non-Hermitian Skin Effect Research Articles

Scale-tailored localization and its observation in non-Hermitian electrical circuits

Anderson localization and non-Hermitian skin effect are two paradigmatic wave localization phenomena, resulting from wave interference and the intrinsic non-Hermitian point gap, respectively. In this study, we unveil a novel localization phenomenon associated with long-range asymmetric coupling, termed scale-tailored localization, where the number of induced localized modes and their localization lengths scale exclusively with the coupling range. We show that the long-range coupling fundamentally reshapes the energy spectra and eigenstates by creating multiple connected paths on the lattice. Furthermore, we present experimental observations of scale-tailored localization in non-Hermitian electrical circuits utilizing adjustable voltage followers and switches. The circuit admittance spectra possess separate point-shaped and loop-shaped components in the complex energy plane, corresponding respectively to skin modes and scale-tailored localized states. Our findings not only expand and deepen the understanding of peculiar effects induced by non-Hermiticity but also offer a feasible experimental platform for exploring and controlling wave localizations.

Evolution of topological extended state in multidimensional non-Hermitian topolectrical circuits

The extended state pertains to the dispersion of the system's eigenfunctions across the whole lattice. Recent studies have shown that the non-Hermitian skin effect (NHSE) can reshape the wavefunction of topological modes. The localized states of topological modes within the bandgap gradually delocalized into extended states through the manipulation of NHSE. Here, we clarify the NHSE direction using the Bloch spectral winding numbers and reestablish the bulk-boundary correspondence through the non-Bloch winding numbers in the generalized Brillouin zone. We elucidate the formation of extended state by employing the localized decay length. Then, we have designed non-Hermitian topological circuits for experimental verification based on the voltage follower. The corner states, edge states, and extended states in 1D, 2D, and 3D circuits were observed through the measurement of node voltage. Our work can achieve the sustainable extended mode and provides significant cases for the analysis of topolectrical circuits.

Tunable non-Hermitian skin effect via gain and loss

Tunable non-Hermitian skin effect via gain and loss

Understanding of topological mode and skin mode morphing in 1D and 2D non-Hermitian resonance-based meta-lattices

Recent advances have demonstrated that the non-Hermitian skin effect (NHSE), induced by system non-Hermiticity, can manipulate the localization of in-gap topological edge modes (TEMs) within mechanical topological insulators. This study introduces a straightforward analytical framework to elucidate the competition between NHSE and TEM localization in a classical mechanical meta-lattice, highlighting its impact on the dynamic behavior of TEMs within separate Bragg scattering band gaps (BSBGs). We propose a 1D non-Hermitian meta-lattice featuring a locally resonant system with active feedback control, characterized by a real-valued transfer function. This local resonance creates two separate BSBGs, each hosting a TEM defined by non-Hermitian bulk-edge correspondence. Our theoretical and numerical analyses reveal that the NHSE, with its asymmetric localization within the two BSBGs, can shift the localization of TEMs in distinct ways. This leads to an asymmetric phase transition, wherein one TEM can be delocalized and relocalized by tuning the transfer function, while the other maintains its initial localization. Moreover, we extend the mechanism of 1D asymmetric TEM delocalization to the non-Hermitian morphing of TEMs, showcasing notable examples such as temporal and spatial topological wave pumping with space- and time-dependent transfer functions in 1D time-varying and 2D stacked meta-lattices. This research bridges a gap between non-Hermitian mechanical constructs and their potential applications in classical mechanics, reinterpreting known topological wave control in 1D and uncovering new mechanisms in 2D.

