Session F25: Superconductivity: Mesoscopic and Nanometer Scale

Magnetic Field Reentrant Superconductivity in Aluminum Nanowires*

Reentrance to the superconducting state through the application of a magnetic field to quasi-one dimensional superconductors driven resistive by current, is counter to the expected properties of superconductors. It was not until recently that a microscopic mechanism explaining the phenomenon was proposed in which superconductivity and phase slip driven dissipation coexist in a non-equilibrium state.$^{\mathrm{1}}$ Here we present additional results of magnetic field induced reentrance into the superconducting state in quasi-one-dimensional aluminum nanowires with an in-plane magnetic field both transverse to, and along the wire axis. The reentrant behavior is seen in the magnetic field dependence of the I-V characteristic and resistance vs. temperature, and in the wire's magnetoresistance at 450mK. $^{\mathrm{1}}$Y. Chen, Y-H. Lin, S.D. Snyder, A.M. Goldman and A. Kamenev, Nature Physics 10, 567-571 (2014). * This work was supported by DOE Basic Energy Sciences Grant DE-FG02-02ER46004. Samples were fabricated at the Minnesota Nanofabrication Center. Parts of this work were carried out in the University of Minnesota Characterization Facility, a member of the Materials Research Facilities Network (www.mrfn.org) funded via the NSF MRSEC program.   

Andreev bound state at a strongly correlated oxide interface

Strongly correlated electrons at oxide interfaces give rise to a set of novel physics phenomena including superconductivity and magnetism. At the LaAlO$_3$/SrTiO$_3$ (LAO/STO) interface, signatures of strong electron pairing persist even for conditions where superconductivity is suppressed. Meanwhile, an Andreev bound state (ABS) is a single quasiparticle excitation that mediates pair transport in confined superconductor-normal systems. Here we report a transition from pair resonant transport to ABS in sketched single electron transistors at the LAO/STO interface. This transition is consistent with a change of electron-electron interaction from attractive to repulsive, occurring at or near the Lifshitz transition. Such new electronically tunable electron-electron interaction may be useful for quantum simulation and engineering of novel quantum states in oxide materials.   

Measuring the winding number instability in mesoscopic superconducting rings

In equilibrium, a flux-biased superconducting ring occupies a state that is characterized by the integer winding number of its complex order parameter. Transitions between states of differing winding number occur via phase slips of the order parameter. A number of aspects of these phase slips remain poorly understood, including the particular value of flux bias at which the transition occurs, and the particular state into which the system relaxes. We use cantilever torque magnetometry to address these questions by measuring the equilibrium supercurrent in arrays of isolated aluminum rings over a wide range of applied flux and temperature. We fit the measured supercurrent using one-dimensional stationary Ginzburg Landau theory over the entire field range --$B_{c3}$ \textless $B$ \textless $B_{c3}$ and for $T_{c}$/2 \textless $T$ \textless $T_{c}$. We show that phase slips occur at the critical flux predicted by Ginzburg Landau theory. The value of this critical flux shows the influence of the rings' finite circumference. We find that in all instances the winding number changes by unity; this may be because the dynamics of the switching events are overdamped in these rings.   

Thermally activated phase slips from metastable states in mesoscopic superconducting rings

In equilibrium, a flux-biased superconducting ring at low temperature can occupy any of several metastable states. The particular state that the ring occupies depends on the history of the applied flux, as different states are separated from each other by flux-dependent energy barriers. There is a critical value of the applied flux at which a given barrier goes to zero, the state becomes unstable, and the system transition into another state. In recent experiments performed on arrays of rings we showed that this transition occurs close to the critical flux predicted by Ginzburg-Landau theory. Here, we will describe experiments in which we have extended these measurements to an individual ring in order to study the thermal activation of the ring over a barrier that has been tuned close to zero. We measure the statistics of transitions as function of temperature and ramp rate.   

Superconducting tunneling on thin film gold nanowires -- a platform for searching Majorana fermions

The metallic surface states of (111)-oriented gold thin film has been theoretically shown to be a superior candidate for Majorana fermions (MF) due to its orders of magnitude stronger spin-orbit coupling compared to semiconductor nanowires.[1] We experimentally demonstrate an ideal platform using heterostructure based nanowires for achieving this, and exploit quantum tunneling to probe the MFs forming at the end of the nanowires. By controlling the material properties of the tunnel barrier, we explore the peculiar behaviors of superconducting gold surface states in both pair tunneling (Josephson like) and quasiparticle tunneling regimes that may hint the signatures of MFs. Additionally, in the mesoscopic 1D gold nanowire superconductor, we observe a new superconducting phase with an energy gap much larger than any of the superconductors in the tunneling device, hinting possible unknown pairing mechanism. Our approach directly demonstrates a crucial step in achieving realistic fault-tolerant quantum computation devices based on non-abelian particles. [1] A. C. Potter and P. A. Lee, Phys Rev B 85, 094516 (2012)   

Spins of Andreev states in double quantum dots

Andreev (or Shiba) states in coupled double quantum dots is an open field. Here we demonstrate the realization of Andreev states in double quantum dots in an InSb nanowire coupled to two NbTiN superconductors. The magnetic field dependence of the Andreev states has been explored to resolve the spins in different double dot configurations. The experiment helps to understand the interplay between pair correlation, exchange energy and charging energy with a well-controlled system. It also opens the possibility to implement Majorana modes in Kitaev chains made of such dots.   

Detection of Majorana Kramers pairs using a quantum point contact

We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of $\pi$ across the Josephson junction. We investigate the detection of these Majorana pairs with the integrated QPC, and find a robust switching from normal to Andreev scattering across the edges due to the presence of Majorana Kramers pairs. This transport signature is expected to be exhibited in measurements of differential conductance and/or current cross-correlation at low bias.   

Conductance through a proximitized nanowire in the Coulomb blockade regime

Motivated by recent experiments of the Copenhagen group on InAs nanowires with epitaxial Al [1], we investigate the two-terminal conductance of a strongly proximitized nanowire in the Coulomb blockade regime. We identify the leading electron transport processes at zero applied magnetic field $B$ as well as at finite fields, suppressing the induced gap $\Delta_\textrm{ind}(B)$. In the conventional superconducting phase, the conductance is controlled by the sequential Cooper pair tunneling if $\Delta_\textrm{ind}(B)$ exceeds the charging energy $E_c$, and by the elastic single-electron processes if $\Delta_\textrm{ind}(B) [Preview Abstract]

Time-reversal asymmetry without local moments via directional scalar spin chirality

Quantum phases of matter that violate time-reversal symmetry invariably develop local spin or orbital moments in the ground state. Here, a directional scalar spin chiral order (DSSCO) phase is introduced, that disrespects time-reversal symmetry but has no static moments. It can be obtained by melting the spin moments in a magnetically ordered phase but retaining residual broken time-reversal symmetry. Orbital moments are then precluded by the spatial symmetries of the spin rotation symmetric state. Interestingly, polar Kerr effect in the 3D DSSCO has the same symmetries as those observed experimentally in the pseudogap phase of several underdoped cuprates. Finally, it is shown that the DSSCO provides a phenomenological route for reconciling the results of Kerr effect and nuclear magnetic resonance experiments in the cuprates, with charge ordering tendencies -- observed in X-ray diffraction studies -- playing a crucial role. The so-called "memory effect" in the cuprates can be incorporated into this picture as well.   

Reentrant phase coherence in a quasi-one-dimensional superconductor

Short coherence lengths characteristic of low-dimensional superconductors are related to high critical fields or temperatures. Fatally, such materials are often sensitive to disorder and suffer from phase fluctuations in the order parameter which diverge with temperature $T$, magnetic field $H$ or current $I$. To solve synthesis and fluctuation problems, we propose to build superconductors from inhomogeneous composites of nanofilaments. Single crystals of quasi-one-dimensional Na$_{2-\delta}$Mo$_6$Se$_6$ featuring Na vacancy disorder ($\delta\sim0.2$) behave as percolative networks of superconducting nanowires. Long range order is established via transverse coupling between individual filaments, yet phase coherence is unstable to fluctuations and localization in the zero-($T$,$H$,$I$) limit. A region of reentrant phase coherence develops upon raising ($T$,$H$,$I$) and is attributed to an enhancement of the transverse coupling due to electron delocalization. The observed reentrance in the electronic transport coincides with a peak in the Josephson energy $E_J$ at non-zero ($T$,$H$,$I$). Na$_{2-\delta}$Mo$_6$Se$_6$ is a blueprint for a new generation of low dimensional superconductors with resilience to phase fluctuations at high ($T$,$H$,$I$).   

Probing Andreev and Majorana States with Voltage Pulses

We study the effect of time-resolved voltage pulses applied to normal-insulator-superconductor junctions. With the aid of cutting-edge numerical techniques, we see that applying an alternating train of voltage pulses allows us to manipulate the (Andreev) quasi-bound states that form between the insulator and superconductor. When the superconductor is rendered topologically nontrivial, the presence of a Majorana state gives a zero-bias peak (ZBP) in the conductivity of the junction\footnote{C. Beenakker, Annu. Rev. Condens. Matter Phys., Vol. 4: 113 -136}. We show that by applying different amplitudes/frequencies of voltage pulses we can eliminate or recreate the ZBP and hence probe its Majorana character\footnote{J. Weston et al., Phys. Rev. B \textbf{92}, 020513(R)}. The persistence of this effect in the presence of finite temperature and moderate disorder is promising for the validation of recent experimental results concerning detection of Majoranas in nanowire-superconductor junctions\footnote{V. Mourik et al., Science \textbf{336}, 1003}.   

Large variance of Tc at large length scales in granular mesoscopic Nb islands

Superconductivity in granular mesoscopic islands, in which the average grain size is smaller than the superconducting coherence length, remains largely unstudied. We performed transport measurements of single Nb islands to study the relation between the critical temperature (Tc) and the island diameter. We found that Tc is largely suppressed at scales much larger than the coherence length of Nb. This can be explained by considering a proximity effect between the grains in the island in which the largest grains define the onset of superconductivity. Following this logic, the grain distribution is proportional to the island area and large Tc fluctuations are expected as the diameter of the island decreases. We perform a Tc variance study of large sets of islands at various diameters, and demonstrate an exponential decay relation reaching bulk Nb properties as the island diameter increases.   

Quantum interference in a Cooper pair splitter device

Cooper pair splitting (CPS) is a process in which the electrons of naturally occurring spin singlet pairs in a superconductor are spatially separated using two quantum dots. In the present work we investigate the evolution of the conductance correlations in an InAs nanowire based CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing B field. Our experiments can be understood in a simple 3 site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition CPS devices were developed where the nanowire segments between the two dots were removed, nonlocal measurement on such CPS devices will also be presented.