Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-dimensional symmetry breaking topological matters   We discuss topological electronic states described by the Dirac Hamiltonian
plus an additional one in three-dimension. When the additional Hamiltonian is
an element of an Abelian group, electronic states become topologically
nontrivial even in the absence of fundamental symmetries such as the
time-reversal and the particle-hole symmety. The symmetry-breaking topological
states are charercterized by the Chern number defined in the two-dimensional
partial Brillouin zone. The topological insulators under Zeeman field are an
example of the symmetry-breaking topological matters. We show the transision
from the topological insulating phase to the topological semimetal one under
the strong Zeeman field.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio