The influence of magnetic field on the superconducting properties and the BCS-BEC crossover in systems with local fermion pairing

TL;DR

This thesis investigates how magnetic fields influence superconductivity and the BCS-BEC crossover in lattice systems with local fermion pairing, using various models and methods across different dimensions and temperature regimes.

Contribution

It provides a comprehensive analysis of the magnetic field effects on superconductivity and the BCS-BEC crossover, extending previous work with new models and beyond mean field approximations.

Findings

Magnetic fields suppress superconductivity in the studied models.

The BCS-BEC crossover behavior is significantly affected by spin polarization.

Critical temperatures are calculated using advanced many-body techniques.

Abstract

The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physics in the ground state. The methods used included: the mean field approximation (BCS-Stoner type) and the estimation of the phase coherence temperature within the Kosterlitz-Thouless (KT) scenario in two dimensions. The BCS-BEC crossover was also analyzed in three dimensions, at finite temperatures, within the spin polarized Attractive Hubbard Model (AHM), going beyond the mean field approximation. In this case, the critical temperatures of the superconducting transition were determined within the self-consistent T-matrix method. The strong coupling expansion was applied to map the spin polarized AHM onto the model of hard-core bosons on the lattice.