Superconductivity presents itself many peculiar and interesting properties and has been deeply studied in many materials with different dimensionalities. Nevertheless, new superconductors are emerging regularly with novel phenomena and unknown mechanisms. In this thesis work, I present investigations on superconductivity in several materials: the Nb doped bulk topological insulator (NbxBi2Se3), 2D interfacial superconductor (Bi2Te3/Fe1+yTe) and 1D nanowires (Sn and Al).
A study of the upper critical field transition in Nb doped Bi2Se3 by field-angle-resolved resistive and magnetization measurements will be presented, which clearly shows the two-fold rotational symmetry that could be well explained by nematic superconductivity, spontaneously breaking the three-fold lattice symmetry. Studies of the resistivity, I-V curves and differential conductance on 2D interface of Bi2Te3/Fe1+yTe will be displayed. Our point-contact spectroscopy (PCS) analyzed by the BTK model show a super large twin-gap structure below Tc and a large pseudogap. Pressure effect show an enhanced Tc with different evolutions of the two energy scales, which demonstrates the pressure pushes the interface from the under-doped towards the optimal doped regime by charge transfer. Further PCS of different thicknesses of the samples reveal that the smaller gap only emerges in the phase-coherent superconducting state in Bi2Te3, while the larger gap occurs from the phase-incoherent state, illustrating the unconventional superconductivity. By electrical transport, magnetization and specific heat characterization or PCS, we observed an enhancement superconductivity in Sn or Al nanowires. The former could be explained by an enhanced effective electron-phonon interaction near the surface of Al nanowire and the strong spin orbital coupling in an open Fermi surface, while the latter origins from possible presence of a Van Hove singularity in the electronic density of states in Al nanowires and an enhanced Debye temperature due to a layer of Al2O3 at the surface. The transverse Josephson coupling was also observed in Sn nanowires.