Study of inhomogeneous superconductivity in the Bogoliubov formulation

Grzegorz Litak A, Paul C. Miller, Balazs L. Gyorffy

Paul R. Auvil

Karan Aryanpour, Elbio R. Dagotto, Matthias Mayr +3 more

Inhomogeneous $s$-wave superconductivity is studied in the two-dimensional, square lattice attractive Hubbard Hamiltonian using the Bogoliubov-de Gennes (BdG) mean field approximation. We find that at weak coupling, and for densities mainly below half-filling, an inhomogeneous interaction in which the on-site interaction ${U}_{i}$ takes on two values, ${U}_{i}=0,\phantom{\rule{0.3em}{0ex}}2U$ results in a larger zero temperature pairing amplitude, and that the superconducting ${T}_{c}$ can also be significantly increased, relative to a uniform system with ${U}_{i}=U$ on all sites. These effects are observed for stripe, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. Monte Carlo calculations which reintroduce some of the fluctuations neglected within the BdG approach see the same effect, both for the attractive Hubbard model and a Hamiltonian with $d$-wave pairing symmetry.

Lucian Covaci, F. Marsiglio

Kouji Nakamura, Hiroomi Umezawa, Y. Yamanaka

The recently developed formulation of time-dependent non-equilibrium thermofield dynamics (TFD) is extended to spatially inhomogeneous field systems in this paper. This inhomogeneous formalism is constructed from introducing momentum mixing thermal Bogoliubov transformation. The momentum mixing number density in the Bogoliubov matrix is related to the number density distribution defined at each space-time point which is to be observed.

Lucian Covaci, François Maria Peeters, Mona Berciu

We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Green's functions of a superconductor. Broken translational invariance of any type (impurities, surfaces, or magnetic fields) can be easily incorporated. We show that limitations due to system size can be easily circumvented and therefore this method opens the way for the study of scenarios and/or geometries that were unaccessible before. The proposed method is highly efficient and amenable to large scale parallel computation. Although we only use it in the context of superconductivity, it is applicable to other inhomogeneous mean-field theories.