Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Hamiltonian for protected edge states in graphene   Edge states in topological insulators (TIs) disperse symmetrically about one
of the time-reversal invariant momenta $\Lambda$ in the Brillouin zone (BZ)
with protected degeneracies at $\Lambda$. 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. We show that
the edge states are determined by a band inversion in both reciprocal and real
space, which allows one to select $\Lambda$ for the edge states without
affecting the bulk spectrum.

9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex