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.
Highlights
The discovery of topological insulators [1,2] has triggered a systematic analysis and classification of topological features of band structures in solids
We have analyzed the non-Hermitian band topology resulting from a momentum-dependent relaxation rate p in a two-dimensional metal with spiral magnetic order
We find that arc-shaped branch cuts connecting exceptional points with opposite topological charges appear in the Brillouin zone
Summary
The discovery of topological insulators [1,2] has triggered a systematic analysis and classification of topological features of band structures in solids. In this letter we show that the combination of two seemingly innocuous ingredients—spiral magnetic order in a two-dimensional metal and a momentum-dependent relaxation rate—can lead to a non-Hermitian Hamiltonian with nontrivial topological features, such as exceptional points and branch cuts in the Brillouin zone. Hole and electron pockets merge at isolated momenta in the Brillouin zone where these degenerate bands cross the Fermi level, leading to a peculiar Fermi surface topology. Electrons traversing such crossing points along the Fermi surface acquire π -phase shifts, which can lead to a nontrivial geometric Berry phase.
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