Non-Hermitian impurities in Dirac systems

TL;DR

This paper explores how non-Hermitian impurities with complex potentials affect quasiparticle states in Dirac systems, revealing unique local density of states patterns and potential experimental tests.

Contribution

It provides a detailed analysis of non-Hermitian impurity effects on LDOS and DOS in Dirac systems, including lattice-specific spatial distributions and impurity configurations.

Findings

Impurities with loss create nontrivial LDOS distributions.

Real part of impurity potential causes DOS peaks or enhancements.

Characteristic trigonal LDOS patterns observed in hexagonal lattices.

Abstract

Quasiparticle states in Dirac systems with complex impurity potentials are investigated. It is shown that an impurity site with loss leads to a nontrivial distribution of the local density of states (LDOS). While the real part of defect potential induces a well-pronounced peak in the density of states (DOS), the DOS is either weakly enhanced at small frequencies or even forms a peak at the zero frequency for a lattice in the case of non-Hermitian impurity. As for the spatial distribution of the LDOS, it is enhanced in the vicinity of impurity but shows a dip at a defect itself when the potential is sufficiently strong. The results for a two-dimensional hexagonal lattice demonstrate the characteristic trigonal-shaped profile for the LDOS. The latter acquires a double-trigonal pattern in the case of two defects placed at neighboring sites. The effects of non-Hermitian impurities could be tested both in photonic lattices and certain condensed matter setups.