Year: 2022
Type: preprint
Abstract: We study solutions of $2 \times 2$ systems $(h D_t + \mathcal{D}) Ψ_t = 0$ on $\mathbb{R}^2$ in the semiclassical regime $h \rightarrow 0$. Our Dirac operator $\mathcal{D}$ is a standard model for interfaces between topological insulators: it represents a semimetal at null energy, and distinct topological phases at positive / negative energies. Its semiclassical symbol has two opposite eigenvalues, intersecting conically along the curve $Γ$ of positions / momenta where the material behaves like a semimetal. We prove that wavepackets solving $(h D_t + \mathcal{D}) Ψ_t = 0$, initially concentrated in phase space on $Γ$, split in two parts. The first part travels coherently along $Γ$ with predetermined direction and speed. It is the dynamical manifestation of the famous "edge state". The second part immediately collapses. Our approach consists of: (i) a Fourier integral operator reduction; (ii) a careful WKB analysis of a canonical model; (iii) a reconstruction procedure. It yields concrete formulas for the speed and profile of the traveling modes. As applications, we analytically describe dynamical edge states for models of magnetic, curved, and strained topological insulators.
Source: arXiv (Cornell University)
Author: Drouot, Alexis
Institution: University of Washington
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4283067900