Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Band Topology or Geometry?   The study of topology of energy bands in solid has always been interesting
and fruitful. Historically, Thouless et al proposed the TKNN number or Chern
number of the energy bands to explain the quantization of Hall conductance in
the integer quantum Hall effect. Recently, Z2 topological insulators have been
intensively studied and similarly topological crystalline insulators are
proposed.These materials exhibit nontrivial charge or spin transport properties
that is due to the existence of metallic edge states. The edge states are
protect by the topology of the energy bands of the bulk material and the band
topology are described by some invariants similar to the TKNN number. However,
these invariants are crude and strongly dependent on the symmetry. Here we give
an unified picture of the relationship of the edge states and the geometry of
the energy bands. We show the band geometry determines not only the topological
but also the geometrical properties of the edge states and the picture is
applicable when the symmetries are broken.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: cs