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Non-Hermiticity naturally arises in many physical systems that exchange energy with their environment. The presence of non-Hermiticity leads to many novel topological physics phenomena and device applications. In the non-Hermitian energy…
The non-Hermitian skin effect (NHSE), an anomalous localization behavior of the bulk states, is an inherently non-Hermitian phenomenon, which can not find a counterpart in Hermitian systems. However, the fragility of NHSE has been revealed…
We establish a novel mechanism for topological transitions in non-Hermitian systems that are controlled by the system size. Based on a new paradigm known as exceptional-bound (EB) band engineering, its mechanism hinges on the unique…
In recent years, non-Hermitian phases in classical and quantum systems have garnered significant attention. In particular, their intriguing band geometry offers a platform for exploring unique topological states and unconventional quantum…
Topology plays an important role in non-hermitian systems. How to characterize a non-hermitian topological system under open-boundary conditions(OBCs) is a challenging problem. A one-dimensional(1D) topological invariant defined on a…
Flat band and non-Hermitian are both significant conceptions in modern physics. In this study, we delve into the behaviours of flat bands in non-Hermitian systems, focusing on the interplay between the flat band and its dispersive…
The non-Bloch topology leads to the emergence of various counter-intuitive phenomena in non-Hermitian systems under the open boundary condition (OBC), which can not find a counterpart in Hermitian systems. However, in the non-Hermitian…
In this work, we propose a theory on the two-dimensional non-Hermitian skin effect by resolving two representative minimal models. Specifically, we show that for any given non-Hermitian Hamiltonian, (i) the corresponding region covered by…
Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in…
Dispersionless bands -- flatbands -- have been actively studied thanks to their interesting properties and sensitivity to perturbations, which makes them natural candidates for exotic states. In parallel non-Hermitian systems have attracted…
Flat bands, in which kinetic energy is quenched and quantum states become macroscopically degenerate, host a rich variety of correlated and topological phases, from unconventional superconductors to fractional Chern insulators. In Hermitian…
A hallmark of topological band theory in periodic media is that bulk properties are not affected by boundary conditions. Remarkably, in certain non-Hermitian lattices the bulk properties are largely affected by boundaries, leading to such…
Non-Hermitian Chern insulators differ from their Hermitian cousins in one key aspect: their edge spectra are incredibly rich and confounding. For example, even in the simple case where the bulk spectrum consists of two bands with Chern…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is…
The spectral properties of a non-Hermitian quasi-1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non-Hermitian diamond chain that presents a zero-energy flat band. The flat band…
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…
In the presence of non-Hermitian skin effect, non-Hermitian lattices generally have complex-valued eigenenergies under periodic boundary condition, but they can have non-Bloch PT symmetry and therefore completely real eigenenergies under…
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper,…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…