Abstract This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly on its rich interplay with topology. The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence, the synergy and hybridization of NHSE and band topology in higher dimensions, as well as, the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology. Following which, emerging topics are introduced such as non-Hermitian criticality, dynamical NHSE phenomena, and the manifestation of NHSE beyond the traditional linear non-interacting crystal lattices, particularly its interplay with quantum many-body interactions. Finally, we survey the recent demonstrations and experimental proposals of NHSE. 

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Topological non-Hermitian skin effect

Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems

Non-Hermitian degeneracies are classified as defective and nondefective exceptional points~(EP). While in defective EPs, both eigenvalues and eigenenergies coalesce, nondefective EPs are characterized merely by the occurrence of degeneracies in their eigenvalues. It is also known that all degeneracies are either symmetry-protected or accidental. In this paper, I prove that anti-unitary symmetries protect all nondefective twofold EPs. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries are composite of various symmetry operations such as discrete or spatial point-group symmetries and Wick's rotation in the non-Hermitian parameter space. Introducing these composite symmetries, I present the protection of nondefective EPs in various parameter regimes of my model. This work paves the way to stabilizing nondefective EPs and offers a new perspective on understanding non-Hermitian band crossings. 

Absorption-lasing effects and exceptional points in parity-time symmetric non-Hermitian metaplates

In this work, we investigate non-Hermitian acoustic waveguides designed with periodically applied feedback eﬀorts using electrodynamic actuators. One-dimensional spectral (inﬁnite-dimensional) and ﬁnite element (ﬁnite-dimensional) models for plane acoustic waves in ducts are used. It is shown that dispersion diagrams of this family of metamaterials exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or ampliﬁcation along opposite directions for all pass bands. The eﬀects of diﬀerent feedback laws are investigated. Furthermore, the non-Hermitian skin eﬀect manifesting as topological modes localized at the boundaries of ﬁnite domains is investigated and successfully predicted by the topology of the reciprocal space. This work extends previous numerical results obtained for a piezoelectric rod system and contributes to recent eﬀorts in designing active metamaterials with novel properties associated with the physics of non-Hermitian systems, which may ﬁnd fruitful technological applications related to noise control, wave localization, and multiplexing.

Non-Hermitian acoustic waveguides with periodic electroacoustic feedback

Non-Hermitian systems have gained a great deal of interest in various wave problems due their ability of exhibiting unprecedented phenomena such as invisibility, cloaking, enhanced sensing, or the skin effect. The latter manifests itself by the localization of all bulk modes in a specific frequency range at a given boundary, with an unconventional bulk-boundary correspondence. In this work, we propose to realize the skin effect for flexural waves in a non-Hermitian piezoelectric phononic beam with feedback control between a sensor and an actuator in each unit cell. By implementing a non-Hermitian parameter, effective gain and loss can be achieved in the phononic beam characterized by complex eigen frequencies, and non-reciprocal pass bands are obtained. We highlight that the split point separating the gain and loss areas can occur not only at the edges of the Brillouin zones but also inside the same Brillouin zone. We further analyze the influence of the geometric and non-Hermitian parameters on the complex dispersions and the split point. The topology of the complex bands is characterized by the winding number, which supports the skin effect together with the non-reciprocity. The localization degree of the skin mode manifested by the enhanced beam's vibration energy at one boundary is related to the strength of the non-reciprocity, and the skin mode can be always excited regardless of the source position. Our results provide a potential platform to introduce non-Hermiticity into phononic or metamaterial systems with novel functions for elastic waves such as topological insulators, vibration attenuation or amplification, and energy harvesting.

Non-Hermitian skin effect in a phononic beam based on piezoelectric feedback control


 Hot ionized gas is important in the baryon cycle of galaxies and contributes the majority of their “missing baryons”. Until now, most semi-analytic models of galaxy formation have paid little attention to hot gaseous haloes and their X-ray emission. In this paper, we adopt the one-dimensional model from Sharma et al. instead of the isothermal sphere to describe the radial distribution of hot gas in the L-Galaxies semi-analytic model. The hot gas halo can be divided into two parts according to the ratio of the local thermal instability time-scale and the free-fall time-scale: a cool core with tTI/tff = 10 and a stable outer halo with tTI/tff > 10. We update the prescriptions of cooling, feedback and stripping based on the new hot gas profiles, and then reproduce several X-ray observational results, like the radial profiles of hot gas density, and the scaling relations of X-ray luminosity and temperature. We find: (1) Consistent with observations, flatter density profiles in halo centers produce lower X-ray emission than an isothermal sphere; (2) Cool core regions prone to precipitation have higher gas temperature than the virial temperature, and a larger TX/T200 ratio in smaller haloes leads to a steeper slope in the LX − TX relation; (3) The ionized gas in the unbounded reservoir and low temperature intergalactic gas in low mass haloes could be the main components of the halo “missing baryons”. Our model outputs can predict the observations of hot gas in the nearby universe and produce mock surveys of baryons probed by future X-ray telescopes.

