Effects of geometric constraints and sample topology on superconductivity

The goal of this dissertation is to explore the effects of geometric constraints and sample topology on superconductivity. This work started with an effort to explore the possibility of superconductivity within a single unit cell crystalline flake. This represents one form of extreme confinement, such that superconductivity is restricted to a two-dimensional sheet. In this section of the dissertation I focused on the layered superconductor NbSe 2, and successfully measured superconducting single unit cell ake devices. In these devices I show that the superconducting Tc is strongly suppressed as the thickness of the ake is reduced. Furthermore, electrostatic tuning of the charge carrier density in these thin akes of NbSe2 shows stronger than expected Tc modulation. This suggests that a simple single band Bardeen-Cooper-Schrieffer(BCS) model is insufficient to describe the superconductivity in NbS2, possibly due to segregated superconducting bands, charge freezing due to the charge density wave transition(CDW), or a crossover to strongly coupled superconductivity in these ultrathin akes of NbSe2.;In an effort to understand the effects of geometric constraints and sample topology further we performed a series of experiments on lithographically fabricated Aluminum devices. The first of these experiments focused on ultrasmall superconducting squares, with lateral sizes, L, approaching the zero temperature superconducting coherence length, xi(0). Samples of this size should not be able to host a Abrikosov vortex, and the superconducting order parameter cannot widely vary. Therefore in the Ginzburg-Landau theory minimal variation of the order parameter is expected, and these devices approach a 0-dimensional limit. We measured the phase diagrams of samples ranging from 140 nm, the quasi- 0-dimensional squares, to 620 nm, mesoscopic squares which are expected to host vortices, and found that the large samples indeed host few vortex states, while intermediate sized samples show the expected vortex free regime. However for the smallest samples we found an unexpected quantization in the phase diagrams, which possibly suggests novel physics, but is more readily attributed to the influence of the measurement electrodes on the device.;These lithographically fabricated ultrasmall devices provide an experimental system to study the effects of different sample topology. Specifically we focused on nanoscopic loops, where de Gennes predicted that superconductivity could be destroyed when the loop was threaded with half ux quanta, resulting in a "destructive regime." de Gennes also predicted that superconductivity within the destructive regime could be restored by adding a superconducting side branch to the loop. We report the first experimental observation of this effect in these lithographically fabricated loops. Furthermore the experimental design, using a loop rather than a cylinder, allows the study of quantum superconducting fluctuations near the destructive regime.;The strong effect of the side branch on superconductivity in ultra small loops stresses the importance of the topology of the entire device on superconductivity. To gain additional insight into this problem we also studied thin lithographically fabricated superconducting nanowires connected to bulk electrodes. In this system, similar to previous experimental results, we observe a magnetic field enhancement of the superconducting critical current, Ic, which is correlated to the suppression of superconductivity within the bulk electrodes. This non-equilibrium effect we attribute to the diffusion of quasi-particles into and out of the superconducting nanowire, leading to enhanced dissipation and cooling respectively.