Study of the specific heat of two-band superconductors

Using a modified two-band Ginzburg–Landau model, we study the specific heat in two-band superconductors. From the free energy of a modified two-band Ginzburg–Landau model, we obtain some formulae of thermodynamic quantities. We obtain the free energies FSC/V∝T4FSC/V∝T4 and FSC/V∝(2πHL/Φ0)2FSC/V∝(2πHL/Φ0)2. When the two bands are in close connection, the specific heat is CV/V∝−g1T3−g2T2+g3T+g4(2πHL/Φ0)2TCV/V∝−g1T3−g2T2+g3T+g4(2πHL/Φ0)2T. When π/2<δ2−δ1<3π/2π/2<δ2−δ1<3π/2, the finite interband Josephson coupling is negative repulsive.