Magnetic field driven instability of charged center in graphene

TL;DR

This paper demonstrates that magnetic fields induce supercritical charge instability in graphene, transforming the behavior of Coulomb centers and potential wells, and links this to magnetic catalysis phenomena.

Contribution

It introduces the concept of magnetic field-driven instability of charged centers in graphene, analyzing both potential wells and Coulomb centers within a perturbative framework.

Findings

Magnetic fields make any charge supercritical in gapless graphene.

Calculated local density of states and polarization charge density.

Identified the instability as a quantum analog of magnetic catalysis.

Abstract

It is shown that a magnetic field dramatically affects the problem of supercritical charge in graphene making any charge in gapless theory supercritical. The cases of radially symmetric potential well and Coulomb center in an homogeneous magnetic field are considered. The local density of states and polarization charge density are calculated in the first order of perturbation theory. It is argued that the magnetically induced instability of the supercritical Coulomb center can be considered as a quantum mechanical counterpart of the magnetic catalysis phenomenon in graphene.