Unconventional vortices and phase transitions in rapidly rotating superfluid 3He

This paper studies vortex-lattice phases of rapidly rotating superfluid 3He based on the Ginzburg-Landau free-energy functional, where strong-coupling effects are included in the pressure dependence of the fourth-order β parameters. To identify stable phases in the p-Ω plane (p=pressure, Ω=angular velocity), the functional is minimized with the Landau-level expansion method using up to 3000 Landau levels. With nine complex order parameters, 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 Ωc2 is neither the Balian-Werthamer state nor the Anderson-Brinkman-Morel state, but the polar state with the smallest superfluid density, as already shown by Schopohl. Thus, multiple phases are anticipated to exist in the p-Ω plane. Six different phases are found in the present calculation performed over 0.0001Ωc2≤Ω≤Ωc2, where Ωc2 is of order (1-T/Tc)x107 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 Ωc2 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 in the angular velocity of order 103-104 rad/s