Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological nodal line semimetals   We review the recent, mainly theoretical, progress in the study of
topological nodal line semimetals in three dimensions. In these semimetals, the
conduction and the valence bands cross each other along a one-dimensional curve
in the three-dimensional Brillouin zone, and any perturbation that preserves a
certain symmetry group (generated by either spatial symmetries or time-reversal
symmetry) cannot remove this crossing line and open a full direct gap between
the two bands. The nodal line(s) is hence topologically protected by the
symmetry group, and can be associated with a topological invariant. In this
Review, (i) we enumerate the symmetry groups that may protect a topological
nodal line; (ii) we write down the explicit form of the topological invariant
for each of these symmetry groups in terms of the wave functions on the Fermi
surface, establishing a topological classification; (iii) for certain classes,
we review the proposals for the realization of these semimetals in real
materials and (iv) we discuss different scenarios that when the protecting
symmetry is broken, how a topological nodal line semimetal becomes Weyl
semimetals, Dirac semimetals and other topological phases and (v) we discuss
the possible physical effects accessible to experimental probes in these
materials.

21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex