Phase-Space Topology and Spectral Flow in Screened Magnetized Plasmas

TL;DR

This paper develops a phase-space framework for topological wave phenomena in screened magnetized plasmas, revealing how spectral flow and topological invariants govern interface modes in noncompact, continuum systems.

Contribution

It introduces a novel phase-space approach with a generalized Schrödinger formulation and a strip-gap Chern number to characterize topology in unbounded plasma spectra.

Findings

Identifies isolated band degeneracies as Berry--Chern monopoles.

Defines a strip-gap Chern number extending band topology to continuum systems.

Demonstrates spectral flow governed by monopole charge persists under damping.

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 Schr\"odinger 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.