Inhomogenous pairing in a S-wave superconductor

Dey, Soumyajit (2019) Inhomogenous pairing in a S-wave superconductor. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Soumyajit Dey (14MS038)) 14MS038.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

Effect of inhomogeneity on a superconductor under different strength of magnetic and non-magnetic disorder have been discussed in this project. BogoliubovdeGennes mean field approach have been used to self-consistently evaluate the order parameters of a superconducting system on a 2-D square lattice. With increasing disorder, the order parameters and other electronic properties like pairing potential (Δ(ri)), local density of states, particle density etc become inhomogenous and deviates completely from their characteristics at zero disorder. We focused on the statistical measurement of the correlation between pairing potential (Δ(r)) and coherence peak height(N(r;Δ₀)) under different disorder strength. Result shows a linear decrease in linear correlation for increasing disorder, indicating how the dependence between two quantities changes as the system goes through superconductor to insulator transition. Using non-parametric, two sample Ansari-Bradley dispersion test, a comparative study of the effect of disorder for Δ(r) and N(r;Δ₀) for different disorder strength has been done. Creation of vortex lines and effect of magnetic field in a disordered system have also been explored to a certain limit. Similar statistical approach has been used to understand the change in correlation between absolute value of Δ(r) and N(r;Δ₀) to understand the effect of magnetic field in a disordered system. The linear correlation coeffcient shows a positive correlation decreasing quadratically under increasing magnetic field. The statistical measurements show that both these quantities evolves similarly in low disorder regime, however at larger disorder, their distributions are significantly different.

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