skip to main content

DOE PAGESDOE PAGES

Title: Effective Hamiltonian for protected edge states in graphene

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.
Authors:
 [1] ;  [2]
  1. Northern Illinois Univ., DeKalb, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Northern Illinois Univ., DeKalb, IL (United States)
Publication Date:
Grant/Contract Number:
AC02-06CH11357
Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 23; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences and Engineering Division; National Science Foundation (NSF); USDOE
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE
OSTI Identifier:
1391720
Alternate Identifier(s):
OSTI ID: 1372526

Winkler, R., and Deshpande, H.. Effective Hamiltonian for protected edge states in graphene. United States: N. p., Web. doi:10.1103/PhysRevB.95.235312.
Winkler, R., & Deshpande, H.. Effective Hamiltonian for protected edge states in graphene. United States. doi:10.1103/PhysRevB.95.235312.
Winkler, R., and Deshpande, H.. 2017. "Effective Hamiltonian for protected edge states in graphene". United States. doi:10.1103/PhysRevB.95.235312. https://www.osti.gov/servlets/purl/1391720.
@article{osti_1391720,
title = {Effective Hamiltonian for protected edge states in graphene},
author = {Winkler, R. and Deshpande, H.},
abstractNote = {Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.},
doi = {10.1103/PhysRevB.95.235312},
journal = {Physical Review B},
number = 23,
volume = 95,
place = {United States},
year = {2017},
month = {6}
}

Works referenced in this record:

Z2 Topological Order and the Quantum Spin Hall Effect
journal, September 2005

Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007

Colloquium: Topological insulators
journal, November 2010

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006
  • Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C.
  • Science, Vol. 314, Issue 5806, p. 1757-1761
  • DOI: 10.1126/science.1133734

The electronic properties of graphene
journal, January 2009
  • Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.
  • Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162
  • DOI: 10.1103/RevModPhys.81.109

Two-dimensional gas of massless Dirac fermions in graphene
journal, November 2005
  • Novoselov, K. S.; Geim, A. K.; Morozov, S. V.
  • Nature, Vol. 438, Issue 7065, p. 197-200
  • DOI: 10.1038/nature04233