Complex dynamics in circular and deformed bilayer graphene inspired billiards with anisotropy and strain

TL;DR

This paper explores how anisotropy and strain in bilayer graphene influence the dynamics of billiard systems, revealing transitions to chaos and stability changes through trajectory analysis.

Contribution

It introduces a trajectory tracing approach to study anisotropic billiards in bilayer graphene, highlighting the impact of anisotropy on system dynamics and stability.

Findings

Anisotropy can induce chaos in otherwise integrable billiards.

Anisotropy can stabilize previously unstable trajectories.

Dynamics are characterized using Lyapunov exponents and Poincaré sections.

Abstract

While billiard systems of various shapes have been used as paradigmatic model systems in the fields of nonlinear dynamics and quantum chaos, few studies have investigated anisotropic billiards. Motivated by the tremendous advances in using and controlling electronic and optical mesoscopic systems with bilayer graphene representing an easily accessible anisotropic material for electrons when trigonal warping is present, we investigate billiards of various anisotropies and geometries using a trajectory tracing approach founded in the concept of ray-wave correspondence. We find that the presence of anisotropy can render the billiards' dynamics dramatically from its isotropic counterpart. It may induce chaotic and mixed dynamics in otherwise integrable systems, and may stabilize originally unstable trajectories. We characterize the dynamics of anisotropic billiards in real and phase space using Lyapunov exponents and the Poincar\'e surface of section as phase space representation.