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The stationary SQUID

Berger Jorge
21 Aug 2015 cond-mat.supr-con cond-mat.mes-hall physics.ins-det arxiv.org/abs/1508.05177

In the customary mode of operation of a SQUID, the electromagnetic field in the SQUID is an oscillatory function of time. In this situation, electromagnetic radiation is emitted, and couples to the sample. This is a back-action that can alter the state that we intend to measure. A circuit that could perform as a stationary SQUID consists of a loop of superconducting material that encloses the magnetic flux, connected to a superconducting and to a normal electrode. This circuit does not contain Josephson junctions, or any other miniature feature. We study the evolution of the order parameter and of the electrochemical potential in this circuit; they converge to a stationary regime and the voltage between the electrodes depends on the enclosed flux. We obtain expressions for the power dissipation and for the heat transported by the electric current; the validity of these expressions does not rely on a particular evolution model for the order parameter. We evaluate the influence of fluctuations. For a SQUID perimeter of the order of 1$\mu$m and temperature $0.9T_c$, we obtain a flux resolution of the order of $10^{-5}\Phi_0/$Hz$^{1/2}$; the resolution is expected to improve as the temperature is lowered.

Correlation of the Superconducting Critical Temperature with Spin and Orbital Excitation Energies In (Ca{x}La{1-x})(Ba{1.75-x}La{0.25+x})Cu{3}O{y} as Measured by Resonant Inelastic X-ray Scattering

Ellis David Shai, Huang Yao-Bo, Olalde-Velasco Paul, Dantz Marcus, Pelliciari Jonanthan, Drachuck Gil, Ofer Rinat, Bazalitsky Galina, Berger Jorge, Schmitt Thorsten
09 Aug 2015 cond-mat.supr-con arxiv.org/abs/1508.02021

Electronic spin and orbital (dd) excitation spectra of (Ca{x}La{1-x})(Ba{1.75-x}La{0.25+x})Cu{3}O{y} samples are measured by resonant inelastic x-ray scattering (RIXS). In this compound, Tc of samples with identical hole dopings is strongly affected by the Ca/Ba substitution x due to subtle variations in the lattice constants, while crystal symmetry and disorder as measured by line-widths are x independent. We examine two extreme values of x and two extreme values of hole-doping content y corresponding to antiferromagnetic and superconducting states. The x dependence of the spin mode energies is approximately the same for both the antiferromagnetic and superconducting samples. This clearly demonstrates that RIXS is sensitive to J even in doped samples. A positive correlation between the superexchange J and the maximum of Tc at optimal doping Tc^{max} is observed. We also measured the x dependence of the d_{xy} -> d_{x^2-y^2} and d_{xz/yz} -> d_{x^2-y^2} orbital splittings. We infer that the effect of the unresolved d_{3z^2-r^2} -> d_{x^2-y^2} excitation on Tc^{max} is much smaller than the effect of J. There appears to be dispersion in the d_{xy} -> d_{x^2-y^2} peak of up to 0.05 eV. Our fitting of the peaks furthermore indicates an asymmetric dispersion for the d_{xz/yz} -> d_{x^2-y^2} excitation. A peak at ~0.8 eV is also observed, and attributed to a dd excitation in the chain layer.

Influence of the boundary conditions on the current flow pattern along a superconducting wire

Berger Jorge
26 Jan 2015 cond-mat.supr-con cond-mat.mes-hall arxiv.org/abs/1501.06411

We study the patterns at which the current flow stabilizes in a 1D superconducting wire, for various experimentally reasonable boundary conditions, for small fixed current densities and temperatures close to $T_c$. We pay special attention to the possible existence of a stationary regime. If the contacts are superconducting, truly stationary or normal regimes do not exist, but can be approached as a limit. In the case of weak superconducting contacts, a rich phase diagram is found, with several periodic regimes that involve two phase slip centers. For some of these regimes, the density of Cooper pairs does not have mirror symmetry. If the contacts are normal, the stationary regime is possible.

Qualitative modifications and new dynamic phases in the phase diagram of 1D superconducting wires driven with electric currents

Kallush Shimshon, Berger Jorge
19 May 2014 cond-mat.supr-con arxiv.org/abs/1405.4773

After an initial transient period, the conduction regime in a 1D superconducting wire that carries a fixed current is either normal or periodic or stationary. The phase diagram for these possibilities was studied in Phys. Rev. Lett. {\bf 99}, 167003 (2007) for particular values of the length and the material parameters. We have extended this study to arbitrary length and to a range of material parameters that includes realistic values. Variation of the length leads to scaling laws for the phase diagram. Variation of the material parameters leads to new qualitative features and new phases, including a parameter region in which all three regimes are possible.

Flux-induced Nernst effect in a superconducting loop

Berger Jorge
03 Sep 2013 cond-mat.supr-con cond-mat.mes-hall arxiv.org/abs/1309.0645

When a superconducting ring encloses a magnetic flux that is not an integer multiple of half the quantum of flux, a voltage arises in the direction perpendicular to the temperature gradient. This effect is entirely due to thermal fluctuations. We study the dependence of this voltage on the temperature gradient, flux, position, average temperature, BCS coherence length, thermal coherence length, and the Kramer--Watts-Tobin parameter. The largest voltages were obtained for fluxes close to $0.3\Phi_0$, average temperatures slightly below the critical temperature, thermal coherence length of the order of the perimeter of the ring and BCS coherence length that is not negligible in comparison to the thermal coherence length. As a rough comparison between the flux-induced and the field-induced effects, we also considered a two dimensional sample.

