Observation of the geometry-dependent skin effect and dynamical degeneracy splitting

Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra

The non-Hermitian skin effect is an iconic phenomenon characterized by the aggregation of eigenstates near the system boundaries in non-Hermitian systems. While extensively studied in one dimension, understanding the skin effect and extending the non-Bloch band theory to higher dimensions encounter a formidable challenge, primarily due to infinite lattice geometries or open boundary conditions. This work adopts a point-gap perspective and unveils that non-Hermitian skin effect in all spatial dimensions originates from point gaps. We introduce the concept of uniform spectra and reveal that regardless of lattice geometry, their energy spectra are universally given by the uniform spectra, even though their manifestations of skin modes may differ. Building on the uniform spectra, we demonstrate how to account for the skin effect with generic lattice cuts and establish the connections of skin modes across different geometric shapes via momentum-basis transformations. Our findings highlight the pivotal roles point gaps play, offering a unified understanding of the topological origin of non-Hermitian skin effect in all dimensions.

Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas

The concept of non-Hermiticity has expanded the understanding of band topology, leading to the emergence of counter-intuitive phenomena. An example is the non-Hermitian skin effect (NHSE)1-7, which involves the concentration of eigenstates at the boundary. However, despite the potential insights that can be gained from high-dimensional non-Hermitian quantum systems in areas such as curved space8-10, high-order topological phases11,12 and black holes13,14, the realization of this effect in high dimensions remains unexplored. Here we create a two-dimensional (2D) non-Hermitian topological band for ultracold fermions in spin-orbit-coupled optical lattices with tunable dissipation, which exhibits the NHSE. We first experimentally demonstrate pronounced nonzero spectral winding numbers in the complex energy plane with nonzero dissipation, which establishes the existence of 2D skin effect. Furthermore, we observe the real-space dynamical signature of NHSE in real space by monitoring the centre of mass motion of atoms. Finally, we also demonstrate that a pair of exceptional points are created in the momentum space, connected by an open-ended bulk Fermi arc, in contrast to closed loops found in Hermitian systems. The associated exceptional points emerge and shift with increasing dissipation, leading to the formation of the Fermi arc. Our work sets the stage for further investigation into simulating non-Hermitian physics in high dimensions and paves the way for understanding the interplay of quantum statistics with NHSE.

Universal Spectral Moment Theorem and Its Applications in Non-Hermitian Systems

The high sensitivity of the spectrum and wave functions to boundary conditions, termed the non-Hermitian skin effect, represents a fundamental aspect of non-Hermitian systems. While it endows non-Hermitian systems with unprecedented physical properties, it presents notable obstacles in grasping universal properties that are robust against microscopic details and boundary conditions. In this Letter, we introduce a pivotal theorem: in the thermodynamic limit, for any non-Hermitian systems with finite-range interactions, all spectral moments are invariant quantities, independent of boundary conditions, posing strong constraints on the spectrum. Utilizing this invariance, we propose a new criterion for bulk dynamical phases based on experimentally observable features and applicable to any dimensions and any boundary conditions. Based on this criterion, we define the bulk dispersive-to-proliferative phase transition, which is distinct from the real-to-complex spectral transition and contrasts with the traditional expectation that the existence of eigenvalues above the real axis implies proliferative behavior. We verify these findings in 1D and 2D lattice models.

Non-Hermitian Skin Effect in Many-Body Thermophotonics

The tight-binding model, foundational in depicting electronic behaviors in solid-state physics, has recently contributed to the understanding of non-Hermitian skin effects in optics, acoustics, and mechanics. However, tight-binding model is primarily built upon scalar nearest couplings, which in turn does not fit to describe the vectorial long-range interactions inherently in thermophotonics. Here, we report a strategy involving many-body radiative interactions in a two-dimensional thermophotonic lattice, and further reveal two types of orthogonal non-Hermitian skin modes in a reciprocal system. For in-plane modes, a pronounced geometry-dependent skin effect manifests at the edges, while for out-of-plane modes, skin effects induced by many-body interactions emerge at the corners instead. Our work provides a pioneering approach for understanding many-body-driven skin effect and unveils a mechanism for unexpected manipulation in thermophotonics.

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.

Construction and Observation of Flexibly Controllable High-Dimensional Non-Hermitian Skin Effects

Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in non-Hermitian physics. It is established that 1D NHSE originates from the nontrivial spectral winding topology. However, the topological origin behind the higher-dimensional NHSE remains unclear, which poses a substantial challenge in constructing and manipulating high-dimensional NHSEs. Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is proposed, through assembling multiple independent 1D NHSEs. Not only the elusive high-dimensional NHSEs can be effectively predicted from the well-defined 1D spectral winding topologies, but also the high-dimensional generalized Brillouin zones can be directly synthesized from the 1D counterparts. As examples, two 2D nonreciprocal acoustic metamaterials are experimentally implemented to demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological effects, where the sound fields can be frequency-selectively localized at any desired corners and boundaries. These results offer a practicable strategy for engineering high-dimensional NHSEs, which can boost advanced applications such as selective filters and directional amplifiers.

Photonic Floquet Skin-Topological Effect

Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.

Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice

Recent studies of non-Hermitian periodic lattices unveiled the non-Hermitian skin effect (NHSE), in which the bulk modes under the periodic boundary conditions (PBC) become skin modes under open boundary conditions. The NHSE is a topological effect owing to the nontrivial spectral winding, and such spectral behaviors appear naturally in nonreciprocal systems. Hence prevailing approaches rely on nonreciprocity to achieve the NHSE. Here, we report the experimental realization of the geometry-dependent skin effect in a two-dimensional reciprocal system, in which the skin effect occurs only at boundaries whose macroscopic symmetry mismatches with the lattice symmetry. The role of spectral reciprocity and symmetry is revealed by connecting reflective channels at given boundaries with the spectral topology of the PBC spectrum. Our work highlights the vital role of reciprocity, symmetry, and macroscopic geometry on the NHSE in dimensionality larger than one and opens new routes for wave structuring using non-Hermitian effects.