Solutions of the Ginzburg -Landau equations for d -wave superconductors and a proof of their fourfold symmetry
Abstract
In some high-temperature superconductors, d-wave pairing with the quadrapole symmetry dominates over the conventional spherically symmetric s-pairing. The Ginzburg-Landau theory of this superconductive state should involve both s-wave and d-wave order parameters, ψs and ψd. There are two critical transition temperatures for these materials Ts and Td. We study the Ginzburg-Landau equations for these d-wave superconductors. Near the d-wave vortex core, we find fourfold symmetric solutions of the equations. More specifically, as the temperature T ↑ Td in the regime Ts < T < Td, we find a locally unique solution, which is a perturbation of ((d0, A 0), 0), of the Ginzburg-Landau equations. Also, we prove that ψ s = ([special characters omitted]ψd) + O([special characters omitted]) which is conjectured by physicists. Besides, we study the equations without magnetic field cases.
Degree
Ph.D.
Advisors
Phillips, Purdue University.
Subject Area
Mathematics
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