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

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.

30 pages and 9 figures

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• The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons
• Induced fermionic charge and current densities in two-dimensional rings
• Finite temperature fermionic condensate in a conical space with a circular boundary and magnetic flux
• Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string
• Casimir effect for fermion condensate in conical rings
• Vacuum currents in elliptic pseudosphere tubes
• Finite temperature fermionic condensate and energy-momentum tensor in cosmic string spacetime