Parity-dependent Casimir forces and Hall currents for a confined Dirac field

TL;DR

This paper investigates how parity symmetry affects Casimir forces and Hall currents in a confined massless Dirac field, revealing that boundary conditions determine whether the force is attractive or repulsive.

Contribution

It demonstrates the impact of parity-dependent boundary conditions on Casimir forces and vacuum-induced Hall currents in a Dirac field system.

Findings

Symmetric boundary conditions produce attractive Casimir forces.

Antisymmetric boundary conditions lead to repulsive Casimir forces.

A Hall-like transverse current is induced in 2+1 dimensions under an external electric field.

Abstract

We study a massless Dirac field subjected to two alternative boundary conditions on two parallel thin walls, in d + 1 dimensions. The two configurations correspond to the system being even or odd under reflection about the midplane between the two walls, and lead to qualitatively different behaviors. The even (symmetric) configuration produces an attractive Casimir force, whereas the odd (antisymmetric) one yields repulsion, in agreement with a general theorem linking parity to the sign of the fermionic Casimir effect. We complement this result by studying two phenomena associated with the vacuum fluctuations responsible for the Casimir interaction, both of which are also sensitive to parity: the correlation between currents concentrated on the walls, and the induced bulk current under the influence of an external electric field. For the latter we show that, in 2 + 1 dimensions, an induced transverse (Hall-like) current arises, whose spatial profile inherits the symmetry of the confining potential.