|
|
|
Periodic electron oscillation in coupled two-dimensional lattices |
| Yan-Yan Lu(陆艳艳), Chao Wang(王超), Jin-Yi Jiang(将金益), Jie Liu(刘洁), and Jian-Xin Zhong(钟建新)† |
| Hunan Key Laboratory of Micro-Nano Energy Materials and Devices, School of Physics and Optoelectronics, Xiangtan University, Hunan 411105, China |
|
|
|
|
Abstract We study the time evolution of electron wavepacket in the coupled two-dimensional (2D) lattices with mirror symmetry, utilizing the tight-binding Hamiltonian framework. We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions. The frequency of this oscillation is determined by the strength of the interlayer hopping. Additionally, we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorder W, with the decay time being inversely proportional to the square of W and the frequency change being proportional to the square of W, which is similar to the case in the coupled 1D disordered lattices. Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal, independent of lattice geometry, as demonstrated in AA-stacked bilayer and tri-layer graphene systems. Unlike the Bloch oscillation driven by electric fields, the periodic oscillation induced by interlayer coupling does not require the application of an electric field, has an ultrafast periodicity much shorter than the electron decoherence time in real materials, and can be tuned by adjusting the interlayer coupling. Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.
|
Received: 27 March 2023
Revised: 18 April 2023
Accepted manuscript online: 20 April 2023
|
|
PACS:
|
03.65.-w
|
(Quantum mechanics)
|
| |
71.23.-k
|
(Electronic structure of disordered solids)
|
| |
72.10.-d
|
(Theory of electronic transport; scattering mechanisms)
|
| |
72.80.Ng
|
(Disordered solids)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11874316), the National Basic Research Program of China (Grant No. 2015CB921103), and the International Visiting Faculty Program of Hunan Provincial Government, China. |
Corresponding Authors:
Jian-Xin Zhong
E-mail: jxzhong@xtu.edu.cn
|
Cite this article:
Yan-Yan Lu(陆艳艳), Chao Wang(王超), Jin-Yi Jiang(将金益), Jie Liu(刘洁), and Jian-Xin Zhong(钟建新) Periodic electron oscillation in coupled two-dimensional lattices 2023 Chin. Phys. B 32 070306
|
[1] Bloch F 1928 Z. Phys. 52 555
[2] Zener C 1934 Proc. R. Soc. London A 145 523
[3] Wannier G H 1962 Rev. Mod. Phys. 34 645
[4] Wannier G H 1960 Phys. Rev. 117 432
[5] Waschke C, Roskos H G, Schwedler R, Leo K, Kurz H and Köhler K 1993 Phys. Rev. Lett. 70 3319
[6] Leo K, Bolivar P H, Brüggemann F, Schwedler R and Köhler K 1992 Solid State Commun. 84 943
[7] Feldmann J, Leo K, Shah J, Miller D A, Cunningham J, Meier T, Von Plessen G, Schulze A, Thomas P and Schmitt-Rink S 1992 Phys. Rev. B 46 7252
[8] Roati G, De Mirandes E, Ferlaino F, Ott H, Modugno G and Inguscio M 2004 Phys. Rev. Lett. 92 230402
[9] Morsch O, Müller J, Cristiani M, Ciampini D and Arimondo E 2001 Phys. Rev. Lett. 87 140402
[10] Dahan M B, Peik E, Reichel J, Castin Y and Salomon C 1996 Phys. Rev. Lett. 76 4508
[11] Battesti R, Cladé P, Guellati-Khélifa S, Schwob C, Grémaud B, Nez F, Julien L and Biraben F 2004 Phys. Rev. Lett. 92 253001
[12] Gustavsson M, Haller E, Mark M, Danzl J G, Rojas-Kopeinig G and Nägerl H C 2008 Phys. Rev. Lett. 100 080404
[13] Ferrari G, Poli N, Sorrentino F and Tino G 2006 Phys. Rev. Lett. 97 060402
[14] Wilkinson S, Bharucha C, Madison K, Niu Q and Raizen M 1996 Phys. Rev. Lett. 76 4512
[15] Lenz G, Talanina I and De Sterke C M 1999 Phys. Rev. Lett. 83 963
[16] Dreisow F, Szameit A, Heinrich M, Pertsch T, Nolte S, Tünnermann A and Longhi S 2009 Phys. Rev. Lett. 102 076802
[17] Morandotti R, Peschel U, Aitchison J, Eisenberg H and Silberberg Y 1999 Phys. Rev. Lett. 83 4756
[18] Corrielli G, Crespi A, Della Valle G, Longhi S and Osellame R 2013 Nat. Commun. 4 1555
[19] Pertsch T, Dannberg P, Elflein W, Bräuer A and Lederer F 1999 Phys. Rev. Lett. 83 4752
[20] Gutiérrez L, Díaz-de-Anda A, Flores J, Méndez-Sánchez R, Monsivais G and Morales A 2006 Phys. Rev. Lett. 97 114301
[21] Jiang J, Lu Y, Wang C, Mosseri R and Zhong J 2022 Sci. China-Phys. Mech. Astron. 65 247211
[22] Zhang Y, Tang T T, Girit C, Hao Z, Martin M C, Zettl A, Crommie M F, Shen Y R and Wang F 2009 Nature 459 820
[23] Novoselov K S, Geim A K, Morozov S V, Jiang D E, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
[24] Chen G, Sharpe A L, Gallagher P, Rosen I T, Fox E J, Jiang L, Lyu B, Li H, Watanabe K and Taniguchi T 2019 Nature 572 215
[25] Liu Y W, Su Y, Zhou X F, Yin L J, Yan C, Li S Y, Yan W, Han S, Fu Z Q and Zhang Y 2020 Phys. Rev. Lett. 125 236102
[26] Novoselov K S, McCann E, Morozov S, Fal'ko V I, Katsnelson M, Zeitler U, Jiang D, Schedin F and Geim A 2006 Nat. Phys. 2 177
[27] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2018 Nature 556 43
[28] McCann E and Fal'ko V I 2006 Phys. Rev. Lett. 96 086805
[29] Zhong J and Mosseri R 1995 J. Phys. Condens. Matter 7 8383
[30] Zhong J, Diener R, Steck D A, Oskay W H, Raizen M G, Plummer E W, Zhang Z and Niu Q 2001 Phys. Rev. Lett. 86 2485
[31] Anderson P W 1958 Phys. Rev. 109 1492
[32] Thouless D J 1974 Phys. Rep. 13 93
[33] Mott N F 1968 Rev. Mod. Phys. 40 677
[34] Abrahams E, Anderson P, Licciardello D and Ramakrishnan T 1979 Phys. Rev. Lett. 42 673
[35] Koshino M and Son Y W 2019 Phys. Rev. B 100 075416
[36] Moon P and Koshino M 2013 Phys. Rev. B 88 241412 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
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.
View more on Altmetrics
|
|
|
