Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene

Ke Huang; Xiao Li; Sankar Das Sarma; Fan Zhang

doi:10.1103/PhysRevB.110.115146

Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene

Ke Huang, Xiao Li^*, Sankar Das Sarma, Fan Zhang

^*Corresponding author for this work

Department of Physics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In particular, we focus on the convergence of the Hartree-Fock calculation with various reference fields and discuss the stability of the FQAH states in PLG. We show that the so-called charge neutrality scheme provides an unambiguous result for the Hartree-Fock calculation, as it ensures a convergence with respect to the momentum cutoff. Based on the Hartree-Fock band structure, we further carry out exact diagonalization calculations to explore the stability of the FQAH states in PLG. Our work provides an improved and unified (minimal) theoretical framework to understand the FQAH effect in rhombohedral PLG and paves the way for future studies. © 2024 American Physical Society

Original language	English
Article number	115146
Number of pages	19
Journal	Physical Review B: covering condensed matter and materials physics
Volume	110
DOIs	https://doi.org/10.1103/PhysRevB.110.115146
Publication status	Published - 24 Sept 2024

Funding

We acknowledge helpful discussions with A. Bernevig, Z. Dong, L. Ju, Z. Lu, J. Pixley, T. Senthil, I. Sodemann, M. Xie, X. Xu, J. Yu, and Y. Zhang. K.H. and X.L. are supported by the Research Grants Council of Hong Kong (Grants No. CityU 11300421, No. CityU 11304823, and No. C7012-21G), and City University of Hong Kong (Projects No. 9610428 and No. 7005938). K.H. is also supported by the Hong Kong Ph.D. Fellowship Scheme. S.D.S. is supported by the Laboratory for Physical Sciences through the Condensed Matter Theory Center (CMTC) at the University of Maryland. This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-2210452.

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COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: Huang, K., Li, X., Das Sarma, S., & Zhang, F. (2024). Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene. Physical Review B, 110, Article 115146 . https://doi.org/10.1103/PhysRevB.110.115146 The copyright of this article is owned by American Physical Society.

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title = "Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene",

abstract = "The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In particular, we focus on the convergence of the Hartree-Fock calculation with various reference fields and discuss the stability of the FQAH states in PLG. We show that the so-called charge neutrality scheme provides an unambiguous result for the Hartree-Fock calculation, as it ensures a convergence with respect to the momentum cutoff. Based on the Hartree-Fock band structure, we further carry out exact diagonalization calculations to explore the stability of the FQAH states in PLG. Our work provides an improved and unified (minimal) theoretical framework to understand the FQAH effect in rhombohedral PLG and paves the way for future studies. {\textcopyright} 2024 American Physical Society",

author = "Ke Huang and Xiao Li and {Das Sarma}, Sankar and Fan Zhang",

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T1 - Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene

AU - Huang, Ke

AU - Li, Xiao

AU - Das Sarma, Sankar

AU - Zhang, Fan

PY - 2024/9/24

Y1 - 2024/9/24

N2 - The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In particular, we focus on the convergence of the Hartree-Fock calculation with various reference fields and discuss the stability of the FQAH states in PLG. We show that the so-called charge neutrality scheme provides an unambiguous result for the Hartree-Fock calculation, as it ensures a convergence with respect to the momentum cutoff. Based on the Hartree-Fock band structure, we further carry out exact diagonalization calculations to explore the stability of the FQAH states in PLG. Our work provides an improved and unified (minimal) theoretical framework to understand the FQAH effect in rhombohedral PLG and paves the way for future studies. © 2024 American Physical Society

AB - The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In particular, we focus on the convergence of the Hartree-Fock calculation with various reference fields and discuss the stability of the FQAH states in PLG. We show that the so-called charge neutrality scheme provides an unambiguous result for the Hartree-Fock calculation, as it ensures a convergence with respect to the momentum cutoff. Based on the Hartree-Fock band structure, we further carry out exact diagonalization calculations to explore the stability of the FQAH states in PLG. Our work provides an improved and unified (minimal) theoretical framework to understand the FQAH effect in rhombohedral PLG and paves the way for future studies. © 2024 American Physical Society

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DO - 10.1103/PhysRevB.110.115146

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Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene

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