Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

Ankur Das; Ribhu K. Kaul; Ganpathy Murthy

doi:10.1103/PhysRevB.101.165416

Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

Ankur Das
, Ribhu K. Kaul
, Ganpathy Murthy

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

8 Scopus citations

Abstract

We study the band structure of electrons hopping on a honeycomb lattice with p/q (p,q are coprime integers) flux quanta through each elementary hexagon. In the nearest-neighbor hopping model the two bands that eventually form the n=0 Landau level have 2q zero-energy Dirac touchings. In this work we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an antiunitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lower the symmetry.

Original language	English
Article number	165416
Journal	Physical Review B
Volume	101
Issue number	16
DOIs	https://doi.org/10.1103/PhysRevB.101.165416
State	Published - Apr 15 2020

Bibliographical note

Publisher Copyright:
© 2020 American Physical Society.

Funding

G.M. thanks D. Mross for a valuable discussion. We acknowledge partial financial support from NSF Grant No. DMR-1611161 (A.D. and R.K.K.) and from NSF Grant No. DMR-1306897 (A.D. and G.M.). We thank the Aspen Center for Physics (NSF Grant No. 1607611), where this work was finalized for publication, for the hospitality. G.M. also thanks the Gordon and Betty Moore Foundation for sabbatical support at MIT and the Lady Davis Foundation for sabbatical support at the Technion.

Funders	Funder number
Lady Davis Fellowship Trust, Hebrew University of Jerusalem
Technion - Israel Institute of Technology
Massachusetts Institute of Technology
Gordon and Betty Moore Foundation
National Science Foundation Arctic Social Science Program	DMR-1611161, 1306897
Aspen Center for Physics	1607611

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

Access to Document

10.1103/PhysRevB.101.165416

Cite this

@article{66f567edc74844d2988bfff7a0725185,

title = "Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem",

abstract = "We study the band structure of electrons hopping on a honeycomb lattice with p/q (p,q are coprime integers) flux quanta through each elementary hexagon. In the nearest-neighbor hopping model the two bands that eventually form the n=0 Landau level have 2q zero-energy Dirac touchings. In this work we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an antiunitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lower the symmetry.",

author = "Ankur Das and Kaul, \{Ribhu K.\} and Ganpathy Murthy",

note = "Publisher Copyright: {\textcopyright} 2020 American Physical Society.",

year = "2020",

month = apr,

day = "15",

doi = "10.1103/PhysRevB.101.165416",

language = "English",

volume = "101",

number = "16",

}

TY - JOUR

T1 - Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

AU - Das, Ankur

AU - Kaul, Ribhu K.

AU - Murthy, Ganpathy

PY - 2020/4/15

Y1 - 2020/4/15

N2 - We study the band structure of electrons hopping on a honeycomb lattice with p/q (p,q are coprime integers) flux quanta through each elementary hexagon. In the nearest-neighbor hopping model the two bands that eventually form the n=0 Landau level have 2q zero-energy Dirac touchings. In this work we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an antiunitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lower the symmetry.

AB - We study the band structure of electrons hopping on a honeycomb lattice with p/q (p,q are coprime integers) flux quanta through each elementary hexagon. In the nearest-neighbor hopping model the two bands that eventually form the n=0 Landau level have 2q zero-energy Dirac touchings. In this work we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an antiunitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lower the symmetry.

UR - https://www.scopus.com/pages/publications/85084667118

UR - https://www.scopus.com/pages/publications/85084667118#tab=citedBy

U2 - 10.1103/PhysRevB.101.165416

DO - 10.1103/PhysRevB.101.165416

M3 - Article

AN - SCOPUS:85084667118

SN - 2469-9950

VL - 101

JO - Physical Review B

JF - Physical Review B

IS - 16

M1 - 165416

ER -

Stability of zero-energy Dirac touchings in the honeycomb Hofstadter problem

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this