Fig. 3: Physical consequences of quadrupole topological PhCs at 1D interfaces.
a, b Two 1D interfaces are created between a strip of quadrupole (trivial) PhC (same as Fig. 1b,c) and perfect electric conductors (PECs). c, d Energy dispersions of the two strip setups. e For the non-trivial setup, Wannier centers of the eigenmodes show two Wannier states at ±0.5, which are outside the bulk Wannier bands owing to the non-trivial bulk quadrupole moment. f In comparison, no in-gap Wannier states are observed in the trivial setup. g Calculation of the spatial density of polarization px(y) shows the in-gap Wannier states are localized at the top (y = 20a) and bottom interfaces (y = 0). h Similar calculations repeated for the trivial PhC, showing no edge polarization, which is consistent with the trivial quadrupole moment.
