L, and Song Z 2023 Sci. Bull. 68 255 |
| [17] | Yankowitz M, Xue J, Cormode D, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P, and LeRoy B J 2012 Nat. Phys. 8 382 |
| [18] | Ponomarenko L A, Gorbachev R V, Yu G L, Elias D C, Jalil R, Patel A A, Mishchenko A, Mayorov A S, Woods C R, Wallbank J R, Mucha-Kruczynski M, Piot B A, Potemski M, Grigorieva I V, Novoselov K S, Guinea F, Fal'ko V I, and Geim A K 2013 Nature 497 594 |
| [19] | Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard K L, Hone J, and Kim P 2013 Nature 497 598 |
| [20] | 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, and Ashoori R C 2013 Science 340 1427 |
| [21] | Woods C R, Britnell L, Eckmann A, Ma R S, Lu J C, Guo H M, Lin X, Yu G L, Cao Y, Gorbachev R V, Kretinin A V, Park J, Ponomarenko L A, Katsnelson M I, Gornostyrev Y N, Watanabe K, Taniguchi T, Casiraghi C, Gao H J, Geim A K, and Novoselov K S 2014 Nat. Phys. 10 451 |
| [22] | Nakajima S, Tomita T, Taie S, Ichinose T, Ozawa H, Wang L, Troyer M, and Takahashi Y 2016 Nat. Phys. 12 296 |
| [23] | Lohse M, Schweizer C, Zilberberg O, Aidelsburger M, and Bloch I 2016 Nat. Phys. 12 350 |
| [24] | Wang R, Wang P, Zhang K L, and Song Z 2020 Phys. Rev. B 102 094207 |
| [25] | Wang R, Yang X M, and Song Z 2021 J. Phys.: Condens. Matter 33 365403 |
| [26] | Yang X M, Zhang X Z, Li C, and Song Z 2018 Phys. Rev. B 98 085306 |
| [27] | Tasaki H 1998 J. Phys. C 10 4353 |
| [28] | Essler F H L, Frahm H, Gohmann F, Klumper A, and Korepin V E 2005 The One-Dimensional Hubbard Model (Cambridge: Cambridge University Press) |
| [29] | Jin L, Chen B, and Song Z 2009 Phys. Rev. A 79 032108 |
| [30] | Jin L and Song Z 2011 Phys. Rev. A 83 052102 |
| [31] | Yang C N 1989 Phys. Rev. Lett. 63 2144 |
| [32] | Corrielli G, Crespi A, Della Valle G, Longhi S, and Osellame R 2013 Nat. Commun. 4 1555 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
