Analogy between two-dimensional dislocation systems and layered superconductors

TL;DR

This paper models two-dimensional dislocation systems under external stress by drawing an analogy with layered superconductors, deriving a nonlinear transition temperature equation, and comparing results with existing models for specific materials.

Contribution

It introduces a novel approach linking dislocation systems to layered superconductors and extends previous models using rigorous RG calculations.

Findings

Derived a nonlinear equation for transition temperature under stress.

Compared model predictions with real material data.

Discussed deviations and potential model extensions.

Abstract

We propose a consistent treatment of the applied external stress on a two-dimensional dislocation systems by using the analogy between our model and the layered superconductors. Using the results of a mathematically rigorous, real-space renormalization-group (RG) calculations in the latter model we extend the original model developed by Khantha {\it et al.} From our recursion relations a nonlinear equation is derived for the transition temperature as a function of the applied stress. Our results are compared with the predictions of Khantha's model for three particular materials and the reasons for the deviations are discussed. Possible extensions of our model are outlined.