The Vortex Phase Diagram of Rotating Superfluid ${}^3$He-B

Abstract

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid ${}^3$He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of ${}^3$He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid ${}^3$He-B. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\,\mbox{G}$ parallel to the rotation axis, $\vec{H}\parallel \vec{\Omega }$, are reported, as well as the supercooling transition line, $T_v^{\ast }(p,H)$. In zero field the vortex phases of ${}^3$He-B are separated by a first-order phase transition line $T_v(p)$ that terminates on the bulk critical line $T_c(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly-quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\beta$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T_v^{\ast }(p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\,\mbox{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating ${}^3$He-B, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating ${}^3$He-B.

arXiv comment14 pages, 11 figures

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