Condensation Energy for Cuprate Superconductors from an Ideal Boson-Fermion Mixture in Multilayers

We report on the condensation energy for a non-interacting mixture of paired fermions (Cooper pairs, which we assume to be composite bosons) and unpaired fermions, trapped in a periodic multilayer structure generated by applying an external Dirac’s delta comb potential in the direction perpendicular to the planes, while in the other two directions parallel to the planes the mixture is free. The total energy of the bosons or fermions is a sum of the energy in their perpendicular motion, which satisfies the Kronig-Penney relation [1], plus the energy associated with their motion parallel to the planes, which for fermions has a quadratic dispersion relation while Cooper pairs have a linear-energy-momentum relation [2]. We show that the condensation energy defined as E_c (T ) = F_n (T ) − F_s (T ), where F_n (T ) and F_s (T ) are the normal and superconducting Helmholtz free energies, respectively, qualitatively reproduces that of optimally doped cuprate superconductors. Moreover, by adjusting the delta strength, the separation between contiguous deltas and the fraction of paired fermions we qualitatively reproduce both the critical temperature and the condensation energy within the order of magnitude for some cuprate superconductors, which we compare with the available experimental data [3].

References

1. R. de L. Kronig & W. G. Penney, Proc. Roy. Soc. (London) A 130, 499 (1931)

2. S.K. Adhikari, M. Casas, A. Puente, A. Rigo, M. Fortes, M.A. Solís, M. de Llano, A.A. Valladares, and O. Rojo, Phys. Rev. B 62 8671 (2000)

3. J. S. Kim, G. N. Tam, & G. R. Stewart, Phys. Rev. B 92, 224509 (2015)