1. Nikolai Kopnin Theory Group Dynamics of Superfluid 3 He and Superconductors

2. Research topics in 2005 - 2006  Structure and dynamics of superfluid 3 He: Superfluid turbulence in rotating 3 He-B  Nonequilibrium properties of mesoscopic superconductors: Study of transport characteristics of multiple normal-superconducting tunnel nanostructures Quantum diffraction effects on the Andreev-reflection related properties of superconducting point contacts Andreev states in mesoscopic superconductors: Giant mesoscopic oscillations of the energy levels Resonance charge pumping in quantum SINIS nanostructures

3. 1. Andreev states in mesoscopic superconductors: Vortex in a mesoscopic cylinder [Phys. Rev. Lett. 95, 197002 (2005)] z superflow Bound states in the vortex core in bulk superconductors μ is the angular momentum, n is the radial quantum number

4. (a) R/ξ = 3.5; (b) R/ξ = 4.5. Critical radius is R c /ξ ≈4 Mesoscopic oscillations Mesoscopic cylinder The cylinder radius R is several ξ Vortex core Energy Spectrum Interplay of Andreev and normal reflections

5. Jarillo-Herrero et al., Nature 439, 953 (2006) Carbon nanotube- Ti/Al electrodes InAs semiconductor nanowire- Ti/Al electrodes Doh et al., Science 309, 272 (2005) Delft group Scheme of the device Possible realizations 2. Resonance charge pumping in quantum SINIS nanostructures [Phys. Rev. Lett. 96, 146802 (2006)]

6. Long SINIS junction for constant bias and gate voltages The gaps at φ=0, 2π and φ=π block the spectral flow from  to  Bloch oscillations of supercurrent There is NO dc current if the relaxation on the levels and the interlevel Zener tunneling are absent Josephson frequency Suggestion: let us close the gaps at  k and  k sequentially in time by tuning the gate voltage in resonance with Josephson frequency.

7. Archimedean screw in the energy space! Jacob Leupold. Theatrum Machinarum.

8. Suggestion for experiment Super- current pumped current Tuning the gate voltage Critical current MAR The gate voltage should be varied between two maxima of I c : Expected IV curve for long contact, d>> ξ Resonances, sin α=0 Dc current is N times larger than the supercurrent, where N is the number of levels in the junction 2Δ/e2Δ/e eV m =ћΩ(2m+1)

9. Research plan for 2007-2009  Vortex dynamics in superconductors and in superfluid 3 He: Superfluid turbulence Dynamics of Josephson vortices in layered superconductors and in weak links  Nonequilibrium properties of mesoscopic superconductors: Heat transport in mesoscopic Andreev wires (vortices, etc.) Nonequilibrium transport in SINIS nanostructures Noise in SINIS nanostructures in the presence of interlevel Zener transitions and relaxation

10. N is the normal region (vortex core) Bulk cylinder: R is much larger than ξ Realizations: Vortex, intermediate state, heterostructures Andreev states: Drift velocity The drift velocity is much lower than the Fermi velocity. Transport is much slower than in normal conductors Ongoing research: Heat current in Andreev wires

11. Heat transport through Andreev wires in finite-size superconductors N is the vortex core Mesoscopic cylinder: R is several ξ Interplay of normal and Andreev reflection processes Heat current: Landauer-type theory P is the transmission probability Transfer factor

12. Spectrum in a mesoscopic cylinder (a) R/ξ = 3.5; (b) R/ξ = 4.5. Critical radius is R c /ξ ≈4 Mesoscopic oscillations The transfer factor, i.e., the number of roots of the equation, is the number of conducting modes (channels), times the transmission probability for each channel. It should be much larger due to the mesoscopic oscillations of levels.