Katarzyna Czajka

Thermodynamics of the two-dimensional Falicov-Kimball model: A classical Monte Carlo study

The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.

Inhomogeneity-induced enhancement of the pairing interaction in cuprate superconductors.

Scanning tunneling spectroscopy has recently discovered a positive correlation between the magnitude of the superconducting gap and positions of dopant oxygen atoms in Bi-based cuprates. We propose a microscopic mechanism that could be responsible for this effect. In particular, we demonstrate that the dopant-induced spatial variation of the atomic levels always enhances the superexchange interaction.

Interplay between impurities and correlations in superconducting nanorings

The properties of nanoscopic rings with electronic correlations and impurities are analyzed numerically by means of two complementary methods. Namely, we perform exact diagonalization of systems up to several lattice sites and Bogoliubov-de Gennes-equations studies of systems consisting of a few hundred sites. We demonstrate how the properties of the systems are affected by various configurations of impurities for both repulsive and attractive electron-electron interactions. In the case of attractive interaction we show that the nanoscopic properties are mainly determined by the competition between tendencies toward pairing and formation of the density waves. Since the impurities act as pinning centers for the density waves, their configuration determines the result of this competition.

Hofstadter butterfly for a finite correlated system

We investigate a finite two-dimensional system in the presence of external magnetic field. We discuss how the energy spectrum depends on the system size, boundary conditions and Coulomb repulsion. On one hand, using these results we present the field dependence of the transport properties of a nanosystem. In particular, we demonstrate that these properties depend on whether the system consists of even or odd number of sites. On the other hand, on the basis of exact results obtained for a finite system we investigate whether the Hofstadter butterfly is robust against strong electronic correlations. We show that for sufficiently strong Coulomb repulsion the Hubbard gap decreases when the magnetic field increases.