Session X21: Fluctuation Phenomena (noise, nonequilibrium effects, localization effects)

Fluctuoscopy of Disordered Two-Dimensional Superconductors

In this talk I will present our results for the fluctuation conductivity (FC) in disordered two-dimensional superconductors placed in a perpendicular magnetic field. In our works [1,2] we finally derived the complete solution in the temperature-magnetic field phase diagram. The obtained expressions allow both to perform straightforward (numerical) calculation of the FC surface $\delta\sigma(T,H)$ and to get all 27 asymptotic expressions in the seven qualitatively different domains of the phase diagram. This surface becomes in particular non-trivial at low temperatures, where it is trough-shaped and close to the quantum phase transition non-monotonic, in agreement with experimental findings. I will show our main results and demonstrate how these can be used as a high precision tool (fluctuoscope) to determine the critical temperature, critical magnetic field, and dephasing time from experimental data in superconducting films. \\[4pt] [1] A. Glatz, A. A. Varlamov, and V. M. Vinokur, EuroPhys. Lett. {\bf 94}, 47005 (2011).\\[0pt] [2] A. Glatz, A. A. Varlamov, and V. M. Vinokur, Phys. Rev. B {\bf 84}, 104510 (2011).   

Majorana modes in a superconducting wire with quasiperiodic and

We present a systematic study of the role quasiperiodic and disordered potentials play in the topology of 1D $p$-wave superconducting systems based on a lattice model which we analyze using a transfer matrix approach. We employ a similarity transformation to demonstrate that the existence of Majorana modes is intimately connected to the band structure of the corresponding normal state system (i.e one which, though otherwise identical, lacks superconducting order). We illustrate this correspondence using the case of an electron moving in a quasiperiodic potential. The Hamiltonian of this system is the so-called ``almost Mathieu operator'' whose bulk spectrum (for a certain choice of parameters) is described by a fractal known as Hofstadter's butterfly. Specifically, we prove that states belonging to this spectrum host end Majoranas for arbitrarily weak superconductivity and that increasing the magnitude of the superconducting gap causes these topologically non-trivial regions of the phase diagram to expand and fill in the butterfly. We show that similar considerations give us excellent theoretical control over the topological phase diagram of systems with disordered potentials.   

A Preformed Pair Approach to Diamagnetism in the Cuprates

Enhanced diamagnetism extending beyond the critical regime is associated with the pseudogap. It has been one of the key experiments supporting the precursor superconductivity scenario for this normal state gap. In this talk we demonstrate how non-condensed pairs (rather than normal state vortices) yield a large low field diamagnetic signal. Our work is based on a 3d BCS-BEC crossover scenario where the diamagnetic susceptibility calculation is well controlled and built on a sum-rule compatible correlation function approach. We demonstrate reasonable semi-quantitative agreement with experiment, with no adjusted parameters.   

Transport theory of superconductors in paramagnetic limit

We report on the study of the quantum phase transition from metastable normal to superconductive state in thin films driven by in-plane magnetic field. In this system resistivity exhibits hysteresis at low temperature when the strong Zeeman field is gradually turned off and on. Quantum fluctuations smear the transition form the metastable normal state to paramagnetically limited superconductivity. The typical energy scale for fluctuations is $\bar{\Omega}=\sqrt{E_z^2 - \Delta^2}$, where $E_z$ is the Zeeman energy and $\Delta$ is zero temperature gap. At the onset of the transition $\bar{\Omega}\rightarrow 0$ quantum fluctuations cause non-analytic corrections to the conductivity. The most singular corrections are presented. The result is strongly sensitive to the strength of the spin-orbit scattering. We argue that our theory qualitatively agrees with experimental findings provided the spin-orbit scattering is taken into account.   

