Non-Hermitian topological phases: principles and prospects

Abstract

The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

“…Exploring correlated physics in open quantum systems attracts great interest mainly because of the systematic treatment of loss and gain in these systems, which quantitatively reproduces experimental observations [51][52][53][54][55]. In recent years, along with brute force studies of open quantum systems, understanding their effective descriptions based on non-Hermitian physics get momentum [56][57][58][59][60][61]. The studies of 4) and ( 5)).…”

Uncovering exceptional contours in non-Hermitian hyperbolic lattices

“…The phase rigidity, r, measures this biorthogonality to quantify the approach to an EP [45,46]. The phase rigidity, r j for the jth eigenstate is defined as [22]…”

“…In a parallel development, non-Hermitian systems have been in the limelight in recent years due to their intriguing fundamental properties, with a potential for interesting applications [18][19][20][21][22]. Beginning with the pioneering ideas of Bender and co-workers [23,24], the interplay with topology has reinvigorated the field and has led to several seminal discoveries.…”

Hall conductance of a non-Hermitian Weyl semimetal

“…Recently, NH topological phases have drawn considerable attention of the research community ranging from photonics to condensed matter physics [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Dissipation in both classical and quantum mechanical systems is quite common, and this may lead to NH loss and gain.…”