Exceptional Topological Insulators

Since their theoretical conception and experimental discovery, 3-dimensional topological insulators (3D TIs) have become the focal point for research on topological quantum matter. Their key feature is a single Dirac electron on the surface, representing an anomaly: in purely 2D such a state can neither be regularized on a lattice nor in the continuum. In this work we search for a non-Hermitian analogue of the 3D TI: what could the anomalous non-Hermitian surface states be which necessitate a 3D topological bulk embedding? As an answer to this question, we introduce exceptional topological insulators (ETIs), a non-Hermitian topological state of matter that features exotic surface states. We show how this phase can evolve from a Weyl semimetal or Hermitian 3D TI close to the topological transition point 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.