Magnetic field dependence of the atomic collapse state in graphene

TL;DR

This paper investigates how magnetic fields influence atomic collapse states in graphene, using exact numerical methods to clarify conflicting theoretical predictions and demonstrating the persistence of collapse phenomena under magnetic fields.

Contribution

The study provides a comprehensive numerical analysis of the interplay between magnetic fields and atomic collapse in graphene, avoiding approximations and revealing a smooth transition between regimes.

Findings

Atomic collapse persists with magnetic fields and the critical charge remains unchanged.

The regime shows Landau level anticrossings characteristic of atomic collapse.

Landau levels do not follow the expected B scaling in the collapse regime.

Abstract

Quantum electrodynamics predicts that heavy atoms ($Z > Z_c \approx 170$) will undergo the process of atomic collapse where electrons sink into the positron continuum and a new family of so-called collapsing states emerges. The relativistic electrons in graphene exhibit the same physics but at a much lower critical charge ($Z_c \approx 1$) which has made it possible to confirm this phenomenon experimentally. However, there exist conflicting predictions on the effect of a magnetic field on atomic collapse. These theoretical predictions are based on the continuum Dirac-Weyl equation, which does not have an exact analytical solution for the interplay of a supercritical Coulomb potential and the magnetic field. Approximative solutions have been proposed, but because the two effects compete on similar energy scales, the theoretical treatment varies depending on the regime which is being considered. These limitations are overcome here by starting from a tight-binding approach and computing exact numerical results. By avoiding special limit cases, we found a smooth evolution between the different regimes. We predict that the atomic collapse effect persists even after the magnetic field is activated and that the critical charge remains unchanged. We show that the atomic collapse regime is characterized: 1) by a series of Landau level anticrossings and 2) by the absence of $\sqrt{B}$ scaling of the Landau levels with regard to magnetic field strength.