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Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. Tropical…
The classification of point gap topology in all local non-Hermitian symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical…
Exotic singular objects, known as exceptional points, are ubiquitous in non-Hermitian physics. They might be spectral singularities in energy bands that produce anomalous effects and defectiveness. The quantum entanglement of a generic…
Exceptional points, also known as non-Hermitian degeneracies, have been observed in parity-time symmetric metasurfaces as the parity-time symmetry breaking point. However, the parity-time symmetry condition puts constraints on the…
Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce…
Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of…
Exceptional points are interesting physical phenomena in non-Hermitian physics at which the eigenvalues are degenerate and the eigenvectors coalesce. In this paper, we find that the universal feature of arbitrary non-Hermitian two level…
Line waves are recently discovered wave entities that are localized along two directions, and therefore can be viewed as the one-dimensional counterpart of surface waves. These waves can be supported at discontinuities of the surface…
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the…
The role of nonlinearity on topology has been investigated extensively in Hermitian systems, while nonlinearity has only been used as a tuning knob in a PT symmetric non-Hermitian system. Here, in our work, we show that nonlinearity plays a…
The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates…
Band topology has been studied as a design principle of realizing robust boundary modes. Here, by exploring non-Hermitian topology, we propose a three-dimensional topological laser that amplifies surface modes. The topological surface laser…
Non-Hermiticity enriches the contents of topological classification of matter including exceptional points, bulk-edge correspondence and skin effect. Gain and loss can be described by imaginary diagonal elements in Hamiltonians and the…
Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop classification of second-order point-gap topological phases protected by reflection…
The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…
We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter…
Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been…
The complex eigenenergies and non-orthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional…