Session S8: Superconductivity Theory: Nano and Mesoscopics

Multiple fluxoid transitions in mesoscopic superconducting rings

We report magnetic measurements of fluxoid transitions in mesoscopic, superconducting aluminum rings over nearly the whole superconducting temperature range. The transitions are induced by applying a flux to the ring so that the induced supercurrent approaches the critical current. Sufficiently close to $T_c$, the fluxoid number $n$ always changes by $\pm$ 1. Upon lowering the temperature, larger changes in $n$ occur. Below approximately 0.3 $T_c$, the final state after a transition is close to the ground state. The dynamics leading to this phenomenon are discussed in terms of the time dependent Ginzburg-Landau theory for gapless and gapped superconductors and a qualitative explanation based on the formation of a local hot spot.   

Imprinting properties of magnetic vortices into superconducting films.

We investigated experimentally the magnetotransport properties of superconducting Al thin films on top of sub-100 nm Fe nanodot arrays. Samples with arrays of single-domain magnetic dots behave similar to plain Al films. A dramatically different behavior is observed for arrays of dots in the so-called magnetic vortex-state. For these, the details of the magnetic reversal are ``imprinted'' into the superconductor and show up in the magnetotransport properties below the superconducting T$_{C}$. The resulting hybrid system shows a giant (up to 10$^{5}$ {\%}) hysteretic magnetoresistance with different reversible/irreversible regimes related to the array's magnetic state. Such controllable effects originate from the stray fields produced by the magnetic vortex cores in the nanodots, which induce a normal/superconducting transition depending on the distribution of the vortex cores polarities.   

Phase diagram and the metallic state in destructive regime in ultrathin doubly connected superconducting Al cylinders

We measured ultrathin, doubly connected superconducting cylinders of Al for which the kinetic energy due to a flux- dependent superfluid velocity, determined by fluxoid quantization, becomes comparable to or higher than the superconducting condensation energy. When the cylinder diameter, $d$, is less than zero-temperature superconducting coherence length, $\xi(0)$, superconductivity is lost around half-integer flux quanta, leading to a destructive regime predicted by de Gennes. Extending our previous work that confirmed de Gennes' prediction, we have discovered the existence of a new phase diagram in which the destructive regime emerges around three-half flux but not half-flux quanta in a cylinder with $d > \xi(0)$, a case not considered by de Gennes. We also measured systematically the resistance in the destructive regime and found that the normal state resistance was fully recovered at $d/\xi(0) \leq 0.77$. The implications of these observations will be discussed.   

Fluctuation Superconductivity in Mesoscopic Quasi-1D Superconducting Rings

We experimentally probe the phase rigidity of quasi-1D superconducting rings in regimes where fluctuation effects are important. The results demonstrate a scanning SQUID microscope technique which can distinguish the field from thermodynamic currents in individual mesoscopic samples from seven orders of magnitude of applied background field. Contrary to earlier results [1] we find agreement with theoretical predictions for phase rigidity when small phase gradients are present around the ring. We show that this theoretical framework can also explain the qualitatively different fluctuations at finite flux $\Phi$ in a regime where the Little-Parks effect is important $T_c(\Phi) < T < T_c(\Phi = 0)$. \\ Reference 1. Xiaxian, Z. and J.C. Price, Susceptibility of a mesoscopic superconducting ring. Physical Review B, 1997. 55(5): p. 3128-40.   

Switching-current distributions for superconducting nanowires.

The decay of metastable states plays a crucial role in the implementation of quantum devices. Switching between the superconducting and resistive states of a superconducting nanowire is an example of such a decay. Here, we report new results on the switching-current distribution measured on amorphous superconducting Mo$_{79}$Ge$_{21}$ and Nb nanowires at various temperatures. A premature switching between the superconducting (V$\sim $0) state and the resistive (V$\sim \Delta )$ state is a stochastic process. To study this process we have performed several thousand measurements at each temperature setting. We observe an anomalous temperature dependence of the switching current distribution. Unlike in other similar measurements, our distribution widens as the temperature is reduced.We have also calculated the escape rates from the superconducting state to the resistive state from these distributions. We discuss the possibility of describing such behavior in terms of thermal and quantum phase slips.   

S-shaped Nonlinearities in the I(V) Characteristic of YBa$_2$Cu$_3$O$_{7-\delta}$ Microstrips Due to the Presence of Phase Slip Lines.

Optimally doped high-$T_c$ superconducting YBa$_2$Cu$_3$O$_{7-\delta}$ microstrips were fabricated using a chemical-free technique based on selective epitaxial growth. Pulsed I(V) measurements of the YBa$_2$Cu$_3$O$_{7-\delta}$ microstrips exhibit steps under current biasing and an s-shaped nonlinearity under voltage biasing. Similar features have been seen in narrow superconductors, where $w < \xi$, and are explained by the formation of phase slip centers. The presence of these features in YBa$_2$Cu$_3$O$_{7-\delta}$ microstrips are indicative of the formation of phase slip lines, 2D analogs of phase slip centers. The evolution of the s-shaped nonlinearity was studied as a function of temperature and applied magnetic field and will be discussed with respect to the stiffness of the phase and the amplitude of the superconducting order parameter in the high-$T_c$ cuprates.   

Microscopic theory of thermal phase slips in clean narrow superconducting wires

We consider structure of a thermal phase-slip center for a simple microscopic model of a clean one-dimensional superconductors in which superconductivity occurs only within one conducting channel or several identical channels. Surprisingly, the Eilenberger equations describing the saddle-point configuration allow for exact analytical solution in the whole temperature and current range. This solution allows us to derive a closed expression for the free-energy barrier, which we use to compute its temperature and current dependences.   

Vortices in superconducting nanoshells.

A nanoshell consists of a nanoscopic grain of insulator (typically Si0$_{2})$ on which a thin layer of metal is deposited. If the material used to make the thin shell is superconducting, the nanoshell itself will exhibit superconducting order. When the superconducting nanoshell is placed in a magnetic field, vortices can be nucleated near the equator of the spherical shell, and will move towards the poles of the nanoshell where they are trapped. Using the Ginzburg-Landau equations adapted for the spherical geometry, we investigate the possibility for giant vorticity and multi-vortex states on thin spherical shells, as a function of shell radius and magnetic field. Furthermore we show that this nanostructure shows potential for flux trapping, as it has a strong magnetization hysteresis.   

Proximity induced superconductivity and multiple Andreev reflections in Graphene

We have investigated electronic transport of a graphene layer connected to superconducting electrodes. The device is prepared by mechanical exfoliation of graphite. A small mesa of graphene is placed on top of a silicon substrate covered by Alumina and 2 electrodes of tungstene separated by 2.5 microns are grown using a focus ion beam. Whereas tungstene electrodes are superconducting below 4K, proximity induced superconductivity in graphene is observed below 1K with a large differential resistance drop at low bias voltage. Signatures of multiple Andreev reflections are observed as peaks located at voltages corresponding to sub-multiple values of 2$\Delta $/e where $\Delta $ is the superconducting gap of the electrodes.   

Size quantization effect in graphite based proximity systems

We discuss size-quantization (SQ) effects in a proximity system made of a graphite thin film deposited onto a superconductor. We show that SQ leads to oscillations of the superconducting critical temperature $T_c$ as a function of the thickness of the graphite layer. This oscillation is due to the peculiar behavior of the density of state in size-quantized systems. The calculated period is directly related to major parameters of the semimetal and thus to the normal state properties of the bilayer. Recent experiments made on graphite/superconductor bilayers are discussed in the framework of the theory.   

Theory of superconductivity in multiwall carbon nanotubes

Recently superconductivity has been observed at 12K in multiwall carbon nanotubes (MWNTs). The key feature in the experimental setup is that almost all the shells in the MWNTs are electrically active. Here we propose a model for the MWNTs where the electrons live in a large number of coupled one- dimensional systems, reminiscent of the hexagonal Fermi surface of the MWNTs. We pay attention to the competition between the screened Coulomb repulsion and phonon-mediated electron- electron interaction. The low-energy behaviour of the model is studied with one-loop renormalization group. We find that by lowering the energy scale the inter-shell Cooper pair tunnelling amplitude grow large, inducing a superconducting instability with p-wave order parameter. The phase diagram shows that the superconducting phase dominates for large radii of the MWNTs and by doping the system. At low doping and small radius a competition with charge density wave instability is observed.   

Synthesis and characterization of superconducting NbN nanowires and nanoribbons

The role of one-dimensional nanostructures has recently gained wide importance due to their novel properties and potential applications in electronics. Here, we report a two-step approach to synthesize one-dimensional superconducting NbN nanowires and nanoribbons by converting NbSe$_{3}$ nanostructures. First, NbSe$_{3}$ nanostructure precursors were prepared by sintering niobium and selenium powders in an evacuated quartz tube. Subsequently, these NbSe$_{3}$ nanostructures were transformed into NbN under an atmosphere of ammonia gas at a reaction temperature of up to 1000 \r{ }C. Superconducting transition temperatures up to 10 K were obtained from both magnetization and four-probe transport measurements. We also carried out morphology and structural characterizations of these NbN nanostructures. This material is based upon work supported by the US Department of Energy, under Award Numbers DE-FG02-06ER46334 and DE-AC02-06CH11357 .   

Magnetoresistance of granular superconductors at low temperatures

I will discuss the resistivity of granular superconductors in the presence of magnetic field at low temperatures. It is assumed that the tunneling between grains is large such that all conventional effects of localization can be neglected. I will show that at low temperatures the superconducting fluctuations reduce the one-particle density of states but do not contribute to transport. As a result the resistivity in the transition region exceeds the normal state value leading to a negative magnetoresistance. I will also analyze the possibility of the formation of a magnetic field induced insulating state in a two dimensional granular superconductors and show that such a state appears in a model with spatial variations of the single grain critical magnetic field. This model describes realistic granular samples with the dispersion in grain sizes and explains a mechanism leading to a giant peak in the magnetoresistance.   

Interplay between electronic transport and mechanical degrees of freedom in metallic atomic-size contacts

Comprehensive measurements of transport properties of the smallest metallic contacts, both in normal and superconducting states, may provide sufficient information to identify their atomic structure. We demonstrated completely reversible mechanical manipulation of the electronic state of niobium atomic-size contacts. This regime includes switching between two distinct configurations manifested as two-level conductance fluctuations. Synergetic first-principles numerical modeling of the structure and transport properties, based on the combination of the Density Functional Theory and Non-Equilibrium Green's Functions formalism, revealed that these contacts consist of niobium dimers trapped between apexes of bulk leads. The observed bistability was associated with the dimer shuttling between a symmetric and an asymmetric configurations in the gap. Point contact spectroscopy of these configurations reveals, on top of the expected signatures due to phonon modes, features, which we associate with the excitation of the vibrational modes of the trapped dimer. Finally, we discuss the evidence that these vibrations can be caused by the intrinsic Josephson radiation.   

Phonon Squeezing in a Superconducting Molecular Transistor

Josephson transport through a single molecule or carbon nanotube is considered in the presence of a local vibrational mode coupled to the electronic charge. The ground-state solution is obtained exactly in the limit of a large superconducting gap and is extended by variational analysis. The Josephson current induces squeezing of the phonon mode, which is controlled by the superconducting phase difference and by the junction asymmetry. Optical probes of nonclassical phonon states are briefly discussed. [Phys. Rev. Lett. 97,196801 (2006)]