Thermodynamic properties of two-band superconductors with low carrier density

A theory of superconductivity is constructed for systems with two overlapping energy bands at the Fermi surface and with low carrier density. The phonon superconductivity mechanism is assumed and allowance is made for all possible pairings of electrons both within one band and of electrons from different bands. A bell-shaped dependence of the temperature $T_c$ of the superconducting transition and a jump of the electron specific heatC ($C_S-C_N$) at $T=T_c$ as a fuction of the carrier density are obtained in the case of strong hybridization. The possibility of an increase in the value of the chemical potential at which the kink at the point $T=T_c$ arises is demonstrated. It is also shown that the relative jump ($C_S-C_N/C_N$) of the specific heat at $T=T_c$ depends on the carrier density and may be both greater or less than 1.43.