Higher-Order Topological Insulator: Corner States (2D)

Ordinary topological insulators protect conducting states on their edges. Higher-order topological insulators go one dimension further: their edges stay insulating, and instead a finite number of protected states pin to the corners. This simulator builds the Benalcazar–Bernevig–Hughes quadrupole lattice — a finite flake of dimerized unit cells with π-flux threaded through every plaquette — diagonalizes its real tight-binding Hamiltonian live as you tune the intracell and intercell hopping strengths, and renders the resulting corner-localized in-gap states as glowing dots in a pannable/zoomable top-down lattice view, alongside a live energy-spectrum panel that shows the gap close exactly where the quadrupole topology predicts it.