Tracking intrinsic non-Hermitian skin effects in lossy lattices

Tracking intrinsic non-Hermitian skin effects in lossy lattices

Non-Bloch band theory for time-modulated discrete mechanical systems

This study establishes a non-Bloch band theory for time-modulated discrete mechanical systems. We consider simple mass–spring chains whose stiffness is periodically modulated in time. Using the temporal Floquet theory, the system is characterized by linear algebraic equations in terms of Fourier coefficients. This allows us to employ a standard linear eigenvalue analysis. Unlike non-modulated linear systems, the time modulation makes the coefficient matrix non-Hermitian, which gives rise to, for example, parametric resonance, non-reciprocal wave transmission, and non-Hermitian skin effects. In particular, we study finite-length chains consisting of spatially periodic mass–spring units and show that the standard Bloch band theory is not valid for estimating their eigenvalue distribution. To remedy this, we propose a non-Bloch band theory based on a generalized Brillouin zone. This novel approach, the combination of the temporal Floquet theory for time-modulated systems and generalized Brillouin zone, enables the prediction of eigenvalue distribution under open boundary conditions and also quantitative characterization of non-Hermitian skin modes. The proposed theory is verified by some numerical experiments.

General Criterion for Non-Hermitian Skin Effects and Application: Fock Space Skin Effects in Many-Body Systems.

Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well established for single-particle systems, but their proper characterization for general systems is elusive. Here, we propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator. The applicable systems include many-body systems and network systems. A system meeting the criterion exhibits enhanced non-normality of the evolution operator, accompanied by exceptional characteristics intrinsic to non-Hermitian systems. Applying the criterion, we discover a new type of non-Hermitian skin effect in many-body systems, which we dub the Fock space skin effect. We also discuss the Fock space skin effect-induced slow dynamics, which gives an experimental signal for the Fock space skin effect.

Many-Body Non-Hermitian Skin Effect for Multipoles.

In this Letter, we investigate the fate of the non-Hermitian skin effect in one-dimensional systems that conserve the dipole moment and higher moments of an associated global U(1) charge. Motivated by field theoretical arguments and lattice model calculations, we demonstrate that the key feature of the non-Hermitian skin effect for m-pole conserving systems is the generation of an (m+1)th multipole moment. For example, in contrast to the conventional skin effect where charges are anomalously localized at one boundary, the dipole-conserving skin effect results in charges localized at both boundaries, in a configuration that generates an extremal quadrupole moment. In addition, we explore the dynamical consequences of the m-pole skin effect, focusing on charge and entanglement propagation. Both numerically and analytically, we provide evidence that long-time steady states have Fock-space localization and an area-law scaling of entanglement entropy, which serve as quantum indicators of the skin effect.

Dynamic protected states in the non-Hermitian system

The non-Hermitian skin effect and nonreciprocal behavior are sensitive to the boundary conditions, which are unique features of non-Hermitian systems. In such systems, eigenenergies can become complex, and all eigenstates tend to localize at the boundary, a phenomenon that contrasts with Hermitian topologies. In this work, we theoretically study the dynamic behavior of the propagation of Gaussian wavepackets inside a non-Hermitian lattice and analyze the self-acceleration process of bulk state or Gaussian wavepackets toward the system’s boundary. The initial wavepackets will not only propagate toward the side where the eigenstates are localized, but also their momentum will approach to a specific value. This value corresponds to the maximum imaginary components of the energy dispersion. In addition, if the wavepackets in the momentum space cover this specific momentum, they will eventually exhibit exponentially increasing amplitudes with time evolution, maintaining the dynamic protected condition for an extended period of time until they approach the boundary. We also take two widely used toy models as examples in one and two dimensions to verify the correspondence of the non-Hermitian skin effect and the dynamic protected state.

Spin-Dependent Localization of Helical Edge States in a Non-Hermitian Phononic Crystal.

As a distinctive feature unique to non-Hermitian systems, non-Hermitian skin effect displays fruitful exotic phenomena in one or higher dimensions, especially when conventional topological phases are involved. Among them, hybrid skin-topological effect is theoretically proposed recently, which exhibits anomalous localization of topological boundary states at lower-dimensional boundaries accompanied by extended bulk states. Here, we experimentally realize the hybrid skin-topological effect in a non-Hermitian phononic crystal. The phononic crystal, before tuning to be non-Hermitian, is an ideal acoustic realization of the Kane-Mele model, which hosts gapless helical edge states at the boundaries. By introducing a staggered distribution of loss, the spin-dependent edge modes pile up to opposite corners, leading to a direct observation of the spin-dependent hybrid skin-topological effect. Our Letter highlights the interplay between topology and non-Hermiticity and opens new routes to non-Hermitian wave manipulations.

