Theory of superconductivity of systems with pairing of spatially separated electrons and holes

The possibility of superconductivity is predicted in systems with pairing of spatially separated electrons and holes. Gor’kov and Ginzburg-Landau equations are obtained for the systems under consideration. It is shown that the gap in the elementary excitation spectrum is Δ=vFpae−1/ζ,ζ=4(pa/pa)2(e2/a0)(p02/2m). Here νF is the velocity; p0 is the Fermi momentum; pa = 1/2 a (2a is the spacing between domains with electron and hole conductivity); a0 is the spacing between carriers; m = m1m2/(m2+m2)(m1,m2 are the effective masses of the electrons and holes). The system response to a weak magnetic field is calculated; the currents it causes are J1= − J2 = − {[N(T) e2]/( m1+ m2)c2 }(A1− A2)(A1A2 are the values of the vector potential in domains with electron and hole conductivity; J1J2 are the current densities in the appropriate domains; N(T) is the concentration of superconducting electrons). The presence of a stationary Josephson effect is established, i.e., the possibility of superconductivity in the systems under consideration is proved.