Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing: A numerical investigation

doi:10.1088/1674-1056/27/8/087306

Abstract

By exactly solving the effective two-body interaction for a two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopotentials (PPs) without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall (FQH) states both in the lowest Landau level (LLL) and first excited Landau level (1LL). The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values, while the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.

Keywords: fractional quantum Hall in-plane magnetic field pseudopotentials Landau level mixing

Received: 02 May 2018
Revised: 11 May 2018
Accepted manuscript online:

PACS:	73.43.Lp	(Collective excitations)
	71.10.Pm	(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11674041 and 91630205) and Chongqing Research Program for Basic Research and Frontier Technology (Grant No. cstc2017jcyjAX0084).

Corresponding Authors: Zi-Xiang Hu
E-mail: zxhu@cqu.edu.cn

Cite this article:

Lin-Peng Yang(杨林鹏), Qi Li(李骐), Zi-Xiang Hu(胡自翔) Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing: A numerical investigation 2018 Chin. Phys. B 27 087306

[1]	Tsui D C, Stormer H L and Gossard A C 1982 Phys. Rev. Lett. 48 1559
[2]	Prange R and Girvin S 1987 The Quantum Hall effect: Graduate texts in contemporary physics (Springer-Verlag)
[3]	Haldane F D M 1983 Phys. Rev. Lett. 51 605
[4]	Haldane F D M 1990 The Quantum Hall Effect (New York: Springer)
[5]	Laughlin R B 1983 Phys. Rev. Lett. 50 1395
[6]	Moore G and Read N 1991 Nucl. Phys. B 360 362
[7]	Greiter M, Wen X G and Wilczek F 1991 Phys. Rev. Lett. 66 3205
[8]	Lilly M P, Cooper K B, Eisenstein J P, Pfeiffer L N and West K W 1999 Phys. Rev. Lett. 82 394
[9]	Du R R, Tsui D C, Stormer H L, Pfeiffer L N, Baldwin K W and West K W 1999 Solid State Commun. 109 389
[10]	Dean C R, Piot B A, Hayden P, Sarma S D, Gervais G, Pfeiffer L N and West K W 2008 Phys. Rev. Lett. 101 186806
[11]	Liu G T, Zhang C, Tsui D C, Knez I, Levine A, Du R R, Pfeiffer L N and West K W 2012 Phys. Rev. Lett. 108 196805
[12]	Chen Y J 1990 Chin. Phys. Lett. 7 514
[13]	Cooper N R 2008 Adv. Phys. 57 539
[14]	Qiu R Z, Kou S P, Hu Z X, Wan X and Yi S 2011 Phys. Rev. A 83 063633
[15]	Haldane F D M 2011 Phys. Rev. Lett. 107 116801
[16]	Yang B, Hu Z X, Lee C H and Papic Z 2017 Phys. Rev. Lett. 118 146403
[17]	Hu Z X, Li Q, Yang L P, Yang W Q, Jiang N, Qiu R Z and Yang B 2018 Phys. Rev. B 97 035140
[18]	Papic Z 2013 Phys. Rev. B 87 245315
[19]	Yang B, Papic Z, Rezayi E H, Bhatt R N and Haldane F D M 2012 Phys. Rev. B 85 165318
[20]	Yang B, Lee C H, Zhang C and Hu Z X 2017 Phys. Rev. B 96 195140
[21]	Rezayi E H and Haldane F D M 2000 Phys. Rev. Lett. 84 4685
[22]	Bishara W and Nayak C 2009 Phys. Rev. B 80 121302
[23]	Peterson M R and Nayak C 2013 Phys. Rev. B 87 245129
[24]	Simon S H and Rezayi E H 2013 Phys. Rev. B 87 155426
[25]	Sodemann I and MacDonald A H 2013 Phys. Rev. B 87 245425

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Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing: A numerical investigation

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