Proliferation of mesoscopic effects in transport of superconductors

Universality of conductance fluctuations is the hallmark of mesoscopic physics. This phenomenon emerges from the quantum coherence of electron trajectories and is sensitive to changes in external magnetic field or gate voltage. There exists compelling physical evidence, ranging from the experiments in sub-micron scale superconducting rings to granular films driven across superconductor-insulator transition, that the role of mesoscopic fluctuations proliferate in the presence of superconducting correlations. We thus study theoretical the fate of universality of mesoscopic fluctuations in superconductors focusing on the kinetic characteristics such as conductance, thermopower, NMR relaxation rate, spin susceptibility etc.   

Superconducting fluctuation regime in the cuprates revealed by torque magnetometry

The extent of the superconducting fluctuation regime in the normal state of the cuprate superconductors has remained unclear. For the single-CuO$_{2}$-layer compounds La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO) and Bi$_{2}$(Sr,La)$_{2}$CuO$_{6+\delta }$ (Bi2201), one class of experiments indicates characteristic temperatures as high as 2-3 times $T_{c}$ at optimal doping, whereas a second class reveals superconducting fluctuations in a relatively narrow temperature range above $T_{c}$. Here we report a systematic torque magnetometry study of the superconducting fluctuation regime in three single-layer compounds, LSCO, Bi2201 and HgBa$_{2}$CuO$_{4+\delta }$. We find in all three cases that the regime of fluctuating diamagnetism is narrow and closely tracks the doping dependence of $T_{c}$, consistent with the second class of experiments [1]. The seemly controversial results can be understood if short-range phase correlations develop only in the vicinity of $T_{c}$, whereas local pair formation appears at a relatively high temperature that is universal among all single-layer cuprates. \\[4pt] [1] G. Yu, D.-D. Xia, N. Bari\v{s}ic, R.-H. He, N Kaneko, Yangmu Li, Yuan Li, T. Sasagawa, A. Shekhter, X. Zhao and M. Greven, unpublished   

The potential for persistent current measurements in mesoscopic rings of underdoped cuprates

Dimensionality, disorder, order parameter symmetry, competing phases, quantum critical points, thermal phase fluctuations, and quantum phase fluctuations all play a role in the physics of the underdoped cuprates. Measurements of the persistent current in mesoscopic rings near phase transitions can provide valuable information about underlying coherent states. We evaluate the prospects for such measurements in the underdoped cuprates, considering both likely signatures of various theoretical scenarios and experimental feasibility in terms of fabrication and signal levels.   

Cantilever torque magnetometry study of multiply connected BSCCO arrays near Tc

The goal of this work is to study the superconducting coherence length in the fluctuation regime in cuprate superconductors. In this work we present cantilever torque magnetometry measurements of micron-size BSCCO flakes patterned with arrays of nanometer scale rings or holes. Using ultrasensitive dynamic torque magnetometry, oscillations in magnetization are observed near Tc as a function of the applied magnetic flux threading the array. Special effort was made to detect the oscillations in magnetization at temperatures above Tc, where the Nernst effect and magnetization measurements suggest the possibility of pairing. To constrain the magnitude of the coherence length in the fluctuation regime, we will present the dependence of the amplitude of the h/2e period oscillations as a function of temperature and hole size.   

Properties of ultrathin Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ films grown by pulsed laser deposition

Thermal and quantum fluctuations in superconductors are expected to grow as film thickness decreases. Such behavior has been observed in YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ (YBCO) films as thickness is reduced to two unit cells. In particular, a Kosterlitz-Thouless like drop in superfluid density appears and shows that 2D fluctuations are correlated through the YBCO film thickness. Since Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ (Bi-2212) plays such a prominent role in important ARPES and Scanning Probe measurements of the superconducting gap, it is important to see how this compound behaves in reduced dimensions. To that end, we are working to grow films of Bi-2212 as thin as possible, by pulsed laser deposition in on-axis and off-axis geometries. One goal is to look for the KT transition in the superfluid density, to see whether 2D fluctuations are correlated layer-to-layer even in this highly anisotropic compound, and complement the cuprate picture dominated by the wealth of YBCO data. This requires films to be quite homogeneous. To effectively improve homogeneity, we focus the ac magnetic field of our two-coil measurement system by masking the film of interest with a thick superconducting film with a hole etched through it. Thus, the film area probed is greatly reduced and transition widths are narrowed.   

