Hidden wave function of twisted bilayer graphene: The flat band as a Landau level

Fedor K. Popov; Alexey Milekhin

doi:10.1103/PhysRevB.103.155150

Hidden wave function of twisted bilayer graphene: The flat band as a Landau level

Fedor K. Popov
, Alexey Milekhin

Physics And Astronomy

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We study zero-energy states of the chirally symmetric continuum model (CS-CM) of twisted bilayer graphene. The zero-energy state obeys the Dirac equation on a torus in the external non-Abelian magnetic field. These zero-energy states could form a flat band - a band where the energy is constant across the Brillouin zone. We prove that the existence of the flat band implies that the wave function of any state from the flat band has a zero and vice versa. We found a hidden flat band of unphysical states in the CS-CM that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as a Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.

Original language	English
Article number	155150
Journal	Physical Review B
Volume	103
Issue number	15
DOIs	https://doi.org/10.1103/PhysRevB.103.155150
State	Published - Apr 27 2021

Bibliographical note

Publisher Copyright:
© 2021 American Physical Society.

Funding

Acknowledgments. We would like to thank Grisha Tarnopolsky and Igor R. Klebanov for the collaboration at the early stages of the work. We would like to thank Vladyslav Kozii, Anastasia Aristova, Alexander Avdoshkin, Nikita Sopenko, and Dumitru Calugaru for useful comments and discussions. We would like to thank Alexander Gorsky, Emil Akhmedov, and Peter Czajka for useful comments on the draft of the paper. The research of F.K.P. was supported in part by the U.S. NSF under Grants No. PHY-1620059 and No. PHY-1914860. The work of A.M. was supported by the Air Force Office of Scientific Research under Award No. FA9550-19-1-0360.

Funders	Funder number
Air Force Office of Scientific Research, United States Air Force	FA9550-19-1-0360
National Science Foundation Arctic Social Science Program	PHY-1914860, PHY-1620059

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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10.1103/PhysRevB.103.155150

Cite this

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abstract = "We study zero-energy states of the chirally symmetric continuum model (CS-CM) of twisted bilayer graphene. The zero-energy state obeys the Dirac equation on a torus in the external non-Abelian magnetic field. These zero-energy states could form a flat band - a band where the energy is constant across the Brillouin zone. We prove that the existence of the flat band implies that the wave function of any state from the flat band has a zero and vice versa. We found a hidden flat band of unphysical states in the CS-CM that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as a Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.",

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Hidden wave function of twisted bilayer graphene: The flat band as a Landau level

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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