Topological phase transitions, invariants and enriched bulk-edge correspondences in fermionic gapless systems with extended Fermi surface

TL;DR

This paper explores how injecting currents in fermionic systems can induce novel topological phases, including gapless metallic states with extended Fermi surfaces, characterized by Hall conductance as a new invariant, and reveals enriched bulk-edge correspondences.

Contribution

It introduces new topological phases induced by currents, identifies Hall conductance as a new invariant, and uncovers a novel class of topological phase transitions without energy non-analyticity.

Findings

Discovery of three new topological phases: Odd CI, Odd CM, Even CM.

Hall conductance as a new topological invariant for gapless phases.

Identification of a class of TPTs without ground state energy non-analyticity.

Abstract

Topological phases and topological phase transitions (TPT) are among the most fantastic phenomena in Nature. Here we show that injecting a current may lead to new topological phases, especially new gapless topological metallic phases with extended Fermi surfaces (FSs) through novel class of TPTs in the bulk or the boundary. Specifically, we study the quantum anomalous Hall (QAH) system in a square lattice under various forms of injecting currents. In addition to the previously known Chern insulator (which will be called even Chern insulator here), band insulator and band metal (BM), we find three new topological phases we name as: the gapped odd Chern insulator (Odd CI), the gapless odd Chern metal (Odd CM) and even Chern metal (Even CM). The Chern number may not be effective anymore in characterizing the topological gapless phases with extended FS. It is the Hall conductance which acts as the new topological invariant in such gapless systems. Its jump is a universal integer or non-integer across the even CM/BM or odd CM/BM TPT respectively where there is also a corresponding TPT in the Longitudinal (L-)edge modes. The Odd/even CM to BM transition is a novel class of TPT without any non-analyticity in the ground state energy density. This presents the first example of a TPT which is not a quantum phase transition (QPT). The original bulk-edge correspondence is enriched into bulk/Longitudinal (L-)/Transverse (T-) edge correspondence. The L-edge reconstruction may happen earlier, later or at the same time as the bulk TPT respectively in the even CI/odd CI/odd CM sequence with the edge dynamic exponent $ z_L=3 $, in the even CI/even CM/odd CM sequence with $ z_L=2 $ or a direct even CI/odd CM with a flat edge. The disappearance of the T-edge always happen at the same time as the bulk TPT with a universal edge critical behaviour.