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Register a new userExact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
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Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary condition. To unveil the origin of boundary sensitivity, we present exact solutions for one-dimensional non-Hermitian models with generalized boundary conditions and study rigorously the interplay effect of lattice size and boundary terms. Besides the open boundary condition, we identify the existence of non-Hermitian skin effect when one of the boundary hopping terms vanishes. Apart from this critical line on the boundary parameter space, we find that the skin effect is fragile under any tiny boundary perturbation in the thermodynamic limit, although it can survive in a finite size system. Moreover, we demonstrate that the non-Hermitian Su-Schreieffer-Heeger model exhibits a new phase diagram in the boundary critical line, which is different from either open or periodical boundary case.
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Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin effect with nonlinear effects can give rise to a host of novel phenomenas, which may be used for nonlinear structure designs. Here we study nonlinear non-Hermitian skin effect and explore nonlocal and substantial effects of edges on stationary nonlinear solutions. We show that fractal and continuum bands arise in a long lattice governed by a nonreciprocal discrete nonlinear Schrodinger equation. We show that stationary solutions are localized at the edge in the continuum band. We consider a non-Hermitian Ablowitz-Ladik model and show that nonlinear exceptional point disappears if the lattice is infinitely long.
Far from being limited to a trivial generalization of their Hermitian counterparts, non-Hermitian topological phases have gained widespread interest due to their unique properties. One of the most striking non-Hermitian phenomena is the skin effect, i.e., the localization of a macroscopic fraction of bulk eigenstates at a boundary, which underlies the breakdown of the bulk-edge correspondence. Here we investigate the emergence of the skin effect in magnetic insulating systems by developing a phenomenological approach to describing magnetic dissipation within a lattice model. Focusing on a spin-orbit-coupled van der Waals (vdW) ferromagnet with spin-nonconserving magnon-phonon interactions, we find that the magnetic skin effect emerges in an appropriate temperature regime. Our results suggest that the interference between Dzyaloshinskii-Moriya interaction (DMI) and nonlocal magnetic dissipation plays a key role in the accumulation of bulk states at the boundaries.
Hermitian theories play a major role in understanding the physics of most phenomena. It has been found only in the past decade that non-Hermiticity enables unprecedented effects such as exceptional points, spectral singularities and bulk Fermi arcs. Recent studies further show that non-Hermiticity can fundamentally change the topological band theory, leading to the non-Hermitian band topology and non-Hermitian skin effect, as confirmed in one-dimensional (1D) systems. However, in higher dimensions, these non-Hermitian effects remain unexplored in experiments. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional (2D) acoustic metamaterials. Using a lattice of coupled whisper-gallery acoustic resonators, we realize a spinful 2D higher-order topological insulator (HOTI) where the spin-up and spin-down states are emulated by the anti-clockwise and clockwise modes, respectively. We find that the non-Hermiticity drives wave localizations toward opposite edge boundaries depending on the spin polarizations. More interestingly, for finite systems with both edge and corner boundaries, the higher-order non-Hermitian skin effect leads to wave localizations toward two corner boundaries for the bulk, edge and corner states in a spin-dependent manner. We further show that such a non-Hermitian skin effect enables rich wave manipulation through the loss configuration in each unit-cell. The reported spin-dependent, higher-order non-Hermitian skin effect reveals the interplay between higher-order topology and non-Hermiticity, which is further enriched by the spin degrees of freedom. This unveils a new horizon in the study of non-Hermitian physics and the design of non-Hermitian metamaterials.
We demonstrate that crystal defects can act as a probe of intrinsic non-Hermitian topology. In particular, in point-gapped systems with periodic boundary conditions, a pair of dislocations may induce a non-Hermitian skin effect, where an extensive number of Hamiltonian eigenstates localize at only one of the two dislocations. An example of such a phase are two-dimensional systems exhibiting weak non-Hermitian topology, which are adiabatically related to a decoupled stack of one-dimensional Hatano-Nelson chains. Moreover, we show that strong two-dimensional point gap topology may also result in a dislocation response, even when there is no skin effect present with open boundary conditions. For both cases, we directly relate their bulk topology to a stable dislocation skin effect. Finally, and in stark contrast to the Hermitian case, we find that gapless non-Hermitian systems hosting bulk exceptional points also give rise to a well-localized dislocation response.
The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the relativistic wavefunction. We show that this expansion induces a non-local effect on the current density throughout the cavity. Our results indicate that a relativistic treatment still contains apparently spurious effects traditionally associated with the unbounded velocities inherent to non-relativistic solutions obtained from the Schroedinger equation. Possible reasons for this behaviour are discussed.
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