Ghost critical field and weak localization phenomena in superconducting Tantalum Nitride films

We study the appearance of superconducting fluctuations and weak localization effects in disordered conducting thin films using magnetotransport measurements. At temperatures above Tc, we observe a positive magnetoresistance that is 4 orders of magnitude larger than the predicted classical effect. Well above Tc this behavior is consistent with the magnetic field dependence of localization quantum corrections to the conductivity in the presence of strong spin-orbit scattering. Close to Tc the observed magnetoresistance is well described by theories that describe both localization and superconducting fluctuations effects. This analysis allows for careful study of the so-called ghost critical field and inelastic scattering rates close to Tc.   

Coexistence of superconducting gap and pseudogap above and below $T_c$ in cuprates

We develop a new method to calculate the full $T$-dependent superconducting (SC) gap from thermodynamic measurements and apply to the cuprates. We find that the SC gap persists high above $T_c$ due to strong SC fluctuations and coexists there with the pseudogap. This allows the (disputed) phase diagram to be mapped more accurately than previously. We apply the results below $T_c$ to understand the doping and temperature evolution of critical currents in practical conductors.   

On-chip detection of photon-assisted shot noise and photocurrent of quantum point contact

We present the first experimental realization of on-chip shot noise detection in capacitively-coupled quantum point contacts (QPCs). The detection is based on the photon-assisted effects. A dc voltage biased QPC: the emitter generates broad frequency current shot noise, inducing voltage fluctuations on the second QPC: the detector. This yields photon induced electron-hole pairs whose partitioning between left and right contact causes a current noise called photon-assisted shot noise (PASN). Alternatively, the electron-hole pairs may also generate a photon-assisted current for energy-dependent transmission. Both the photocurrent and PASN are proportional to the product D(1-D), where D is the transmission of a QPC. Our sample is realized using a set of quantum point contacts positioned onto two separate mesas of a two-dimensional electron gas. The QPC emitter is DC biased and emits high-frequency shot noise that is converted into voltage fluctuations at the QPC detector via an interdigital capacitor, $C$. Two additional QPCs next to the emitter and the detector serve as tunable quantum resistors and are used to control impedance of the circuit. We show that by varying both the emitter and detector transmissions, D$^{E}$, D$^{D}$, the measured current at the QPC detector is proportional to D$^{D}$(1-D$^{D})$ D$^{E}$(1-D$^{E})$ for a given V$_{ds}$, which is in good agreement with the theoretical prediction. This new way of detection should find fundamental applications in electronic quantum physics.   

Direct access to quantum non-Gaussian noise through cross-correlation measurements

Detection of quantum non-Gaussian fluctuations is often difficult since they are dominated by the classical Gaussian noise, and requires the use of high frequency amplifiers. In our work we investigate the possibility to employ the cross-correlation technique in order to overcome these difficulties. We propose to measure the cross-correlator of outputs of a pair of two-level detectors, coupled to the source of fluctuations via an electric circuit. In the weak coupling regime, the noise induces rare stochastic transitions in the detectors, that allows one to perform the long time measurement. The transition rates can be derived from the evolution of the density matrix, calculated to the fourth order in level mixing of the two-level detectors. We express the cross-correlator in terms of these rates, and demonstrate that there is a range of parameters, where the main contribution to the cross-correlator is proportional to the intensity of the quantum non-Gaussian noise.   

Interferometric and Noise Signatures of Majorana Fermion Edge States in Transport Experiments

Domain walls between superconducting and magnetic regions placed on top of a topological insulator support transport channels for Majorana fermions. We propose to study noise correlations in a Hanbury Brown-Twiss type interferometer and find three signatures of the Majorana nature of the channels. First, the average charge current in the outgoing leads vanishes. Furthermore, we predict an anomalously large shot noise in the output ports for a vanishing average current signal. Adding a quantum point contact to the setup, we find a surprising absence of partition noise which can be traced back to the Majorana nature of the carriers.