Topological Crystalline Insulator

C₄-symmetric Band Inversion & Corner States

Parameters

Phase: Trivial

Topological Crystalline Insulators (TCIs) are protected by crystal symmetry rather than time-reversal. With C₄ rotation symmetry, band inversion at high-symmetry points can generate in-gap corner states. Tuning m through ±2t crosses topological phase transitions visible in the gap closing.