Vortex Dynamics and the Hall-Anomaly: a Microscopic Analysis

We present a microscopic derivation of the equation of motion for a vortex in a superconductor. A coherent view on vortex dynamics is obtained, in which {\it both} hydrodynamics {\it and} the vortex core contribute to the forces acting on a vortex. The competition between these two provides an interpretation of the observed sign change in the Hall angle in superconductors with mean free path $l$ of the order of the coherence length $\xi$ in terms of broken particle-hole symmetry, which is related to details of the microscopic mechanism of superconductivity.Comment: 12 pages, late

Derivation of the transverse force on a moving vortex in a superfluid

We describe an exact derivation of the total nondissipative transverse force acting on a quantized vortex moving in a uniform background. The derivation is valid for neutral boson or fermion superfluids, provided the order parameter is a complex scalar quantity. The force is determined by the one-particle density matrix far away from the vortex core, and is found to be the Magnus force proportional to the superfluid density.Comment: Latex, 6 page

Universal scaling of the Hall resistivity in MgB2 superconductors

The mixed-state Hall resistivity and the longitudinal resistivity in superconducting MgB2 thin films have been investigated as a function of the magnetic field over a wide range of current densities from 100 to 10000 A/cm^2. We observe a universal Hall scaling behavior with a constant exponent of 2.0, which is independent of the magnetic field, the temperature, and the current density. This result can be interpreted well within the context of recent theories.Comment: 4 page

Phase diagram of turbulence in superfluid 3He-B

In superfluid 3He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52--0.59Tc and has a narrow width of 0.06Tc while at zero pressure turbulence is not observed above 0.45Tc.Comment: To be published in J. Low Temp. Phys. (QFS2004 proceedings

Quasiparticle spectrum of d-wave superconductors in the mixed state: a large Fermi-velocity anisotropy study

The quasiparticle spectrum of a two-dimensional d-wave superconductor in the mixed state, H_c1 << H << H_c2, is studied for large values of the ``anisotropy ratio'' alpha_D = v_F/v_Delta. For a square vortex lattice rotated by 45 degrees from the quasiparticle anisotropy axes (and the usual choice of Franz--Tesanovic singular gauge transformation) we determine essential features of the band structure asymptotically for large alpha_D, using an effective one-dimensional model, and compare them to numerical calculations. We find that several features of the band structure decay to zero exponentially fast for large alpha_D. Using a different choice of singular gauge transformation, we obtain a different band structure, but still find qualitative agreement between the 1D and full 2D calculations. Finally, we distort the square lattice into a non-Bravais lattice. Both the one- and two-dimensional numerical calculations of the energy spectra show a gap around zero-energy, with our gauge choice, and the two excitation spectra agree reasonably well.Comment: 14 pages, 13 figures, revte

Magnetic field effects on the density of states of orthorhombic superconductors

The quasiparticle density of states in a two-dimensional d-wave superconductor depends on the orientation of the in-plane external magnetic field H. This is because. in the region of the gap nodes, the Doppler shift due to the circulating supercurrents around a vortex depend on the direction of H. For a tetragonal system the induced pattern is four-fold symmetric and, at zero energy, the density of states exhibits minima along the node directions. But YBa_2C_3O_{6.95} is orthorhombic because of the chains and the pattern becomes two-fold symmetric with the position of the minima occuring when H is oriented along the Fermi velocity at a node on the Fermi surface. The effect of impurity scattering in the Born and unitary limit is discussed.Comment: 24 pages, 11 Figure

Transition to Superfluid Turbulence

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid 3He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction -- the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of 1/q < 1 the dynamics is vortex number conserving, while at low friction and large 1/q > 1 vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of 3He-A and 3He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin-Helmholtz instability.Comment: Short review; to be published in Journal of Low Temperature Physics (2006

Vortex with Fractional Quantum Numbers in Chiral p-Wave Superconductor

We show that a vortex in a chiral p-wave superconductor, which has the p_{x}+ i p_{y}-wave pairing state and breaks U(1), parity and time reversal symmetry simultaneously, has fractional charge -{n e}/{4} and fractional angular momentum -n^{2}/{16} (n; vorticity). This suggests that the vortex could be anyon and could obey fractional statistics. Electromagnetic property of the vortex is also discussed and we find that an electric field is induced near the vortex core.Comment: 10 pages, 3 figures, accepted for publication in Phys. Rev.