Magnetisation oscillations, boundary conditions and the Hofstadter butterfly in graphene flakes

Yang Liu; Matej Brada; Eugene J. Mele; Feodor V. Kusmartsev

doi:10.1002/andp.201400143

Magnetisation oscillations, boundary conditions and the Hofstadter butterfly in graphene flakes

Yang Liu, Matej Brada, Eugene J. Mele, Feodor V. Kusmartsev

Physics

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4 Scopus citations

Abstract

New quantum oscillations in the magnetization of graphene flakes induced by magnetic fields, which depend on the shape of the flake, are described. At small values of the field they are due to the Aharonov-Bohm effect and with increasing field they are transformed into dHvA oscillations. The specific form of the dHvA oscillations is analyzed in terms of their energy spectrum, which has a form of Hofstadter's butterfly. Numerical results using a lattice tight-binding model and a continuum Dirac equation are presented and compared. Possible experiments to investigate the quantum oscillations in Moiré and graphene anti-dot superlattices are discussed.

Original language	British English
Pages (from-to)	449-460
Number of pages	12
Journal	Annalen der Physik (Leipzig)
Volume	526
Issue number	9-10
DOIs	https://doi.org/10.1002/andp.201400143
State	Published - 1 Oct 2014

Keywords

Aharonov Bohm effect
Boundary conditions
Dirac equation
Edge states
Graphene flakes
Hofstadter energy spectrum
Magnetization
Topological insulators

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10.1002/andp.201400143

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title = "Magnetisation oscillations, boundary conditions and the Hofstadter butterfly in graphene flakes",

abstract = "New quantum oscillations in the magnetization of graphene flakes induced by magnetic fields, which depend on the shape of the flake, are described. At small values of the field they are due to the Aharonov-Bohm effect and with increasing field they are transformed into dHvA oscillations. The specific form of the dHvA oscillations is analyzed in terms of their energy spectrum, which has a form of Hofstadter's butterfly. Numerical results using a lattice tight-binding model and a continuum Dirac equation are presented and compared. Possible experiments to investigate the quantum oscillations in Moir{\'e} and graphene anti-dot superlattices are discussed.",

keywords = "Aharonov Bohm effect, Boundary conditions, Dirac equation, Edge states, Graphene flakes, Hofstadter energy spectrum, Magnetization, Topological insulators",

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AU - Liu, Yang

AU - Brada, Matej

AU - Mele, Eugene J.

AU - Kusmartsev, Feodor V.

PY - 2014/10/1

Y1 - 2014/10/1

N2 - New quantum oscillations in the magnetization of graphene flakes induced by magnetic fields, which depend on the shape of the flake, are described. At small values of the field they are due to the Aharonov-Bohm effect and with increasing field they are transformed into dHvA oscillations. The specific form of the dHvA oscillations is analyzed in terms of their energy spectrum, which has a form of Hofstadter's butterfly. Numerical results using a lattice tight-binding model and a continuum Dirac equation are presented and compared. Possible experiments to investigate the quantum oscillations in Moiré and graphene anti-dot superlattices are discussed.

AB - New quantum oscillations in the magnetization of graphene flakes induced by magnetic fields, which depend on the shape of the flake, are described. At small values of the field they are due to the Aharonov-Bohm effect and with increasing field they are transformed into dHvA oscillations. The specific form of the dHvA oscillations is analyzed in terms of their energy spectrum, which has a form of Hofstadter's butterfly. Numerical results using a lattice tight-binding model and a continuum Dirac equation are presented and compared. Possible experiments to investigate the quantum oscillations in Moiré and graphene anti-dot superlattices are discussed.

KW - Aharonov Bohm effect

KW - Boundary conditions

KW - Dirac equation

KW - Edge states

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KW - Hofstadter energy spectrum

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Magnetisation oscillations, boundary conditions and the Hofstadter butterfly in graphene flakes

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