Exceptional topological insulators

M Michael Denner,Ronny Thomale,Titus Neupert,Tomáš Bzdušek,Frank Schindler,Anastasiia Skurativska,Mark H Fischer

doi:10.1038/s41467-021-25947-z

M Michael Denner, Ronny Thomale + Show 5 more

Open Access

https://doi.org/10.1038/s41467-021-25947-z

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Abstract

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.

Highlights

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding
Starting from the initial classification of topological matter based on Hermitian Hamiltonians, the study of systems with non-negligible loss and gain calls for an extension to non-Hermitian topological matter. At this early stage of the field, several principles have been uncovered: (i) non-Hermitian systems have stable band degeneracies in two dimensions (2D), called exceptional points[15,16,17] (Fig. 1a). (ii) Two different types of gaps have to be distinguished when eigenvalues are complex—line gaps, which can be adiabatically transformed into a Hermitian system, and point gaps, where this is not the case18. (iii) The topological bulk-boundary correspondence may break down for non-Hermitian systems due to the skin effect, which leads to dramatic shifts in the spectrum for open versus periodic boundary conditions (PBCs) as well as to a piling up of bulk states at the boundary19–26. (iv) The structure of topological invariants becomes more intricate, as complex-valued energy eigenvalues can themselves acquire a winding number[27,28]
We demonstrate that our ETI models do not exhibit a non-Hermitian skin effect, such that the surface states are not overshadowed by a collapse of the point gap

Summary

Introduction

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. 1234567890():,; Since their theoretical conception[1,2] and experimental discovery[3,4], three-dimensional topological insulators (3D TIs) have become the focal point for research on topological quantum matter Their key feature are conducting surface states resembling a single species of gapless Dirac electrons, which are protected against surface perturbations as long as time-reversal and charge-conservation symmetry are preserved[5]. Transcending the realm of quantum matter, the TI phase has since been realized in many different settings including meta-materials, such as photonic and phononic crystals[6,7,8,9] Most of such meta-material platforms are accidentally or tunably lossy, such that their effective Hamiltonian description involves non-Hermitian terms due to the lack of energy conservation[10]. In contrast to the conventional 3D TI, the surface states of an ETI do not require time-reversal symmetry for their protection and may generically occur in non-Hermitian systems

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