Arbitrarily Configurable Nonlinear Topological Modes.

Topological modes (TMs) are typically localized at boundaries, interfaces and dislocations, and exponentially decay into the bulk of a large enough lattice. Recently, the non-Hermitian skin effect has been leveraged to delocalize the wave functions of TMs from the boundary and thus to increase the capacity of TMs dramatically. Here, we explore the capability of nonlinearity in designing and configuring the wave functions of TMs. With growing intensity, wave functions of these in-gap nonlinear TMs undergo an initial deviation from exponential decay, gradually merge into arbitrarily designable plateaus, then encompass the entire nonlinear domain, and eventually concentrate at the nonlinear boundary. Intriguingly, such extended nonlinear TMs are still robust against defects and disorders, and stable in dynamics under external excitation. Advancing the conceptual understanding of the nonlinear TMs, our results open new avenues for increasing the capacity of TMs and developing compact and configurable topological devices.

Experimental probe of point gap topology from non-Hermitian Fermi-arcs

The gap in spectra of a physical system is fundamental in physics, while gap topology further restricts possible occurrent gaps of topological boundary states. The emergence of non-Hermiticity unveils a unique gap type known as the point gap, which forecasts the wavefunction localization, known as the non-Hermitian skin effect. Therefore, experimentally identifying the point gap in the complex frequency plane through a real operating frequency can become a tool for the systematic investigation of skin effects. Here, we utilize a Weyl phononic crystal to demonstrate that the point gap constituted by bulk and Fermi-arc surface states can be observed experimentally by a real-space field mapping technique. The identified point gaps forecast various skin effects and their evolutions. We further experimentally demonstrate the hinge skin effect in a parallelogram structure. Our work provides a feasible recipe to explore point gap topology experimentally in a variety of systems and certainly stimulates the research on skin effects in three-dimensional systems.

Non‐Hermitian Skin Effect in Non‐Hermitian Optical Systems

AbstractThe development of non‐Hermitian (NH) physics in nonconservative systems has led to various interesting wave phenomena, including the emergence of the non‐Hermitian skin effect (NHSE). NHSE is a topological effect caused by the nontrivial winding number of the energy spectrum, which results in many bulk eigenmodes localized on low‐dimensional boundaries under open boundary conditions. Although this phenomenon is striking, the flexible and dynamic tuning of NHSE has not been reviewed in optics systems. As an ideal NH platform, an optical system can introduce artificially constructed gains and losses and flexibly design optical structures to control the transmission and regulation of light. This exploration based on NH optical systems deepens the understanding of NHSE and facilitates technological breakthroughs in high‐energy directional localized optics applications. In this review, the focus is on the latest progress and applications of NHSE in NH optical systems, including the basic theory and local property modulation methods. Finally, possible future research directions for NHSE based on NH optical systems are discussed.

Observation of Topological Transition in Floquet Non-Hermitian Skin Effects in Silicon Photonics.

Non-Hermitian physics has greatly enriched our understanding of nonequilibrium phenomena and uncovered novel effects such as the non-Hermitian skin effect (NHSE) that has profoundly revolutionized the field. NHSE has been predicted in systems with nonreciprocal couplings which, however, are challenging to realize in experiments. Without nonreciprocal couplings, the NHSE can also emerge in systems with coexisting gauge fields and loss or gain (e.g., in Floquet non-Hermitian systems). However, such Floquet NHSE remains largely unexplored in experiments. Here, we realize the Floquet NHSEs in periodically modulated optical waveguides integrated on a silicon photonic platform. By engineering the artificial gauge fields induced by the periodical modulation, we observe various Floquet NHSE phases and unveil their rich topological transitions. Remarkably, we discover the transitions between the unipolar NHSE phases and an unconventional bipolar NHSE phase, which is accompanied by the directional reversal of the NHSEs. The underlying physics is revealed by the band winding in complex quasienergy space which undergoes a topology change from isolated loops with the same winding to linked loops with opposite windings. Our work unfolds a new route toward Floquet NHSEs originating from the interplay between gauge fields and dissipation effects, and thus offers fundamentally new ways for steering light and other waves.

