Bound states in semi-Dirac semi-metals

TL;DR

This paper investigates the spectral stability and existence of bound states in semi-Dirac materials with mixed dispersion, providing conditions for eigenvalues and highlighting spectral instability in weak coupling regimes.

Contribution

It offers new theoretical criteria for bound state existence in semi-Dirac systems and analyzes their spectral stability under perturbations.

Findings

Spectral instability observed in weakly coupled regimes.

Derived necessary and sufficient conditions for discrete eigenvalues.

Numerical experiments support theoretical predictions.

Abstract

New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations. Physically relevant sufficient and necessary conditions to guarantee the existence of discrete eigenvalues are derived under rather general assumptions on external fields. One of the most interesting features of the analysis is the evident spectral instability of the systems in the weakly coupled regime. The rigorous theoretical results are illustrated by numerical experiments and predictions for physical experiments are made.