Finite temperature fermionic charge and current densities in conical space with a circular edge

We study the finite temperature and edge induced effects on the charge and current densities for a massive spinor field localized on a 2D conical space threaded by a magnetic flux. The field operator is constrained on a circular boundary, concentric with the cone apex, by the bag boundary condition and by the condition with the opposite sign in front of the term containing the normal to the edge. In two-dimensional spaces there exist two inequivalent representations of the Clifford algebra and the analysis is presented for both the fields realizing those representations. The circular boundary divides the conical space into two parts, referred as interior (I-) and exterior (E-) regions. The radial current density vanishes. The edge induced contributions in the expectation values of the charge and azimuthal current densities are explicitly separated in the both regions for the general case of the chemical potential. They are periodic functions of the magnetic flux and odd functions under the simultaneous change of the signs of magnetic flux and chemical potential. In the E-region all the spinorial modes are regular and the total charge and current densities are continuous functions of the magnetic flux. In the I-region the corresponding expectation values are discontinuous at half-integer values of the ratio of the magnetic flux to the flux quantum. 2D fermionic models, symmetric under the parity and time-reversal transformations (in the absence of magnetic fields) combine two spinor fields realizing the inequivalent representations of the Clifford algebra. The total charge and current densities in those models are discussed for different combinations of the boundary conditions for separate fields. Applications are discussed for electronic subsystem in graphitic cones described by the 2D Dirac model.