Polarization jumps across Weyl semimetal phase in two-dimensional materials

The electric polarization in insulating systems is described by the Berry phase of Bloch states according to the modern theory of polarization. The polarization changes continuously and smoothly as we change a parameter of the system as long as the system remains insulating. In this talk, we present our recent discovery of the jump of polarization in two-dimensional materials when the system goes across the Weyl semimetal phase, which is protected by a symmetry. For two-dimensional Weyl semimetals, a parameter M is introduced to break the symmetry and make the system insulating. We compare values of polarization in two limits M→0⁺ and M→0^- and see that there is a finite jump of polarization. This jump of polarization is described by the newly introduced “Weyl dipole” representing how the Weyl points with monopole charges are displaced in the reciprocal space [1]. We also discuss another scenario where a Weyl semimetal phase appears at transitions between normal insulator to topological insulator phases. In such cases, Weyl points do not appear in pairs generally but a finite jump of polarization still exists. We clarify how to modify the discussion above to describe these jumps.