Fig. 4: Topologically protected corner states and filling anomaly in a 2D system.
a For a finite PhC with N×N unit cells enclosed by PECs, the counting of the number of eigenstates below and above an energy gap are distinct between quadrupole and trivial phases. b Eigenstates of a 10 × 10 quadrupole PhC, showing four degenerate corner states inside the bulk gap, shaded in yellow. c Mode profile (∣Ez∣) of one of the corner states. d Spatial distribution of the accumulative electromagnetic energy density for the lowest 200 energy eigenstates in the quadrupole PhC, showing fractional occupations (2 ± 0.5) at the corners.
