Band inversion-driven warping and high valley degeneracy

Band inversion is a physical phenomenon that can warp the band structure in topological insulators, generating multiple electronic valleys for conducting carriers. However, the conditions under which band inversion induces warping are not well understood. Here, we derive two general rules that must be satisfied for band warping to occur in centrosymmetric and non-magnetic topological insulators: (1) bands must be sufficiently inverted, and (2) secondary bands must have opposite parity and be close in energy to the band edges. We chart the valley degeneracies that can emerge from band inversion in each of the 11 centrosymmetric point groups, revealing that an increase in the valley degeneracy between 2- and 48-fold is possible from band inversion. The generalized rules offer a unique band engineering approach by capitalizing on the non-trivial electronic structures of topological insulators.