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Physica B Condensed Matter

Vortices and finite-size scaling of superfluid phase transitions

Gary A. Williams

Published Aug 1, 1990• 12 citations
Publisher
DOI
10.1016/0921-4526(90)90776-q

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In zero magnetic field the ground-state manifold of a ferromagnetic spin-1 condensate is SO(3) and exhibits Z_{2} vortices as topological defects. We investigate the phase-ordering dynamics of this system after being quenched into this ferromagnetic phase from a zero-temperature unmagnetized phase. Following the quench, we observe the ordering of both magnetic and gauge domains. We find that these domains grow diffusively, i.e., with domain size L(t)∼t^{1/2}, and exhibit dynamic scale invariance. The coarsening dynamics progresses as Z_{2} vortices annihilate; however, we find that at finite energy a number of these vortices persist in small clumps without influencing magnetic or gauge order. We consider the influence of a small nonzero magnetic field, which reduces the ground-state symmetry, and show that this sets a critical length scale such that when the domains reach this size the system dynamically transitions in order parameter and scaling behavior from an isotropic to an anisotropic ferromagnetic superfluid.
We have studied the distinctive features of the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability and phase transitions in two-dimensional (2D) mesoscopic superconductors placed in magnetic field of arbitrary orientation and rotating superfluid Fermi gases with imbalanced state populations. Using a generalized version of the phenomenological Ginzburg-Landau theory we have shown that the FFLO states are strongly modified by the effect of the trapping potential confining the condensate. The phenomenon of the inhomogeneous state formation is determined by the interplay of three length scales: (i) length scale of the FFLO instability; (ii) 2D system size; (iii) length scale associated with the orbital effect caused either by the Fermi condensate rotation or magnetic field component applied perpendicular to the superconducting disk. We have studied this interplay and resulting quantum oscillation effects in both superconducting and superfluid finite-size systems with FFLO instability and described the hallmarks of the FFLO phenomenon in a restricted geometry. The finite size of the system is shown to affect strongly the conditions of the observability of switching between the states with different vorticities.