Juha Kopu

Dynamics of vortices and interfaces in superfluid 3he

Rapid new developments have occurred in superfluid hydrodynamics since the discovery of a host of unusual phenomena which arise from the diverse structure and dynamics of quantized vortices in 3He superfluids. These have been studied in rotating flow with NMR measurements which at best provide an accurate mapping of the different types of topological defects in the superfluid order parameter field. Four observations are reviewed here: (1) the interplay of different vortex structures at the first-order interface between the two major superfluid 3He phases, 3He-A and 3He-B; (2) the shear flow instability of this phase boundary, which is now known as the superfluid Kelvin–Helmholtz instability; (3) the hydrodynamic transition from turbulent to regular vortex dynamics as a function of increasing dissipation in vortex motion; and (4) the peculiar propagation of vortex lines in a long rotating column which even in the turbulent regime occurs in the form of a helically twisted vortex state behind a well-developed vortex front. The consequences and implications of these observations are discussed, as inferred from measurements, numerical calculations and analytical work.

Critical Velocity of Vortex Nucleation in Rotating Superfluid {sup {bold 3}}He-A

We have measured the critical velocity {upsilon}{sub c} at which {sup 3}He{minus}A in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that {upsilon}{sub c} is distributed between a maximum and a minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentun axis {bold {cflx l}}({bold r}) in the cylinder. Slow cooldown through T{sub c} in rotation yields {bold {cflx l}}({bold r}) textures for which the measured {upsilon}{sub c} {close_quote}s are in good agreement with the calculated instability of the expected {bold {cflx l}} texture. {copyright} {ital 1997} {ital The American Physical Society}

Proximity effect and multiple Andreev reflections in diffusive superconductor-normal-metal-superconductor junctions

We present a theory of the current-voltage characteristics in diffusive superconductor-normal-metal-superconductor junctions. By solving the time-dependent Usadel equations we are able to describe the phase-coherent transport for arbitrary length of the normal wire. We show how the interplay between proximity effect and multiple Andreev reflections gives rise to a rich subgap structure in the conductance and how it is revealed in the non-equilibrium distribution function.

Vortex multiplication in applied flow: A precursor to superfluid turbulence.

A surface-mediated process is identified in 3He-B which generates vortices at a roughly constant rate. It precedes a faster form of turbulence where intervortex interactions dominate. This precursor becomes observable when vortex loops are introduced in low-velocity rotating flow at sufficiently low mutual friction dissipation at temperatures below 0.5Tc. Our measurements indicate that the formation of new loops is associated with a single vortex interacting in the applied flow with the sample boundary. Numerical calculations show that the single-vortex instability arises when a helical Kelvin wave expands from a reconnection kink at the wall and then intersects again with the wall.

One-dimensional textures and critical velocity in superfluid3He−A

We study theoretically the stability of flow in superfluid 3He-A. The calculations are done using a one-dimensional model where the order parameter depends only on the coordinate in the direction of the superfluid velocity v_s. We concentrate on the case that the external magnetic field H is perpendicular to v_s, where only few results are available analytically. We calculate the critical velocity v_c at which the superflow becomes unstable against the formation of continuous vortices. The detailed dependence of v_c on the temperature and on the form of the underlying orbital texture l(r) is investigated. Both uniform and helical textures and two types of domain-wall structures are studied. The results are partially in agreement with experiments made in a rotating cylinder.

NMR Line Shape of Rotating 3He-B at Large Counterflow Velocity

We have investigated the NMR line shapes of superfluid 3He-B in a rotating cylinder. In the vortex-free state at sufficiently large angular velocity of rotation, Ω≳1 rad/s, the main feature of the absorption spectrum is a large frequency-shifted peak above the Larmor frequency. The shape of this counterflow peak is both measured and calculated as a function of external magnetic field strength, angular velocity, temperature, and number of vortex lines. The NMR spectrum is derived from the calculated order-parameter texture. Reasonable agreement with the measured line shape is obtained by including line-broadening effects due to the external field inhomogeneity and Leggett–Takagi relaxation.

Precessing Vortex Motion and Instability in a Rotating Column of Superfluid 3He-B

In a rotating circular cylinder of superfluid 3He-B, an evolving vortex expands longitudinally such that its end point describes a helically spiralling trajectory along the cylinder wall. The spiral motion is found to give rise to a periodically oscillating NMR signal, which is brought about by the modulation in the superfluid counterflow and its influence on the “flare-out” order parameter texture. The new NMR signal becomes observable within a narrow temperature interval close to the onset temperature of turbulence, when new vortices are continuously generated by the single-vortex instability at the cylindrical wall at a slow rate, ∼1 vortex/s. We use numerical vortex filament calculations to examine the precessing motion of the evolving vortices, while they expand towards their stable state as rectilinear line vortices.

Superconducting proximity effect through a magnetic domain wall

We study the superconducting proximity effect in a superconductor-ferromagnet-superconductor (SFS) heterostructure, containing a domain wall in the ferromagnetic region. For the ferromagnet we assume an alloy with an exchange splitting of the conduction bands comparable to the superconducting gaps. We calculate the modification of the density of states in the center of the domain wall as a result of the proximity effect. We show that the density of states is sensitive to domain wall parameters due to triplet-pairing correlations created in vicinity of the domain wall. We present a theoretical tool which in a very effective way enables retaining the full spatially dependent spin-space structure of the problem.

Onset of Turbulence in Superfluid 3He‐B and its Dependence on Vortex Injection in Applied Flow

Vortex dynamics in 3He‐B is divided by the temperature dependent damping into a high‐temperature regime, where the number of vortices is conserved, and a low‐temperature regime, where rapid vortex multiplication takes place in a turbulent burst. We investigate experimentally the hydrodynamic transition between these two regimes by injecting seed vortex loops into vortex‐free rotating flow. The onset temperature of turbulence is dominated by the roughly exponential temperature dependence of vortex friction, but its exact value is found to depend on the injection method.

Pseudo-contact angle due to superfluid vortices in 4He

We have investigated spreading of superfluid 4He on top of polished MgF2 and evaporated SiO2 substrates. Our results show strongly varying contact angles of 0–15 mrad on the evaporated layers. According to our theoretical calculations, these contact angles can be explained by a spatially varying distribution of vortex lines, the unpinning velocity of which is inversely proportional to the liquid depth.