Disorder-induced Inhomogeneities in Strongly Correlated d-wave Superconductors

Chakraborty, Debmalya (2017) Disorder-induced Inhomogeneities in Strongly Correlated d-wave Superconductors. PhD thesis, Indian Institute of Science Education and Research Kolkata.

PDF (PhD thesis of Debmalya Chakraborty (10IP12)) Thesis_Debmalya.pdf - Submitted Version Restricted to Repository staff only Download (5MB)

Abstract

The strong repulsive electron-electron interactions are known to be significant for the hightemperature superconductors as they turn the undoped compound into an insulator. This is quite different from the metallic non-superconducting state of a standard isotropic superconductor. Disorder, on the other hand, is inherent to all real systems, especially high-temperature superconductors. In this thesis, we analyze the complex interplay of the strong correlations and impurities within an inhomogeneous mean field theory augmented with Gutzwiller approximation. Exploring the disorder dependences of the key signatures of superconductivity like off-diagonal long range order, superfluid stiffness and density of states, we show that while strong correlations make superconductivity in this system immune to weak disorder, superconductivity is destroyed efficiently when disorder strength is comparable to the effective bandwidth. Our analysis describes quantitatively how the many body effects of strong electronic repulsions are captured within a one particle Hamiltonian. The initial robustness of superconductivity to weak disorder is attributed to the strong repulsive correlation that smears out charge inhomogeneities by reorganizing the hopping on the bonds of underlying lattice. This prohibits the formation of superconducting “islands". In weak disorder limit, strong interactions are treated non-perturbatively using Schrieffer- Wolff transformation to obtain a low energy effective Hamiltonian and disorder potential is added to this description afterwards, which fails to account for the fact that if the potential difference across a bond is much larger than the hopping scale, it is energetically unfavourable for the electron to hop across that bond. In this thesis, we also consider appropriate extension of Schrieffer-Wolff transformation which builds in the absence of hopping across bonds with large potential difference across them, and thus includes the Anderson mechanism of localization in a more direct way. The suppression of charge motion in regions of strong potential fluctuation leads to formation of Mott insulating patches, which anchor a larger nonsuperconducting region around them. The system thus breaks into islands of Mott insulating and superconducting regions, with Anderson insulating regions occurring along the boundary of these regions. Thus, electronic correlation and disorder, when both are strong, aid each other in destroying superconductivity, in contrast to their competition at weak disorder.

Actions (login required)

View Item