Dynamics of a Rydberg hydrogen atom near a topologically insulating surface

TL;DR

This paper explores the classical dynamics of a Rydberg hydrogen atom near a topological insulator surface, revealing how topological properties influence atomic motion and phase space structure.

Contribution

It introduces a detailed analysis of the classical phase space of a hydrogen atom near a topological insulator, highlighting the role of topological magnetoelectric effects.

Findings

Phase space exhibits vibrational and rotational regions.

Transitions between vibrational and rotational states can be tuned by topological parameters.

The study uses numerical methods and Poincaré surfaces of section to analyze dynamics.

Abstract

We investigate the classical dynamics of a Rydberg hydrogen atom near the surface of a planar topological insulator. The system is described by a Hamiltonian consisting of the free-hydrogen part and the hydrogen-surface potential. The latter includes the interactions between the electron and both image electric charges and image magnetic monopoles. Owing to the axial symmetry, the $z$ component of angular momentum $l_{z}$ is conserved. Here we consider the $l_{z} = 0$ case. The structure of the phase space is explored extensively by means of numerical techniques and Poincar\'{e} surfaces of section for the recently discovered topological insulator TlBiSe$_{2}$. The phase space of the system is separated into regions of vibrational and rotational motion. We show that vibrational-rotational-vibrational type transitions can be tuned with the topological magnetoelectric polarizability.