Non-Hermitian band topology from momentum-dependent relaxation in two-dimensional metals with spiral magnetism

TL;DR

This paper explores how momentum-dependent relaxation rates in two-dimensional metals with spiral magnetism induce non-Hermitian band topology, leading to exceptional points, Fermi surface topology changes, and observable Fermi arcs.

Contribution

It demonstrates the emergence of non-Hermitian topological features in metals due to momentum-dependent relaxation, revealing new phenomena in Fermi surface evolution and spectral functions.

Findings

Exceptional points appear in the Brillouin zone with opposite topological charges.

Fermi surface topology can drastically change by merging pockets at exceptional points.

Spectral functions show Fermi arcs with smooth momentum dependence despite nonanalyticities.

Abstract

We study the emergence of non-Hermitian band topology in a two-dimensional metal with planar spiral magnetism due to a momentum-dependent relaxation rate. A sufficiently strong momentum dependence of the relaxation rate leads to exceptional points in the Brillouin zone, where the Hamiltonian is nondiagonalizable. The exceptional points appear in pairs with opposite topological charges and are connected by arc-shaped branch cuts. We show that exceptional points inside hole and electron pockets, which are generally present in a spiral magnetic state with a small magnetic gap, can cause a drastic change of the Fermi surface topology by merging those pockets at isolated points in the Brillouin zone. We derive simple rules for the evolution of the eigenstates under semiclassical motion through these crossing points, which yield geometric phases depending only on the Fermi surface topology. The spectral function observed in photoemission exhibits Fermi arcs. Its momentum dependence is smooth -- despite of the nonanalyticities in the complex quasiparticle band structure.