Effective Hamiltonian for protected edge states in graphene
Abstract
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:
-
- Northern Illinois Univ., DeKalb, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
- Northern Illinois Univ., DeKalb, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (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
- OSTI Identifier:
- 1391720
- Alternate Identifier(s):
- OSTI ID: 1372526
- Grant/Contract Number:
- AC02-06CH11357
- Resource 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)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Winkler, R., and Deshpande, H. Effective Hamiltonian for protected edge states in graphene. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.95.235312.
Winkler, R., & Deshpande, H. Effective Hamiltonian for protected edge states in graphene. United States. https://doi.org/10.1103/PhysRevB.95.235312
Winkler, R., and Deshpande, H. Thu .
"Effective Hamiltonian for protected edge states in graphene". United States. https://doi.org/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 = {Thu Jun 15 00:00:00 EDT 2017},
month = {Thu Jun 15 00:00:00 EDT 2017}
}
Web of Science
Works referenced in this record:
Finite Size Effects on Helical Edge States in a Quantum Spin-Hall System
journal, December 2008
- Zhou, Bin; Lu, Hai-Zhou; Chu, Rui-Lin
- Physical Review Letters, Vol. 101, Issue 24
Topological insulators and superconductors
journal, October 2011
- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Reviews of Modern Physics, Vol. 83, Issue 4
General approach to the envelope-function approximation based on a quadrature method
journal, September 1993
- Winkler, R.; Rössler, U.
- Physical Review B, Vol. 48, Issue 12
Electronic states of graphene nanoribbons studied with the Dirac equation
journal, June 2006
- Brey, L.; Fertig, H. A.
- Physical Review B, Vol. 73, Issue 23
Topological Order and the Quantum Spin Hall Effect
journal, September 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 14, Article No. 146802
Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007
- Konig, M.; Wiedmann, S.; Brune, C.
- Science, Vol. 318, Issue 5851, p. 766-770
Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
journal, July 2002
- Ryu, Shinsei; Hatsugai, Yasuhiro
- Physical Review Letters, Vol. 89, Issue 7
Quantum Spin Hall Effect in Graphene
journal, November 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 22
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
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
Quantum Spin Hall Effect in Inverted Type-II Semiconductors
journal, June 2008
- Liu, Chaoxing; Hughes, Taylor L.; Qi, Xiao-Liang
- Physical Review Letters, Vol. 100, Issue 23
Invariant expansion for the trigonal band structure of graphene
journal, December 2010
- Winkler, R.; Zülicke, U.
- Physical Review B, Vol. 82, Issue 24
Valley-isospin dependence of the quantum Hall effect in a graphene junction
journal, July 2007
- Tworzydło, J.; Snyman, I.; Akhmerov, A. R.
- Physical Review B, Vol. 76, Issue 3
Robust level coincidences in the subband structure of quasi-2D systems
journal, December 2012
- Winkler, R.; Wang, L. Y.; Lin, Y. H.
- Solid State Communications, Vol. 152, Issue 23
Spin--Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems
book, January 2003
- Winkler, Roland; Höhler, Gerhard; Kühn, Johann H.
- Springer Tracts in Modern Physics, Vol. 191
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988
- Haldane, F. D. M.
- Physical Review Letters, Vol. 61, Issue 18
Peculiar Localized State at Zigzag Graphite Edge
journal, July 1996
- Fujita, Mitsutaka; Wakabayashi, Katsunori; Nakada, Kyoko
- Journal of the Physical Society of Japan, Vol. 65, Issue 7
Topological Insulators and Topological Superconductors
book, January 2013
- Bernevig, B. Andrei
- Princeton University Press
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
Edge accumulation and currents of moment in two-dimensional topological insulators
journal, September 2010
- Sonin, E. B.
- Physical Review B, Vol. 82, Issue 11
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
Works referencing / citing this record:
Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents
journal, September 2018
- Marmolejo-Tejada, J. M.; García, J. H.; Petrović, M. D.
- Journal of Physics: Materials, Vol. 1, Issue 1