Phase-Space Topology and Spectral Flow in Screened Magnetized Plasmas

TL;DR

The paper presents a phase-space topological framework for screened magnetized plasmas by casting the linearized dynamics into a pseudo-Hermitian Schrödinger form and analyzing the Weyl symbol of the bulk generator. It reveals a spin-1 band degeneracy at $k_z=0$ with topological charge $+2$, which splits into two spin-$ frac{1}{2}$ Weyl points for $k_z eq0$, and introduces a strip-gap Chern number $C_{ ext{gap}}$ to extend band topology to continua. The bulk–interface correspondence is established in phase space: the net spectral flow of interface modes across a real-frequency strip gap equals the enclosed monopole charge, and numerical results confirm this for various magnetic-field profiles. The robustness of spectral flow under damping is shown to persist as long as a finite strip gap remains, delineating the regime where the topological description remains valid in dissipative continua. Overall, the work provides a systematic, phase-space approach to topological wave transport in continuous media beyond compact-band and Hermitian settings, with potential applications to plasmas, fluids, and EM continua.

Abstract

Topological wave phenomena in continuous media are fundamentally challenged by unbounded spectra and the absence of a compact Brillouin zone, which obstruct conventional bulk--interface formulations. We develop a unified phase-space framework for screened magnetized plasma based on a pseudo-Hermitian formulation with a positive-definite metric, enabling a generalized Schrödinger description and a Weyl-symbol analysis of the bulk generator. We show that the bulk symbol hosts isolated band degeneracies acting as Berry--Chern monopoles, including a higher-order spin-1 degeneracy with topological charge $+2$ that generically splits into two spin-$\tfrac{1}{2}$ Weyl points under symmetry breaking. To characterize topology in this noncompact setting, we introduce a strip-gap Chern number associated with finite real-frequency strips of the bulk spectrum, extending band Chern topology to continuum systems. This invariant governs the spectral flow of interface modes induced by spatial variations of the magnetic field and establishes a bulk--interface correspondence at the level of phase-space symbols. By solving the interface eigenvalue problem, we demonstrate that the net spectral flow across the strip gap is determined by the enclosed monopole charge. We further show that this correspondence persists under collisional damping, provided that a finite strip gap remains and no exceptional points enter it. Our results provide a systematic phase-space framework for topological wave transport in continuous media beyond compact-band and idealized Hermitian settings.

Figures (3)

• Figure 1: Schematic illustration of the bulk band structure of the Weyl symbol $\eta^{-1}H$ in the parameter space $(\mu,k_x,k_y)$ for fixed $k_z$. Isolated band degeneracies appear as Weyl points (marked by arrows), each carrying a topological charge. (a) For $k_z=0$, the spectrum exhibits a single higher-order Weyl point with topological charge $+2$. (b) For $k_z\neq0$, this degeneracy splits into two Weyl points, each carrying a unit topological charge $+1$.
• Figure 2: Eigenvalue spectra of the interface problem as functions of $k_y$ for different magnetic configurations $\mu(x)$. Discrete eigenvalues inside the strip gap are marked by plus symbols. (a,b) Cases with a common strip gap. For $k_z=0$, the variation of $\mu(x)$ crosses a single higher-order degeneracy carrying topological charge $+2$; for $k_z\neq0$, it crosses two Weyl points each carrying unit topological charge $+1$. In both cases, two chiral branches traverse the strip gap, yielding a net spectral flow of $+2$, consistent with the gap Chern number. (c) Case without a strip gap at $k_y=0$. Although the gap is locally closed, the variation crosses a single Weyl point with unit topological charge, resulting in a single chiral branch connecting the two continuous spectra. (d) Case with a strip gap but no band degeneracy crossed during the variation, for which no discrete interface modes appear within the gap.
• Figure 3: Interface eigenvalue spectra in the presence of finite damping for $\nu=0.5$, $1.5$, and $2.5$. Panels (a--c) show the real parts of the eigenfrequencies as functions of $k_y$, while panels (d--f) display the corresponding spectral clouds in the complex-frequency plane. (a,d) For $\nu=0.5$, complex eigenfrequencies appear, but the real parts of the spectrum retain a finite strip gap, within which two discrete branches traverse between the two continuous spectra. (b,e) For $\nu=1.5$, the strip gap in the real spectrum is reduced, and the separation between the two continuous spectra in the spectral cloud becomes narrower, while the gap-crossing branches remain identifiable. (c,f) For $\nu=2.5$, the strip gap closes completely and the two continuous spectra merge in the real-frequency projection; the spectral cloud consists of two families of discrete eigenvalues parameterized by $k_y$, corresponding to the continuation of the gap-crossing branches observed at smaller damping.