Symmetry and structure of quantized vortices in superfluidB3

We present a symmetry classification for the vortices in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. We find that in superfluid ${}_{}{}^3{}_{}{}^{}\mathit{B}$ there may exist five different singly quantized axially symmetric vortex lines, which are different from each other in their internal discrete symmetries. A phenomenological Landau theory is constructed for all the possible phase transitions between the singly quantized axisymmetric vortices. Our detailed numerical calculations of the vortex core structure in the Ginzburg-Landau regime show that the vortex with minimum free energy, the one that we have identified with the vortex actually observed near $T_c$ in the NMR experiments on rotating ${}_{}{}^3{}_{}{}^{}\mathit{B}$, possesses a novel new structure: The discrete broken symmetry in this vortex is space parity P; the vortex has a superfluid core with the A phase and a spontaneously ferromagnetic β phase, which is not known to occur in bulk ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. This core structure explains the measured large magnetic moment of the vortex, and also the orienting effect of the vortices on the ${}_{}{}^3{}_{}{}^{}\mathit{B}$ order parameter in the rotating superfluid through the susceptibility anisotropy. For this superfluid core vortex we find that there exist nodes in the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle energy gap inside a finite radius from the vortex axis. We define the distance—two to three Ginzburg-Landau coherence lengths—at which the nodes first appear as the core radius of the B-phase vortex. Physical properties of vortices with broken symmetry are discussed: The vortices may display a spontaneous electric polarization and/or a spontaneous axial supercurrent, depending on the symmetry of the vortex core matter.