Unconventional Vortices and Phase Transitions in Rapidly Rotating Superfluid ^{3}He

TL;DR

This study explores the complex vortex phases of rapidly rotating superfluid helium-3 using advanced Ginzburg-Landau calculations, revealing multiple exotic vortex structures and phase transitions near critical angular velocities.

Contribution

It introduces a detailed phase diagram of vortex states in superfluid helium-3 under rapid rotation, identifying new vortex structures and their evolution with angular velocity.

Findings

Six distinct vortex phases identified in the p-Omega plane.

The double-core vortex originates from the polar state near Omega_{c2}.

Predicted disappearance of the double-core vortex at high angular velocities.

Abstract

This paper studies vortex-lattice phases of rapidly rotating superfluid ^3He based on the Ginzburg-Landau free-energy functional. To identify stable phases in the p-Omega plane (p: pressure; Omega: angular velocity), the functional is minimized with the Landau-level expansion method using up to 3000 Landau levels. This system can sustain various exotic vortices by either (i) shifting vortex cores among different components or (ii) filling in cores with components not used in the bulk. In addition, the phase near the upper critical angular velocity Omega_{c2} is neither the A nor B phases, but the polar state with the smallest superfluid density as already shown by Schopohl. Thus, multiple phases are anticipated to exist in the p-Omega plane. Six different phases are found in the present calculation performed over 0.0001 Omega_{c2} <= Omega <= Omega_{c2}, where Omega_{c2} is of order (1- T/T_c) times 10^{7} rad/s. It is shown that the double-core vortex experimentally found in the B phase originates from the conventional hexagonal lattice of the polar state near Omega_{c2} via (i) a phase composed of interpenetrating polar and Scharnberg-Klemm sublattices; (ii) the A-phase mixed-twist lattice with polar cores; (iii) the normal-core lattice found in the isolated-vortex calculation by Ohmi, Tsuneto, and Fujita; and (iv) the A-phase-core vortex discovered in another isolated-vortex calculation by Salomaa and Volovik. It is predicted that the double-core vortex will disappear completely in the experimental p-T phase diagram to be replaced by the A-phase-core vortex for Omega >~ 10^{3} ~ 10^{4} rad/s. C programs to minimize a single-component Ginzburg-Landau functional are available at {http://phys.sci.hokudai.ac.jp/~kita/index-e.html}.