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تسجيل مستخدم جديدZ2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
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It has been known that an anti-unitary symmetry such as time-reversal or charge conjugation is needed to realize Z2 topological phases in non-interacting systems. Topological insulators and superconducting nanowires are representative examples of such Z2 topological matters. Here we report the first-known Z2 topological phase protected by only unitary symmetries. We show that the presence of a nonsymmorphic space group symmetry opens a possibility to realize Z2 topological phases without assuming any anti-unitary symmetry. The Z2 topological phases are constructed in various dimensions, which are closely related to each other by Hamiltonian mapping. In two and three dimensions, the Z2 phases have a surface consistent with the nonsymmorphic space group symmetry, and thus they support topological gapless surface states. Remarkably, the surface states have a unique energy dispersion with the Mobius twist, which identifies the Z2 phases experimentally. We also provide the relevant structure in the K-theory.
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Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we complete the class
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