In the last two decades, the ubiquitous effect of dissipation has proven to entail astonishing non-Hermitian features, rather than just being an inescapable nuisance. As an alternative route to non-Hermiticity, we tailor the anisotropy of a lattice, which constitutes an, up to now, barely exploited degree of freedom. In this case, the appearance of an interface dramatically alters the entire eigenmode spectrum, leading to the exponential localization of all modes at the interface, which goes beyond the expectations for Hermitian systems. This effect is dubbed "non-Hermitian skin effect". We experimentally demonstrate it by studying the propagation of light in a large scale photonic mesh lattice. For arbitrary excitations, we find that light is always transported to the interface, realizing a highly efficient funnel for light.
Non-Hermitian skin effect denotes the exponential localization of a large number of eigen-states in a non-Hermitian lattice under open boundary conditions. Such a non-Hermiticity-induced skin effect can offset the penetration depth of in-gap edge states, leading to counterintuitive delocalized edge modes, which have not been studied in a realistic photonic system such as photonic crystals. Here, we analytically reveal the non-Hermitian skin effect and the delocalized edge states in Maxwell's equations for non-Hermitian chiral photonic crystals with anomalous parity-time symmetry. Remarkably, w…
A hallmark of photonic transport in non-Hermitian lattices with asymmetric hopping is the robust unidirectional flow of light, which is responsible for important phenomena such as the non-Hermitian skin effect. Here we show that the same effect can be induced by stochastic fluctuations in lattices which maintain a symmetric hopping on average. We illustrate such a fluctuation-induced non-Hermitian transport by discussing stochastic funneling of light, in which light is pushed toward an interface by the stochastic-induced skin effect.
We explore absorbing open-boundary modes in non-Hermitian photonic systems. The modes have a continuum spectrum in the infinite system-size limit and can exhibit the non-Hermitian skin effect. In contrast to the conventional non-Hermitian skin modes under the fixed-end open-boundary condition, the modes concerned exhibit a strongly size-dependent spectrum that gradually converges to the non-Bloch-band dispersion. The modes correspond to the poles of the $S$ matrix, and are closely related to the lasing. We demonstrate these properties in a two-dimensional non-Hermitian photonic crystal with ga…
In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and symmetry breaking phase transitions in systems with open boundaries. Recently, it has been shown that a correct description requires to extend Bloch band theory into complex plane. A still open question is whether non-Hermitian skin effect and non-Bloch symmetry-breaking phase transitions can be probed by real-space wave dynamics far from edges, which is entirely governed by ordinary Bloch bands. …
We study the time evolution processes of non-Hermitian systems under the open boundary condition and confirm that the dynamical skin effect exists in non-Hermitian systems analytically, and unveil the mechanism of its formation, which is caused by both the non-Hermitian skin effect and the Hermitian wave packet spreading. Furthermore, we find that in contrast to the uniform speed motion in Hermitian situations, the Gaussian wave packet can be accelerated and amplified during its time evolution in non-Hermitian systems. This additional motion is found to be responsible for the dynamic skin effe…
A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero …
Non-Hermitian skin effect exhibits the collapse of the extended bulk modes into the extensive number of localized boundary states in open boundary conditions. Here we demonstrate the disorder-driven phase transition of the trivial non-Hermitian system to the higher-order non-Hermitian skin effect phase. In contrast to the clean systems, the disorder-induced boundary modes form an arc in the complex energy plane, which is the manifestation of the disorder-driven dynamical phase transition. At the phase transition, the localized corner modes and bulk modes characterized by trivial Hamiltonian co…
The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain non-Hermitian lattice Hamiltonians, particularly those with nonreciprocal couplings, can host an extensive number of eigenmodes condensed to the boundary, called skin modes. Although the NHSE has mostly been studied in the classical regime, we show that it can also manifest in quantum systems containing boson number nonconserving processes arising from uniform parametric driving. We study lattices of coupled nonlinear resonators that can function as reciprocal quantum amplifiers. A one-dimensional chain exhibiting NHSE can pe…
A unique feature of non-Hermitian (NH) systems is the NH skin effect, i.e. the edge localization of an extensive number of bulk-band eigenstates in a lattice with open or semi-infinite boundaries. Unlike extended Bloch waves in Hermitian systems, the skin modes are normalizable eigenstates of the Hamiltonian that originate from the intrinsic non-Hermitian point-gap topology of the Bloch band energy spectra. Here we unravel a fascinating property of NH skin modes, namely self-healing, i.e. the ability to self-reconstruct their shape after being scattered off by a space-time potential.