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The hot gas distribution, X-ray luminosity and baryon budget in the L-Galaxies semi-analytic model of galaxy formation


 We reanalyze the Fermi-LAT GeV γ-ray emission in the region of supernova remnant (SNR) G51.26+0.11 and investigate its interstellar molecular environment with the CO-line data. At GeV energies, based on 13.2 years of Fermi-LAT data, the extended γ-ray emission observed in this region is resolved into a uniform-disk source (‘Src A’) with a significance of 19.5σ and a point source (4FGL J1924.3+1628) with a significance of 4.2σ in 0.2–500 GeV. With an angular radius of ∼ 0.17○, ‘Src A’ overlaps with SNR G51.26+0.11 significantly in the line of sight. On the other hand, the morphological coincidence between the SNR and the ∼+54 km s−1 molecular clouds (MCs) together with the asymmetric or broad 12CO line profiles near the SNR boundary provides evidence for the very likely SNR-MC interaction. The SNR-MC interaction and the H I absorption features indicate that SNR G51.26+0.11 is located at a kinematic distance of 6.2 ± 0.5 kpc. Combined with the results from the multi-wavelength analysis, the γ-ray emission of the SNR (‘Src A’) can be naturally explained by a hadronic model with a soft power-law proton spectrum of index ∼ 2.25.

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A Study of GeV Gamma-ray Emission toward Supernova Remnant G51.26+0.11 and Its Molecular Environment

Skin effect is one of the intriguing phenomena exhibited by non-Hermitian wave systems. It reflects the localization of the modes at the boundaries of the structure. We demonstrated the skin effect for elastic waves propagating in a non-Hermitian phononic plate containing piezoelectric components in their unit cells. The latter behave as sensors and actuators by using the direct and inverse piezoelectric effects. The demonstration is based on the calculation of the complex non-reciprocal dispersion curves and their analysis for any direction of the wavevector in the two-dimensional space. Therefore, localization phenomena at different boundaries and corners of a finite square structure are presented. Furthermore, by applying different levels of non-Hermiticity in different parts of a square structure, it is shown that the localized features can appear at different positions and with various shapes. These localized phenomena can be reconfigured by acting on the non-Hermiticity parameters. Our results provided a feedback control strategy to introduce the non-Hermitian skin effect in two-dimensional elastic systems for potential applications, such as vibration control, energy harvesting, and sensing.

https://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0152606/17936600/222203_1_5.0152606.pdf

Reconfigurable localized effects in non-Hermitian phononic plate

We create mock X-ray observations of hot gas in galaxy clusters with a new extension of the L-Galaxies semi-analytic model of galaxy formation, which includes the radial distribution of hot gas in each halo. Based on the model outputs, we first build some mock light cones, then generate mock spectra with the SOXS package and derive the mock images in the light cones. Using the mock data, we simulate mock X-ray spectra for the ROSAT all-sky survey, and compare the mock spectra with the observational results. Then, we consider the design parameters of the HUBS mission and simulate the observation of the halo hot gas for HUBS as an important application of our mock work. We find: (1) our mock data match the observations by current X-ray telescopes. (2) The survey of hot baryons in resolved clusters by HUBS is effective below redshift 0.5, and the observations of the emission lines in point-like sources at z > 0.5 by HUBS help us understand the hot baryons in the early universe. (3) By taking advantage of the large simulation box and flexibility in semi-analytic models, our mock X-ray observations provide the opportunity to select targets and observation strategies for forthcoming X-ray facilities.

Wenxin Zhong

Papers

Non-Hermitian skin effect in a phononic beam based on piezoelectric feedback control

The hot gas distribution, X-ray luminosity and baryon budget in the L-Galaxies semi-analytic model of galaxy formation

A Study of GeV Gamma-ray Emission toward Supernova Remnant G51.26+0.11 and Its Molecular Environment

Reconfigurable localized effects in non-Hermitian phononic plate

Mock X-Ray Observations of Hot Gas with L-Galaxies Semi-analytic Models of Galaxy Formation