Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-reversal-symmetry-broken quantum spin Hall effect   Quantum spin Hall (QSH) state of matter is usually considered to be protected
by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in
the presence of the Rashba spin-orbit coupling and an exchange field, which
break both inversion and TR symmetries. It is found that the QSH state
characterized by nonzero spin Chern numbers $C_{\pm}=\pm 1$ persists when the
TR symmetry is broken. A topological phase transition from the TR
symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a
critical exchange field, where the bulk band gap just closes. It is also shown
that the transition from the TR symmetry-broken QSH phase to an ordinary
insulator state can not happen without closing the band gap.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg