Connecting the Microscopic and Macroscopic in Unconventional Superconductors

Abstract

In this thesis, a Linked-Cluster Expansion is utilized to derive expressions for the macroscopic Ginzburg-Landau constants in terms of variables connected to the microscopic Bogoliubov Hamiltonian. The resultant Ginzburg-Landau free energy is then numerically minimized in order to study the existence of a local Time-Reversal symmetry breaking state existing at the surface of a superconductor in which both triplet and singlet Cooper pairs can form. Both centrosymmetric and non-centrosymmetric systems are considered. These states are deemed physically achievable, and other features of the system are described and analysed. A brief history of superconductivity and primers on basic techniques used in the examination of many-particle quantum systems are also included. This investigation was motivated by the microscopic study of similar systems by C. Timm, S. Rex, and P. M. R. Brydon in the paper “Surface Instability in Nodal Noncentrosymmetric Superconductors”, published in Phys. Rev. B. vol 91, p. 180503(R), 2015. Although we use a substantially different approach to the problem, we obtain results in great qualitative agreement with Timm et al., as well as providing additional insight into the origin of the local Time-Reversal symmetry breaking state at the surface.