Hofstadter butterflies in magnetically modulated graphene bilayer : An algebraic approach
Arora, Manisha ; Sachdeva, Rashi LU
and Ghosh, Sankalpa
(2022)
In Physica E: Low-Dimensional Systems and Nanostructures
142.
- Abstract
It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly (Novoselov et al., 2006). In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper–Hofstadter equation for such BLG system in a periodic magnetic modulation. We further demonstrate the topological quantisation of Hall conductivity in such system and point out... (More)
It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly (Novoselov et al., 2006). In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper–Hofstadter equation for such BLG system in a periodic magnetic modulation. We further demonstrate the topological quantisation of Hall conductivity in such system and point out that the quantised Hall plateaus are equally spaced for all quantum numbers for the quantised Hall conductivity.
(Less)
- author
- Arora, Manisha
; Sachdeva, Rashi
LU
and Ghosh, Sankalpa
- organization
- publishing date
- 2022-08
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bilayer graphene, Hofstadter butterfly, Magnetic modulation, Topological quantisation: Magnetic translation symmetry
- in
- Physica E: Low-Dimensional Systems and Nanostructures
- volume
- 142
- article number
- 115311
- publisher
- Elsevier
- external identifiers
-
- scopus:85131088193
- ISSN
- 1386-9477
- DOI
- 10.1016/j.physe.2022.115311
- language
- English
- LU publication?
- yes
- id
- c9746684-69d9-4c31-bc29-5b1e922a0b5e
- date added to LUP
- 2022-12-28 10:14:44
- date last changed
- 2023-11-21 14:44:35
@article{c9746684-69d9-4c31-bc29-5b1e922a0b5e,
abstract = {{<p>It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly (Novoselov et al., 2006). In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper–Hofstadter equation for such BLG system in a periodic magnetic modulation. We further demonstrate the topological quantisation of Hall conductivity in such system and point out that the quantised Hall plateaus are equally spaced for all quantum numbers for the quantised Hall conductivity.</p>}},
author = {{Arora, Manisha and Sachdeva, Rashi and Ghosh, Sankalpa}},
issn = {{1386-9477}},
keywords = {{Bilayer graphene; Hofstadter butterfly; Magnetic modulation; Topological quantisation: Magnetic translation symmetry}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Physica E: Low-Dimensional Systems and Nanostructures}},
title = {{Hofstadter butterflies in magnetically modulated graphene bilayer : An algebraic approach}},
url = {{http://dx.doi.org/10.1016/j.physe.2022.115311}},
doi = {{10.1016/j.physe.2022.115311}},
volume = {{142}},
year = {{2022}},
}