Abstract
We study what kind of topological crystalline insulator phase emerges from nodal line semimetal phases in the face-centered cubic system which is not indicated by topological indices when spin-orbit coupling (SOC) is introduced. We construct an effective model which hosts two different nodal lines phases, and calculated mirror Chern numbers in it by introducing SOC. As a result, we find that the two nodal line phases with different nodal line configurations are mapped to different topological crystalline insulator phases. This result shows that turning off SOC and checking the nodal line configuration can distinguish the two topological crystalline insulator phases, which have not been distinguished by previous methods.
Highlights
The development of an easy and simple diagnostic method of topological insulators is one of the greatest goals in the field of topological materials science [1,2,3,4,5,6]
The symmetry-based indicator is given by checking irreducible representations on the high-symmetry point of Brillouin zone (BZ), and it works as a diagnostic method for topological insulators with spin-orbit coupling (SOC) [7,8,9]
The local models are discussed separately, they are originated from a two-bands model in the whole BZ as we assumed first
Summary
The development of an easy and simple diagnostic method of topological insulators is one of the greatest goals in the field of topological materials science [1,2,3,4,5,6]. Since the methods use the same concept with the symmetry-based indicator, a mapping between them has been discussed, i.e., what kind of topological insulator emerges from a topolog-. Ical semimetal (parent state) when SOC is introduced [10] This mapping is not understood well for the former group, which is topological semimetals with nodes on the high-symmetry lines. For inversion and time-reversal (TR) symmetric nodal line semimetals without SOC, a diagnostic method called the Z2 index is defined [11] This Z2 index is defined in the same way as the well-known Fu-Kane Z2 index for TR protected topological insulators [1]. Distinguishes two topological crystalline insulator phases, which can not be distinguished by previous methods, it can lead to a subdividing diagnostic method beyond the symmetry-based indicator
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