Characterization of the spontaneous symmetry breaking due to quenching of a one-dimensional superconducting loop

Berger Jorge
05 Jan 2013 cond-mat.stat-mech cond-mat.mes-hall cond-mat.supr-con arxiv.org/abs/1301.0912

We study the final distribution of the winding numbers in a 1D superconducting ring that is quenched through its critical temperature in the absence of magnetic flux. The study is conducted using the stochastic time-dependent Ginzburg--Landau model, and the results are compared with the Kibble--Zurek mechanism (KZM). The assumptions of KZM are formulated and checked as three separate postulates. We find a characteristic length and characteristic times for the processes we study. Besides the case of uniform rings, we examined the case of rings with several weak links. For temperatures close or below $T_c$, the coherence length does not characterize the correlation length. In order to regard the winding number as a conserved quantity, it is necessary to allow for a short lapse of time during which unstable configurations decay. We found criteria for the validity of the 1D treatment. The is no lower bound for final temperatures that permit 1D treatment. For moderate quenching times $\tau_Q$, the variance of the winding number obeys the scaling $< n^2>\propto \tau_Q^{-1/4}$, as predicted by KZM in the case of mean field models; for $\tau_Q\alt 10^5\hbar /k_BT_c$, the dependence is weaker. We also studied the behavior of the system when fluctuations of the gauge field are suppressed, and obtained that the scaling $< n^2>\propto \tau_Q^{-1/4}$ is obeyed over a wider range.

Parallel and Perpendicular Susceptibility Above $T_{c}$ in La$_{2-x}$Sr$_{x}$CuO$_{4}$ Single Crystals

Drachuck Gil, Shay Meni, Bazalitsky Galina, Berger Jorge, Keren Amit
02 Nov 2011 cond-mat.supr-con arxiv.org/abs/1111.0470

We report direction-dependent susceptibility and resistivity measurements on La${2-x}$Sr${x}$CuO${4}$ single crystals. These crystals have rectangular needle-like shapes with the crystallographic "c" direction parallel or perpendicular to the needle axis,which, in turn, is in the applied field direction. At optimal doping we find finite diamagnetic susceptibility above $T{c}$, namely fluctuating superconductivity (FSC), only when the field is perpendicular to the planes. In underdoped samples we could find FSC in both field directions. We provide a phase diagram showing the FSC region, although it is sample dependent in the underdoped cases. The variations in the susceptibility data suggest a different origin for the FSC between underdoping (below 10%) and optimal doping. Finally, our data indicates that the spontaneous vortex diffusion constant above $T_c$ is anomalously high.

Supercurrent fluctuations in short filaments

Berger Jorge
11 Sep 2011 cond-mat.supr-con cond-mat.mes-hall cond-mat.stat-mech arxiv.org/abs/1109.2334

We evaluate the average and the standard deviation of the supercurrent in superconducting nanobridges, as functions of the temperature and the phase difference, in an equilibrium situation. We also evaluate the autocorrelation of the supercurrent as a function of the elapsed time. The behavior of supercurrent fluctuations is qualitatively different from from that of the normal current: they depend on the phase difference, have a different temperature dependence, and for appropriate range their standard deviation is independent of the probing time. We considered two radically different filaments and obtained very similar results for both. Fluctuations of the supercurrent can in principle be measured.

Fluctuations in superconducting rings with two order parameters

Berger Jorge,
14 May 2011 cond-mat.supr-con cond-mat.mes-hall cond-mat.stat-mech arxiv.org/abs/1105.2869

Starting from the Ginzburg-Landau energy functional, we discuss how the presence of two order parameters and the coupling between them influence a superconducting ring in the fluctuative regime. Our method is exact, but requires numerical implementation. We also study approximations for which some analytic expressions can be obtained, and check their ranges of validity. We provide estimates for the temperature ranges where fluctuations are important, calculate the persistent current in magnesium diboride rings as a function of temperature and enclosed flux, and point out its additional dependence on the cross-section area of the ring. We find temperature regions in which fluctuations enhance the persistent currents and regions where they inhibit the persistent current. The presence of two order parameters that can fluctuate independently always leads to larger averages of the order parameters at Tc, but only for appropriate parameters this yields larger persistent current. In cases of very different material parameters for the two coupled condensates, the persistent current is inhibited.

Derivation of the Langevin equation from the principle of detailed balance

Berger Jorge
03 Sep 2009 cond-mat.stat-mech arxiv.org/abs/0909.0579

For a system at given temperature, with energy known as a function of a set of variables, we obtain the thermal fluctuation of the evolution of the variables by replacing the phase-space with a lattice and invoking the principle of detailed balance. Besides its simplicity, the asset of this method is that it enables us to obtain the Langevin equation when the phase-space is anisotropic and when the system is described by means of curvilinear coordinates. As an illustration, we apply our results to the Kramer--Watts-Tobin equation in superconductivity. The choice between the It\^{o} and the Stratonovich procedures is discussed.