Type-II quadrupole topological insulators

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadrupole topological insulator (dubbed type-II) that violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously. We find that, similar to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We demonstrate that such new topological phenomena can appear from quench dynamics in non-equilibrium systems, which can be experimentally observed in ultracold atomic gases. We also propose an experimental scheme with electric circuits to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints.
Comment: 32 pages, 17 figures