Mean-Field Theory For Unconventional Superconductivity

In this thesis we study the physical properties of unconventional superconductors by mean-field theory. Using mean-field method, we solve the gap function for unconventional supercon-ductors self-consistently. Then we calculate specific heat and penetration depth, by which we can distinguish the superconductivity pairing symmetry. The self-consistent equations for supercon-ductivity gap are obtained from the mean-field Hamiltonian Bogoliubov transformation. We solve these gap equations and obtain the energy dispersion for Bogoliubov quasiparticles. The specif-ic heat and London penetration depth at weak magnetic field can be evaluated with the help of Bogoliubov quasiparticles. Then we can deduce the pairing symmetry from the low temperature power law behaviors of specific heat and penetration depth. We also study the newly found super-conductors A2Cr3As3 form the view of 3 band Hubbard model, and found that f-wave spin-triplet pairing state dominate the superconductivity.