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We theoretically predict two new classes of three-dimensional topological crystalline insulators (TCIs), which have an odd number of unpinned surface Dirac cones protected by crystal symmetries. The first class is protected by a single nonsymmorphic glide plane symmetry; the second class is protected by a composition of a twofold rotation and time-reversal symmetry (a magnetic group symmetry). Both classes of TCIs are characterized by a quantized -Berry phase associated with surface states and a Z₂ topological invariant associated with the bulk bands. In the presence of disorder, these TCI surface states are protected against localization by the average crystal symmetries, and exhibit critical conductivity in the universality class of the quantum Hall plateau transition. These new TCIs exist in time-reversal-breaking systems with or without spin-orbital coupling, and their material realizations are discussed.
Fang et al. (Wed,) studied this question.