In open, driven systems where parity-time symmetry is preserved, phenomena that defy conventional wisdom emerge near exceptional points, promising advances in photonics. While most studies focus on two-level systems of a conventional exceptional point, unconventional exceptional points as well as reentrant phases have been discovered in separate studies of higher-dimensional phase spaces. In this article, we present a minimal, analytical model that encompasses several key phenomena in higher-dimensional phase spaces, including reentrant $\mathcal{PT}$ phases, higher-order exceptional points, and anisotropic exceptional points. Using the exact analytical solution, we identify a topological index as the unifying origin of these different phenomena. The simplicity of the model may furthermore facilitate experimental implementations for enhanced sensing and efficient polariton devices.
In this work, we propose a theory on the two-dimensional non-Hermitian skin effect by resolving two representative minimal models. Specifically, we show that for any given non-Hermitian Hamiltonian, (i) the corresponding region covered by its open boundary spectrum on the complex energy plane should be independent of the open boundary geometry; and (ii) for any given open boundary eigenvalue $E_0$ , its corresponding two-dimensional asymptotic generalized Brillouin zone is determined by a series of geometry-independent Bloch/non-Bloch Fermi points and geometry-dependent non-Bloch equal frequency contours that connect them. A corollary of our theory is that most symmetry-protected exceptional semimetals should be robust to variations in OBC geometry. Our theory paves the way to the discussion on the higher dimensional non-Bloch band theory and the corresponding non-Hermitian bulk-boundary correspondence.
The authors demonstrate the existence of helical damping and dynamical critical skin effect in quantum open systems and show that the change of generalized Brillouin zone equation is the origin of critical skin effect.
A fundamental tenet of quantum mechanics is that the energy spectrum of a quantum system shall remain stable against infinitesimally weak and spatially confined perturbations. In this article, we demonstrate that this principle of spectral stability fails in non-Hermitian systems at the thermodynamic limit. Consider, for instance, a non-interacting non-Hermitian system $H_0$ with a couple of point-like impurities, each of which introduces a local short-range potential $V_i$ with $i=1, \ldots, n$ labeling the impurities. If the impurity potentials are sufficiently weak, introducing a single impurity will not alter the spectrum; that is, $H_0$ and $H_0 + V_1$ have nearly identical energy spectra. However, if a second impurity is introduced, $H_0 + V_1 + V_2$, we find that no matter how weak these local potentials are, as long as the distance between them is sufficiently large, significant alterations in the energy spectrum can arise, directly contradicting the traditional expectation of a stable spectrum. Remarkably, this phenomenon is non-local, and the impact of the perturbations increases exponentially with the distance between the two impurities. In other words, although the Hamiltonian is entirely local, its energy spectrum, which is blind to the presence of a single infinitesimally weak impurity, is capable of detecting the presence of two infinitesimally weak impurities separated by a large distance in space. Using Green's function techniques, we uncover the origin of this spectral sensitivity, which arises from the formation of non-local bi-impurity bound states: non-local stationary states with wavepackets propagating back-and-forth between the two impurities. We provide an analytic theory to identify and characterize such spectral instabilities, showing perfect agreement with numerical solutions.
Chirality-induced spin selectivity (CISS) generates giant spin polarization in transport through chiral molecules, paving the way for novel spintronic devices and enantiomer separation. Unlike conventional transport, CISS magnetoresistance (MR) violates Onsager's reciprocal relation, exhibiting significant resistance changes when reversing electrode magnetization at zero bias. However, its underlying mechanism remains unresolved. In this work, we propose that CISS MR originates from charge trapping that modifies the electron tunneling barrier and circumvents Onsager's relation, distinct from previous spin polarization-based models. Charge trapping is governed by the non-Hermitian skin effect, where dissipation leads to exponential wavefunction localization at the ferromagnet-chiral molecule interface. Reversing magnetization or chirality alters the localization direction, changing the occupation of impurity/defect states in the molecule (i.e., charge trapping) – a phenomenon we term magnetochiral charge pumping. Our theory explains why CISS MR can far exceed the ferromagnet spin polarization and why chiral molecules violate the reciprocal relation but chiral metals do not. Furthermore, it predicts exotic phenomena beyond the conventional CISS framework, including asymmetric MR induced by magnetic fields alone (without ferromagnetic electrodes), as confirmed by recent experiments. This work offers a deeper understanding of CISS and opens avenues for controlling electrostatic interactions in chemical and biological systems through the magnetochiral charge pumping. Some chiral molecules can produce a giant spin polarization, a feature termed chirality-induced spin selectivity. The origin of this has been hotly debated. In this theory work, Zhao, Zhang and coauthors propose that the origin of the effect lies in charge trapping induced barrier modification, termed magnetochiral charge pumping.
We provide a systematic and self-consistent method to calculate the generalized Brillouin zone (GBZ) analytically in one-dimensional non-Hermitian systems, which helps us to understand the non-Hermitian bulk-boundary correspondence. In general, a $n$-band non-Hermitian Hamiltonian is constituted by $n$ distinct sub-GBZs, each of which is a piecewise analytic closed loop. Based on the concept of resultant, we can show that all the analytic properties of the GBZ can be characterized by an algebraic equation, the solution of which in the complex plane is dubbed as auxiliary GBZ (aGBZ). We also provide a systematic method to obtain the GBZ from aGBZ. Two physical applications are also discussed. Our method provides an analytic approach to the spectral problem of open boundary non-Hermitian systems in the thermodynamic limit.
In this paper, we introduce the concept of dynamical degeneracy splitting to describe the anisotropic decay behaviors in non-Hermitian systems. We demonstrate that systems with dynamical degeneracy splitting exhibit two distinctive features: (i) the system shows frequency-resolved non-Hermitian skin effect; (ii) Green's function exhibits anomalous at given frequency, leading to uneven broadening in spectral function and anomalous scattering. As an application, we propose directional invisibility based on wave packet dynamics to investigate the geometry-dependent skin effect in higher dimensions. Our work elucidates a faithful correspondence between non-Hermitian skin effect and Green's function, offering a guiding principle for exploration of novel physical phenomena emerging from this effect.
An exact bulk-edge correspondence between winding (in the bulk) and skin modes (on the surface) in non-Hermitian systems establishes that a nonzero winding number in the bulk leads to skin effect on the edge, and vice versa.
In this paper, we establish an effective edge theory to characterize non-Hermitian edge-skin modes in higher dimensions. We begin by proposing a bulk projection criterion to straightforwardly identify the localized edges of skin modes. Through an exact mapping, we show that the edge-skin mode shares the same bulk-boundary correspondence and localization characteristics as the zero-energy edge states in a Hermitian semimetal under open-boundary conditions, bridging the gap between non-Hermitian edge-skin effect and Hermitian semimetals. Another key finding is the introduction of ``skewness,'' a term we proposed to describe the characteristic decay direction of skin mode from the localized edge into the bulk. Remarkably, we demonstrate that skewness is an intrinsic quantity of the skin mode and can be analytically determined using the corresponding cylinder-geometry bulk Hamiltonian, without requiring any boundary details. Furthermore, we reveal that, in the edge-skin effect, the spectrum exhibits anomalous spectral sensitivity to weak local disturbances, a feature that crucially distinguishes it from the corner-skin effect.
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