Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nontrivial surface topological physics from strong and weak topological
  insulators and superconductors   We investigate states on the surface of strong and weak topological
insulators and superconductors that have been gapped by a symmetry breaking
term. The surface of a strong 3D topological insulator gapped by a magnetic
material is well known to possess a half quantum Hall effect. Furthermore, it
has been known that the surface of a weak 3D topological insulator gapped by a
charge density wave exhibits a half quantum spin Hall effect. To generalize
these results to all Altland-Zirnbauer symmetry classes of topological
insulators and superconductors, we reproduce the classification table for the
ten symmetry classes by using the representation theory of Clifford algebras
and construct minimal-size Dirac Hamiltonians. We find that if the surface
dimension and symmetry class possesses a $\mathbb{Z}$ or $\mathbb{Z}_2$
topological invariant, then the resulting surface state with a gapped symmetry
breaking term may have a nontrivial topological phase.

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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
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The categories of this paper are: q-alg