Observation of higher-order non-Hermitian skin effect

Abstract

Beyond the scope of Hermitian physics, non-Hermiticity fundamentally changes the topological band theory, leading to interesting phenomena, e.g., non-Hermitian skin effect, as confirmed in one-dimensional systems. However, in higher dimensions, these effects remain elusive. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher-order topological insulators. We find that non-Hermiticity drives wave localizations toward opposite edges upon different spin polarizations. More interestingly, for finite systems with both edges and corners, the higher-order non-Hermitian skin effect leads to wave localizations toward two opposite corners for all the bulk, edge and corner states in a spin-dependent manner. We further show that such a skin effect enables rich wave manipulation by configuring the non-Hermiticity. Our study reveals the intriguing interplay between higher-order topology and non-Hermiticity, which is further enriched by the pseudospin degree of freedom, unveiling a horizon in the study of non-Hermitian physics.

Progress in Topological Mechanics

“…Recently, topological phases of non-Hermitian systems have attracted extensive research, whose exceptional points and complex-valued spectra can produce many notable properties, including the non-Hermitian skin effects [169,170], bulk Fermi arcs [171] and Weyl exceptional rings [172], to name a few. At present, HOTIs of non-Hermitian systems have been realized in sonic crystals [173,174]. As such, we can study how to connect the higher-order topological physics with non-Hermitian systems in mechanics by inducing friction.…”

Amplification of quantum signals by the non-Hermitian skin effect

“…Unlike a related topological traveling wave amplifier proposed by Peano et al [60], the modes in our system are dynamically stable and do not require additional damping to provide stability. The phenomenon also generalizes to a 2D lattice whose BdG Hamiltonian exhibits a corner NHSE [28,34,36], allowing for directional amplification between different corners of a 2D sample. Fig.…”

“…In higher dimensions, the relationship between bandstructures and the NHSE remains under investigation [28][29][30]. The NHSE has been realized in photonic systems [31][32][33], as well as in classical electrical [34,35], acoustic [36,37], and mechanical [38] metamaterials, though the application possibilities for this intriguing phenomenon are still unclear. Both the original theoretical formulation of the NHSE and the above experimental demonstrations have been based on single-particle models, applicable to non-interacting quantum particles or linear classical waves.…”

“…1(a), with reciprocal inter-chain hoppings t 3 and t 4 . Under the BdG transformation, this maps to a singleparticle 2D lattice that exhibits a corner NHSE, with all eigenstates localized at certain corners [28,34,36] (see Supplemental Materials [74]). In Fig.…”

Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect

“…For instance, PT symmetry breaking involves two modes of a non-Hermitian system coalescing and taking on iden-tical frequencies and different gain/loss [19]; coupledcavity lasers can use this to suppress half the modes that might lase [1][2][3], and for other forms of gain management [17]. Other exotic aspects of non-Hermitian wave dynamics occur in periodic lattices [20][21][22][23][24][25][26][27][28], like the "non-Hermitian skin effect" (NHSE), whereby the bulk modes of a non-Hermitian lattice collapse into boundary modes [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Longhi [11] has proposed a laser array based on a Su-Schrieffer-Heeger (SSH) lattice with asymmetric couplings that induce the NHSE.…”