Electronic Structure of Vortices in Type-II Superconductors

Dash, Avinash (2022) Electronic Structure of Vortices in Type-II Superconductors. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Avinash Dash (16MS036)) 16MS036_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (5MB)

Abstract

We begin by showing why vortices occur only in a certain category of materials using the phenomenological Ginzburg-Landau (GL) theory and derive the Abrikosov vortex lattice near criticality. Recognising the limitations of the GL-theory in describing microscopic properties of a vortex, we then move on to an analytical treatment of the Boguliubov-de Gennes (BdG) equations to estimate, via a myriad of reasonable assumptions and approximations, the low-lying bound-state eigenspectrum of a single, isolated s-wave vortex core in a 2D disc, as done by Caroli et. al. The analytical treatment has too much simplication to fully describe the features of the cylindrical vortex; hence, we utilize the advantage of numerical simulations as done by Gygi and Schluter to get the full picture of the electronic structure by solving the gap equation self-consistently for a 2D disc, retaining only the fundamental assumptions of the work of Caroli et. al. We present the results along with some fruitful discussions regarding their correctness and some caveats that must be kept in mind when dealing with the numerical procedure. Keeping in mind some of our future prospects, we then use concepts from scattering theory to understand the relationship between the two-body bound state and pairing instability in 2D for a general two-body potential of abstract origin. Motivated by this, we assume a coupling of abstract origin having d-wave symmetry and numerically solve the d-wave gap and density equations in continuum. Analytical solution of the above gap equation is also presented with some interesting and surprising results. Finally, in the same spirit as the Gygi-Schluter procedure, a numerical methodology for a single, isolated d-wave vortex in a 2D disc is presented following a prescription done by Franz and Tesanovic. However, we are yet to present our numerical results for the same.

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