New Forms of Superconductivity

Abstract

Flat band superconductivity in strained Dirac materials and transport properties of superconductors with a spin-splitting field are studied in this thesis. Flat band superconductivity is a route to high temperature superconductivity. Strain induced flat band in Dirac materials provides a new mechanism to the flat band superconductivity. Superconductors with a spin-splitting field reveal novel features which do not exist or very small in non spin-split superconductors, for example, longrange spin accumulation and thermoelectric effects. Exploring other effects is beneficial for understanding the transport phenomena in such systems. For the flat band superconductivity in strained Dirac materials, the Bogoliubov-de Gennes equation is used to study the properties of the strained Dirac materials in the superconducting state, including the inhomogeneous pair potential, local density of states and a finite supercurrent. For the superconductors with a spin-splitting field, quasiclassical Green’s function method is used to study the transport properties of such systems. The properties studied in this thesis include those in equilibrium and out of equilibrium. The noncollinearity of the spin-splitting fields between two spin-split superconductors introduces new features to the tunnelling conductance and gives rise to a finite Josephson current in the absence of external voltage. In the presence of a supercurrent, the shortrange charge imbalance is converted to long-range spin accumulation in the presence of a homogeneous spin-splitting field. The inhomogeneous spin-splitting field alters many physical observables, such as the spin current density, domain wall size, and density of states. As a precursor to the domain wall motion in a superconductor with an inhomogeneous spin-splitting field, the domain wall motion in a diffusive weak ferromagnet reveals characteristic features like time dependent domain wall velocity for the force much larger than the torque, and occurring of the intrinsic pinning eventually for the torque much larger then the force. The study on flat band superconductivity in strained Dirac materials show how this model results an inhomogeneous superconductivity, including its various properties. The study on the transport properties of superconductors with a spin-splitting field, by considering the effect of supercurrent, noncollinearity and inhomogeneity of the spin-splitting fields, fill many gaps in the previous research.