Sebastian Schmidt

We study the effect of electron-electron interactions on transport and thermodynamic properties of small, chaotic metallic grains. Our analysis is based on an effective Hamiltonian that combines a superconducting BCS-like term and a ferromagnetic Stoner-like term originating in pairing and spin-correlations, respectively. This description is valid for disordered systems with a large dimensionless Thouless conductance. In the first part of this thesis we use an exact solution of the many-body Hamiltonian to compute the ground-state phase diagram in the fluctuation-dominated regime, where the single-particle mean level spacing δ is comparable to the bulk BCS pairing gap Δ. We show that pairing and spin exchange correlations can coexist in this regime. We also show that the presence of spin jumps in the ground-state phase diagram is a unique signature of this coexistence and that an external Zeeman field can be used to tune the size of this regime. In the second part of this thesis, we calculate the tunneling conductance for an almost-isolated metallic grain in the Coulomb blockade regime using a rate equation approach. We study the competition of superconductivity and ferromagnetism in the mesoscopic fluctuations of the conductance using random-matrix theory (RMT) and propose statistical signatures of this competition that can be observed experimentally. In the last part of this thesis we study thermal quantities for the pairing Hamiltonian using an auxiliary-field Monte Carlo (AFMC) method. We compare our results with a simple semi-analytic static-path approximation.