Spatial Structures in a Generalized Ginzburg-Landau Free Energy

TL;DR

This paper investigates spatial structures and energies associated with higher order phase transitions in superconductors, providing theoretical predictions for domain walls, supercurrent effects, and phase slip centers relevant to experimental identification.

Contribution

It introduces a generalized Ginzburg-Landau free energy framework for higher order phase transitions and calculates spatial profiles and energies of various structures in one dimension.

Findings

Domain wall energy scales as a^{p-1/2}

Critical current scales as a^{(2p-1)/2}

Profiles of phase slip centers are characterized

Abstract

Searching for characteristic signatures of a higher order phase transition (specifically of order three or four), we have calculated the spatial profiles and the energies of a spatially varying order parameter in one dimension. In the case of a $p^{th}$ order phase transition to a superconducting ground state, the free energy density depends on temperature as $a^p$, where $a = a_o(1-T/T_c)$ is the reduced temperature. The energy of a domain wall between two degenerate ground states is $\epsilon_p \simeq a^{p-1/2}$. We have also investigated the effects of a supercurrent in a narrow wire. These effects are limited by a critical current which has a temperature dependence $J_c(T) \simeq a^{(2p-1)/2}$. The phase slip center profiles and their energies are also calculated. Given the suggestion that the superconducting transtion in \bkbox, for $x = 0.4$, may be of order four, these predictions have relevance for future experiments.