Electric charge catalysis by magnetic fields and a nontrivial holonomy

TL;DR

This paper introduces a universal mechanism where Dirac fermions in thermal equilibrium acquire electric charge in magnetic fields due to nontrivial holonomy, with applications to graphene and hot QCD.

Contribution

It reveals a novel charge induction mechanism involving magnetic fields and holonomy, applicable to condensed matter and high-energy physics systems.

Findings

Charge accumulation occurs due to Landau level degeneracy differences.

The phenomenon is demonstrated in graphene and hot QCD calorons.

Holonomy fluctuations can suppress charge fluctuations in quark-gluon plasma.

Abstract

We describe a generic mechanism by which a system of Dirac fermions in thermal equilibrium acquires electric charge in an external magnetic field. To this end the fermions should have an additional quantum number, isospin or color, and should be subject to a second magnetic field, which distinguishes the isospin/color, as well as to a corresponding isospin chemical potential. The role of the latter can be also played by a nontrivial holonomy (Polyakov loop) along the Euclidean time direction. The charge is accumulated since the degeneracies of occupied lowest Landau levels for particles of positive isospin and anti-particles of negative isospin are different. We discuss two physical systems, where this phenomenon can be realized. One is monolayer graphene, where the isospin is associated with two valleys in the Brillouin zone and the strain-induced pseudo-magnetic field acts differently on charge carriers in different valleys. Another is hot QCD, for which the relevant non-Abelian field configurations with both nonzero chromo-magnetic field and a nontrivial Polyakov loop can be realized as calorons - topological solutions of Yang-Mills equations at finite temperature. The induced electric charge on the caloron field configuration is studied numerically. We argue that due to the fluctuations of holonomy external magnetic field should tend to suppress charge fluctuations in the quark-gluon plasma and estimate the importance of this effect for off-central heavy-ion collisions.