Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space

TL;DR

This paper calculates fermion condensate, charge, and current densities in a (2+1)-dimensional conical space with magnetic flux, revealing their periodic dependence on flux and behavior near the cone apex, with implications for nanocones.

Contribution

It provides new analytical expressions for fermion condensate and current densities in conical geometries with magnetic flux, including parity and time-reversal symmetric cases.

Findings

Fermion condensate and charge density vanish for massless, zero chemical potential fields.

Azimuthal current density is odd in magnetic flux and independent of representation.

Vacuum contributions dominate near the cone apex.

Abstract

We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even function of the chemical potential. The behavior of the expectation values in various asymptotic regions of the parameters are discussed in detail. In particular, we show that for points near the cone apex the vacuum parts dominate. For a massless field with zero chemical potential the fermion condensate and charge density vanish. Simple expressions are derived for the part in the total charge induced by the planar angle deficit and magnetic flux. Combining the results for separate irreducible representations, we also consider the fermion condensate, charge and current densities in parity and time-reversal symmetric models. Possible applications to graphitic nanocones are discussed.