Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal characterizing topological insulator and topological
  semi-metal with Wannier functions   The nontrivial evolution of Wannier functions (WF) for the occupied bands is
a good starting point to understand topological insulator. By modifying the
definition of WFs from the eigenstates of the projected position operator to
those of the projected modular position operator, we are able to extend the
usage of WFs to Weyl metal where the WFs in the old definition fails because of
the lack of band gap at the Fermi energy. This extension helps us to
universally understand topological insulator and topological semi-metal in a
same framework. Another advantage of using the modular position operators in
the definition is that the higher dimensional WFs for the occupied bands can be
easily obtained. We show one of their applications by schematically explaining
why the winding numbers $\nu_{3D}=\nu_{2D}$ for the 3D topological insulators
of DIII class presented in Phys. Rev. Lett. 114, 016801(2015).

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat