Novel Topological Phase with Zero Berry Curvature

TL;DR

This paper introduces a 2D lattice model showcasing a unique topological phase driven by Berry connection rather than Berry curvature, leading to fractional polarization and degenerate edge states.

Contribution

It presents a novel topological phase characterized by Berry connection and fractional polarization, expanding the understanding of topological phenomena beyond Berry curvature.

Findings

Demonstrates a 2D lattice model with topological phase without Berry curvature

Shows fractional wave polarization in each direction

Identifies degenerate edge states with opposite parities

Abstract

We present a two-dimensional (2D) lattice model that exhibits a nontrivial topological phase in the absence of the Berry curvature. Instead, the Berry connection provides the topological nontrivial phase in the model, whose integration over the momentum space, the so-called 2D Zak phase, yields a fractional wave polarization in each direction. These fractional wave polarizations manifest themselves as degenerated edge states with opposite parities in the model.