Bloch state constrained by spatial and time-reversal symmetries

Abstract

Abstract The time-reversal symmetry in a nonmagnetic condensed-matter system is revised to the form dependent on the spatial symmetry of two-fold rotation in addition to the conventional inversion. The Bloch state within the constraints of spatial and time-reversal symmetries is demonstrated for representative systems of Si and GaAs on the basis of first-principles calculations. The nondegenerate gapless state in a topological system is also assessed.