Finite temperature fermionic charge and current densities induced by a   cosmic string with magnetic flux
  We investigate the finite temperature expectation values of the charge and current densities for a massive fermionic field with nonzero chemical potential, $\mu$, in the geometry of a straight cosmic string with a magnetic flux running along its axis. These densities are decomposed into the vacuum expectation values and contributions coming from the particles and antiparticles. The charge density is an even periodic function of the magnetic flux with the period equal to the quantum flux and an odd function of the chemical potential. The only nonzero component of the current density corresponds to the azimuthal current. The latter is an odd periodic function of the magnetic flux and an even function of the chemical potential. At high temperatures, the parts in the charge density and azimuthal current induced by the planar angle deficit and magnetic flux are exponentially small. The asymptotic behavior at low temperatures crucially depends whether the value $|\mu|$ is larger or smaller than the mass of the field quanta, $m$. For $|\mu|<m$ the charge density and the contributions into the azimuthal current coming from the particles and antiparticles are exponentially suppressed at low temperatures. In the case $|\mu|>m$, the charge and current densities receive two contributions coming from the vacuum expectation values and from particles or antiparticles (depending on the sign of chemical potential). At large distances from the string the latter exhibits a damping oscillatory behavior with the amplitude inversely proportional to the square of the distance. 
A. Mohammadi, E. R. Bezerra de Mello and A. A. Saharian
hep-th gr-qc