Skipping and snake orbits of electrons: singularities and catastrophes

TL;DR

This paper studies the complex behavior of electron trajectories near edges and magnetic steps, revealing singularities like caustics and bifurcations that cause observable oscillations in electronic conductance.

Contribution

It uncovers the geometric and topological structures of electron orbits, such as caustics and bifurcations, in magnetic fields, linking them to conductance oscillations in 2D metals.

Findings

Identification of caustics, cusps, and bifurcations in electron orbits.

Connection between singularities and magneto-oscillations.

Insight into electron dynamics near edges and magnetic steps.

Abstract

Near the sample edge, or a sharp magnetic field step the drift of two-dimensional electrons in a magnetic field has the form of skipping/snake orbits. We show that families of skipping/snake orbits of electrons injected at one point inside a 2D metal generically exhibit caustics folds, cusps and cusp triplets, and, in one extreme case, a section of the batterfly bifurcation. Periodic appearance of singularities along the $\pm B$-interface leads to the magneto-oscillations of nonlocal conductance in multi-terminal electronic devices.