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

S Bellucci,A A Saharian,E R Bezerra De Mello,E Bragança

doi:10.1140/epjc/s10052-016-4195-5

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.

Highlights

Fermionic field theoretical models in three-dimensional spacetime rise in a number of physical problems
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
In the present paper we investigate the finite temperature effects on the fermion condensate and on the expectation values of the charge and current densities for a massive fermionic field with nonzero chemical potential in a (2+1)-dimensional conical spacetime in the presence of a magnetic flux located at the cone apex

Summary

Introduction

Fermionic field theoretical models in three-dimensional spacetime rise in a number of physical problems. The long-wavelength dynamics, equivalent to relativistic Dirac fermions with a controllable mass, is exhibited by ultracold fermionic atoms in an optical lattice [6] Another motivation comes from the connection of three-dimensional models to high temperature behavior in 4-dimensional field theories [7]. In the present paper we investigate the finite temperature effects on the fermion condensate and on the expectation values of the charge and current densities for a massive fermionic field with nonzero chemical potential in a (2+1)-dimensional conical spacetime in the presence of a magnetic flux located at the cone apex. The finite temperature effects on the fermionic condensate and current densities in models with an arbitrary number of toroidally compact spatial dimensions are discussed in [53]. In the Appendix we derive the relations used in the evaluation of the topological part in the total charge

Fermion condensate

Charge density

Current density

Expectation values in parity and time-reversal symmetric models

Conclusion