Nontrivial Topological Phase in the Absence of Berry Curvature*

In conventional topological materials, the existence of topological states is characterized by the topological quantity such as nonzero Berry curvature, which corresponds to the magnetic field in momentum space. In this talk, we discuss a new type of nontrivial topological phase in two-dimensional systems in the absence of Berry curvature, but by the presence of nonzero Berry connection, which corresponds to the vector potential in momentum space. This is an application of the analogue of Aharanov-Bohm effect in momentum space. This nontrivial topological phase is demonstrated in a tight-binding model with alternated hopping both for square¹ and honeycomb lattices². A corresponded realization made by the all-dielectric photonic crystal is also proposed³.


1. F. Liu and K. Wakabayashi, Phys. Rev. Lett. 118 076803 (2017).
2. F. Liu, M. Yamamoto and K. Wakabayashi, submitted to J. Phys. Soc. Jpn.
3. F. Liu, H.-Y. Deng and K. Wakabayashi, to be submitted.