Atomic Collapse in Graphene: Lost of Unitarity

TL;DR

This paper investigates atomic collapse phenomena in graphene with electric and magnetic monopole impurities, revealing conditions under which unitarity is lost or preserved, and linking these to the presence or absence of atomic collapse.

Contribution

It introduces a supersymmetric quantum mechanics framework to analyze atomic collapse in graphene and identifies critical charges affecting unitarity and collapse.

Findings

Electric impurities lead to loss of unitarity at critical charge.

Magnetic monopole impurities do not cause atomic collapse.

Unitarity preservation depends on impurity type and parameters.

Abstract

We explore the problem of atomic collapse in graphene by monopole impurities, both electric and magnetic, within the context of supersymmetric quantum mechanics. For electric impurities, upon factorizing the radial Dirac Hamiltonian and identifying the supercharges, existence of a critical charge that makes the ground state {\em fall-into-the-center} translates into lost of hermicity for the corresponding Hamiltonian and hence lost of unitarity of the theory. For the problem of magnetic monopole impurities, preservation of unitarity for all values of the parameters of the corresponding potential translates into the absence of atomic collapse in this case.