Casimir effect for fermion condensate in conical rings

TL;DR

This paper studies the fermion condensate in a (2+1)-dimensional conical geometry with magnetic flux, revealing boundary and edge effects, and their implications for symmetry breaking and applications to graphitic cones.

Contribution

It provides explicit formulas for the fermion condensate in conical geometries with various boundary conditions, including edge-induced effects and symmetry considerations.

Findings

Fermion condensate is an even periodic function of magnetic flux.

Boundary conditions can make the condensate positive or negative.

Edge effects dominate the condensate for massless fields.

Abstract

The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the period equal to the flux quantum. Depending on the boundary conditions, the condensate can be either positive or negative. For a massless field the FC in the boundary-free conical geometry vanishes and the nonzero contributions are purely edge-induced effects. This provides a mechanism for time-reversal symmetry breaking in the absence of magnetic fields. Combining the results for the fields corresponding to two inequivalent irreducible representations of the Clifford algebra, the FC is investigated in the parity and time-reversal symmetric fermionic models and applications are discussed for graphitic cones.