The non-Hermitian skin effect is a unique feature of non-Hermitian systems, in which an extensive number of boundary modes appear under the open boundary conditions. Here, we discover higher-order counterparts of the non-Hermitian skin effect that exhibit new boundary physics. In two-dimensional systems with the system size $L \times L$, while the conventional (first-order) skin effect accompanies $O\,( L^{2} )$ skin modes, the second-order skin effect accompanies $O\,( L )$ corner skin modes. This also contrasts with Hermitian second-order topological insulators, in which only $O\,( 1 )$ corn…
The topological spin-Hall effect causes different spins to propagate in opposite directions based on Hermitian physics. The non-Hermitian skin effect causes the localization of a large number of modes of a system at its edges. Here we propose a system based on exciton-polariton elliptical micropillars hosting both the effects. The polarization splitting of the elliptical micropillars gives rise to the topological spin-Hall effect in a one dimensional lattice. When a circularly polarized external incoherent laser is used to imbalance effective decay rates of the different spin polarizations, th…
In this paper, we study the conditions under which on-site dissipations can induce non-Hermitian skin modes in non-Hermitian systems. When the original Hermitian Hamiltonian has spinless time-reversal symmetry, it is impossible to have skin modes; on the other hand, if the Hermitian Hamiltonian has spinful time-reversal symmetry, skin modes can be induced by on-site dissipations under certain circumstance. As a concrete example, we employ the Rice-Mele model to illustrate our results. Furthermore, we predict that the skin modes can be detected by the chiral tunneling effect, that is, the tunne…
A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology. Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects---symmetry-protected skin effects. In particular, we discover the $\mathbb{Z}_{2}$ skin effect protected by time-reversal symmetry. On the basis of topological classification, we also discuss possible other skin effects in arbitrary dimensions. Our…
We study nonreciprocal nonlinear Schrödinger systems. As a prototype we analyze the Hatano-Nelson model together with a typical nonlinear term introduced and its generalization to two dimensions. We employ the quench dynamics, where a pulse is given to one site and its time evolution is analyzed. It is found that the skin state is always formed due to the nonreciprocal hopping and hence that the system is topological. However, the structure of the skin state is essentially modified by the nonlinear interaction because it favors a self-trapping. Four typically different states emerge as an inte…
In conventional Hermitian systems with the open boundary condition, Bloch's theorem is perturbatively broken down, which means although the crystal momentum is not a good quantum number, the eigenstates are the superposition of several extended Bloch waves. In this paper, we show that Bloch's theorem can be non-perturbatively broken down in some Hermitian Bosonic systems. The quasiparticles of the system are the superposition of localized non-Bloch waves, which are characterized by the complex momentum whose imaginary part determines the localization properties. Our work is a Hermitian general…
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the…
The non-Hermitian skin effect, i.e. eigenstate condensation at the edges in lattices with open boundaries, is an exotic manifestation of non-Hermitian systems. In Bloch theory, an effective non-Hermitian Hamiltonian is generally used to describe dissipation, which however is not norm-preserving and neglects quantum jumps. Here it is shown that in a self-consistent description of the dissipative dynamics in a one-band lattice, based on the stochastic Schrödinger equation or Lindblad master equation with a collective jump operator, the skin effect and its dynamical features are washed out. Never…
Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. The generalization of inversion symmetry is unique to non-Hermitian systems. We show that parities of the winding numbers can be determined from energy eigenvalues on the inversion-invariant momenta when generalized inversion symmetry is present. The simple expressions for the winding numbers allow us to easily analyze skin effects and exceptional point…
We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit non-trivial point gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be either made of lossy isotropic media which is reciprocal, or lossy magneto-optical media which is non-reciprocal. We discuss the effects of reciprocity on the properties of the point gap topology. We also show that such a non-trivial point gap topology leads to non-Hermitian skin effect when the photonic crystal is truncated. In contrast to most previous studies on point gap t…
Non-Hermitian skin effect (NHSE) is a unique phenomenon studied intensively in non-Hermitian systems during the past few years. In this work, we discuss the energy dependence of NHSE by introducing nonreciprocity beyond the nearest-neighboring hopping in the one-dimensional lattices. The direction of NHSE reverses as the eigenenergy of the system under open boundary conditions (OBCs) sweeps across some critical energies. To characterize such a phenomenon, we introduce the concept of non-Hermitian skin effect edges, which separate the eigenstates localized at opposite ends of the lattice in the…
We present a one-dimensional coupled ring resonator lattice exhibiting a variant of the non- Hermitian skin effect (NHSE) that we call the anomalous Floquet NHSE. Unlike existing approaches to achieving the NHSE by engineering gain and loss on different ring segments, our design uses fixed on-site gain or loss in each ring. The anomalous Floquet NHSE is marked by the existence of skin modes at every value of the Floquet quasienergy, allowing for broadband asymmetric transmission. Varying the gain/loss induces a non-Hermitian topological phase transition, reversing the localization direction of…
We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For systems with fourfold rotation symmetry, we show that in the presence of disclination lines with a total Frank angle which is an integer multiple of $2π$, there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines. This results in disclination-induced non-Hermitian skin effects. By doubling a non-Hermitian Hamiltonian to a Hermitian three-dimensional chiral topological insulator, we show that the disclination-induced skin m…
Non-Hermitian lattices under semi-infinite boundary conditions sustain an extensive number of exponentially-localized states, dubbed non-Hermitian skin modes. Such states can be predicted from the nontrivial topology of the energy spectrum under periodic boundary conditions via a bulk-edge correspondence. However, the selective excitation of the system in one among the infinitely-many topological skin edge states is challenging both from practical and conceptual viewpoints. In fact, in any realistic system with a finite lattice size most of skin edge states collapse and become metastable state…
Non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems, associated with a point gap on the complex energy plane, has attracted great theoretical and experimental interest. Much less is studied on the so-called second-order non-Hermitian skin effect, where the bulk does not support a point gap but localization at the corner still occurs. This work discovers a class of hybrid skin-topological modes as the second-order non-Hermitian skin effect without asymmetric couplings. Specifically, by only adding gain/loss to two-dimensional Chern insulators and so long as the gain/loss strength …
