Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-Order Topological Insulators   Three-dimensional topological (crystalline) insulators are materials with an
insulating bulk, but conducting surface states which are topologically
protected by time-reversal (or spatial) symmetries. Here, we extend the notion
of three-dimensional topological insulators to systems that host no gapless
surface states, but exhibit topologically protected gapless hinge states. Their
topological character is protected by spatio-temporal symmetries, of which we
present two cases: (1) Chiral higher-order topological insulators protected by
the combination of time-reversal and a four-fold rotation symmetry. Their hinge
states are chiral modes and the bulk topology is $\mathbb{Z}_2$-classified. (2)
Helical higher-order topological insulators protected by time-reversal and
mirror symmetries. Their hinge states come in Kramers pairs and the bulk
topology is $\mathbb{Z}$-classified. We provide the topological invariants for
both cases. Furthermore we show that SnTe as well as surface-modified
Bi$_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and
propose a realistic experimental setup to detect the hinge states.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: econ
28
The categories of this paper are: alg-geom