Predicted multiple cores of a magnetic vortex threading a two-dimensional metal proximity coupled to a superconductor.

The structure of a proximity induced vortex core in a two-dimensional metallic layer covering a superconducting half-space is calculated. We predict the formation of a multiple vortex core characterized by two-scale behavior of the local density of states. For coherent tunneling between the two-dimensional layer and the bulk superconductor, the spectrum has two subgap branches while for incoherent tunneling only one of them remains. The resulting splitting of the zero-bias anomaly and the multiple peak structure in the local density of states should be visible in the tunneling spectroscopy experiments.

Information flow and optimal protocol for a Maxwell-demon single-electron pump.

We study the entropy and information flow in a Maxwell-demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages, which minimizes irreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems in which barriers between different regions can be manipulated.

Recombination-limited energy relaxation in a Bardeen-Cooper-Schrieffer superconductor.

We study quasiparticle energy relaxation at subkelvin temperatures by injecting hot electrons into an Al island and measuring the energy flux from quasiparticles into phonons both in the superconducting and in the normal state. The data show strong reduction of the flux at low temperatures in the superconducting state, in qualitative agreement with the theory for clean superconductors. However, quantitatively the energy flux exceeds the theoretical predictions both in the superconducting and in the normal state, suggesting an enhanced or additional relaxation process.

BCS Superconductivity of Dirac electrons in graphene layers.

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.

Resonance energy and charge pumping through quantum SINIS contacts.

We propose a mechanism of quantum pumping mediated by the spectral flow in a voltage-biased superconductor/insulator/normal-metal/insulator/superconductor quantum junction and realized via the sequential closing of the minigaps in the energy spectrum in resonance with the Josephson frequency. We show that the pumped dc current exhibits giant peaks at rational voltages.

Giant oscillations of energy levels in mesoscopic superconductors.

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one-dimensional Andreev states in a quantum box and (ii) a single vortex in a mesoscopic cylinder.

Vortex instability and the onset of superfluid turbulence.

Quantized circulation, the absence of Galilean invariance due to a clamped normal component, and the vortex mutual friction are the major factors that make superfluid turbulence behave in a way different from that in classical fluids. The model is developed for the onset of superfluid turbulence that describes the initial avalanchelike multiplication of vortices into a turbulent vortex tangle.

An intrinsic velocity-independent criterion for superfluid turbulence.

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid.

In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing forms of quantized vorticity: sheets displace lines if the frequency of the external drive exceeds a critical limit. The resulting topologically stable state consists of multiple vortex sheets and has much faster dynamics than the state with vortex lines.

Superconducting vortices in ac fields: does the Kohn theorem work?

Electrodynamics of clean pinning-free type II superconductors in the mixed state is derived using the Boltzmann kinetic equations for excitations. The condition of the vortex cyclotron resonance is found. The reason why this resonance does not comply with the Kohn theorem is discussed.