Instability and Fluctuations of Flux Lines with Point Impurities in a Parallel Current

TL;DR

This paper investigates how point impurities and parallel currents destabilize flux lines in superconductors, showing that impurities do not stabilize flux lines but delay their instability, with detailed analytical and numerical analysis of the fluctuations involved.

Contribution

It provides a combined analytical and numerical study of flux line stability under impurities and current, revealing the delayed onset of instability and the destruction of long-range order.

Findings

Impurities increase flux line fluctuations but do not stabilize them.

Parallel current destabilizes flux lines, with instability delayed by large potential barriers.

Short-range order is destroyed by impurities, thermal fluctuations, and current.

Abstract

A parallel current can destabilize a single flux line (FL), or an array of FLs. We consider the effects of pinning by point impurities on this instability. The presence of impurities destroys the long-range order of a flux lattice, leading to the so called Bragg glass (BrG) phase. We first show that the long-range topological order of the BrG is also destroyed by a parallel current. Nonetheless, some degree of short-range order should remain, whose destruction by thermal and impurity fluctuations, as well as the current, is studied here. To this end, we employ a cage model for a single FL in the presence of impurities and current, and study it analytically (by replica variational methods), and numerically (using a transfer matrix technique). The results are in good agreement, and in conjunction with a Lindemann criterion, provide the boundary in the magnetic field--temperature plane for destruction of short-range order. In all cases, we find that the addition of impurities or current (singly or in combination) leads to further increase in equilibrium FL fluctuations. Thus pinning to point impurities does not stabilize FLs in a parallel current $j_z$, although the onset of this instability is much delayed due to large potential barriers that diverge as $j_z^{-\mu}$.