Non-Hermitian Mott Skin Effect.

We propose a novel type of skin effects in non-Hermitian quantum many-body systems that we dub a "non-Hermitian Mott skin effect." This phenomenon is induced by the interplay between strong correlations and the non-Hermitian point-gap topology. The Mott skin effect induces extreme sensitivity to the boundary conditions only in the spin degree of freedom (i.e., the charge distribution is not sensitive to boundary conditions), which is in sharp contrast to the ordinary non-Hermitian skin effect in noninteracting systems. Concretely, we elucidate that a bosonic non-Hermitian chain exhibits the Mott skin effect in the strongly correlated regime by closely examining an effective Hamiltonian. The emergence of the Mott skin effect is also supported by numerical diagonalization of the bosonic chain. The difference between the ordinary non-Hermitian skin effect and the Mott skin effect is also reflected in the time evolution of physical quantities; under the time evolution spin accumulation is observed while the charge distribution remains spatially uniform.

Observation of Non-Hermitian Edge Burst in Quantum Dynamics.

The non-Hermitian skin effect, by which the eigenstates of the Hamiltonian are predominantly localized at the boundary, has revealed a strong sensitivity of non-Hermitian systems to the boundary condition. Here we experimentally observe a striking boundary-induced dynamical phenomenon known as the non-Hermitian edge burst, which is characterized by a sharp boundary accumulation of loss in non-Hermitian time evolutions. In contrast to the eigenstate localization, the edge burst represents a generic non-Hermitian dynamical phenomenon that occurs in real time. Our experiment, based on photonic quantum walks, not only confirms the prediction of the phenomenon, but also unveils its complete space-time dynamics. Our observation of edge burst paves the way for studying the rich real-time dynamics in non-Hermitian topological systems.

Stability of the Non-Hermitian Skin Effect in One Dimension

Stability of the Non-Hermitian Skin Effect in One Dimension

Nonreciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs

Nonreciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs

Observation of dynamic non-Hermitian skin effects

Non-Hermitian physics has emerged as a new paradigm that profoundly changes our understanding of non-equilibrium systems, introducing novel concepts such as exceptional points, spectral topology, and non-Hermitian skin effects (NHSEs). Most existing studies focus on non-Hermitian eigenstates, whereas dynamic properties have been discussed only recently, and the dynamic NHSEs are not yet confirmed in experiments. Here, we report the experimental observation of non-Hermitian skin dynamics using tunable one-dimensional nonreciprocal double-chain mechanical systems with glide-time symmetry. Remarkably, dynamic NHSEs are observed with various behaviors in different dynamic phases, which can be understood via the generalized Brillouin zone and the related concepts. Moreover, the observed dynamic NHSEs, amplifications, bulk unidirectional wave propagation, and boundary wave trapping provide promising ways to manipulate waves in a controllable and robust way. Our findings open a new pathway toward non-Hermitian dynamics, which will fertilize the study of non-equilibrium phases of matter.

Controlling acoustic non-Hermitian skin effect via synthetic magnetic fields

Non-Hermitian skin effect (NHSE) is an intrinsic non-Hermitian phenomenon where an extensive number of eigenmodes, called skin modes, are localized at the boundary of a system. Recent theories have suggested that the NHSE can be well-tuned by external fields, opening a route to manipulating wave localization. Here, we experimentally demonstrate the diverse interactions between NHSE and synthetic magnetic fields (SMFs) in coupled acoustic ring resonator lattices. We observe that the NHSE and SMFs can, via different physical mechanisms, compete or synergize, resulting in either the suppression or the creation of NHSE. With the aid of the complex frequency excitation technique, we experimentally observe that SMFs can suppress the NHSE by introducing Landau quantization, causing localization to move toward the bulk. In contrast, we show that the presence of SMF generates topological edge modes in the lattice, which then become corner skin modes by the second-order NHSE. Our results evidence the rich physics and diverse consequences that arise from the interplay of magnetic fields and NHSE, paving the way for actively controlling wave localization.