Phase-slip Processes Research Articles

End-current injection contacts for anisotropic materials: Fabrication and application to the quasi-one-dimensional conductorNbSe3

We have developed a technique for making low-resistance end-current injection contacts to geometrically, electronically, and mechanically anisotropic crystals of charge-density-wave (CDW) conductors. Transport measurements on $\mathrm{Nb}{\mathrm{Se}}_{3}$ show that contact resistances are reduced by nearly 2 orders of magnitude compared with the standard side-contact geometry, and yield qualitatively similar results for the contact-sensitive phase-slip process. This end-contact technique should be useful for characterizing collective transport in fully gapped CDW conductors such as $\mathrm{Ta}{\mathrm{S}}_{3}$, for studying CDW physics on scales smaller than $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, and more broadly for characterizing other materials with large electronic and mechanical anisotropies.

Resistivity of inhomogeneous superconducting wires

We study the contribution of quantum phase fluctuations in the superconducting order parameter to the low-temperature resistivity $\ensuremath{\rho}(T)$ of a dirty and inhomogeneous superconducting wire. In particular, we account for random spatial fluctuations of arbitrary size in wire thickness. For a typical wire thickness above the critical value for a superconductor-insulator transition, phase-slip processes can be treated perturbatively. We use a memory formalism approach, which underlines the role played by a weak violation of conservation laws in the mechanism for generating finite resistivity. Our calculations yield an expression for $\ensuremath{\rho}(T)$, which exhibits a smooth crossover from a homogeneous to a ``granular'' limit upon increase of $T$, controlled by a ``granularity parameter'' $D$ characterizing the size of thickness fluctuations. For extremely small $D$, we recover the power-law dependence $\ensuremath{\rho}(T)\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ obtained by unbinding quantum phase slips. However in the strongly inhomogeneous limit, the exponent $\ensuremath{\alpha}$ is modified and the prefactor is exponentially enhanced. We examine the dependence of the exponent $\ensuremath{\alpha}$ on an external magnetic field applied parallel to the wire. Finally, we show that the power-law dependence at low $T$ is consistent with a series of experimental data obtained in a variety of long and narrow samples, which earlier studies have attempted to fit by an exponential trial function. The values of $\ensuremath{\alpha}$ extracted from the data, and the corresponding field dependence, are consistent with known parameters of the corresponding samples.

Influence of microwave irradiation on the current inducing phase-slip processes in wide tin films

The temperature dependences of the microwave-enhanced maximum current ImP(T) at which a resistive vortex state exists in wide and thin tin films are investigated experimentally and analyzed. It is shown that the experimentally obtained temperature dependences of the current ImP(T) are well approximated by formulas analogous to that for the equilibrium case of the Aslamazov–Lempitskiĭ theory but with the critical temperature Tc replaced by an enhanced critical temperature TcP, and this is valid for the whole temperature region of existence of the wide-film regime. It is found that with increasing frequency of the irradiation the absolute value of ImP(T) increases, and the temperature region of enhancement of ImP(T) is broadened to lower temperatures.

AC Josephson properties of phase slip lines in wide tin films

Current steps in the current–voltage characteristics of wide superconducting Snfilms exposed to microwave irradiation were observed in the resistive state withphase slip lines. The behavior of the magnitude of the steps with the appliedirradiation power was found to be similar to that for the current steps in narrowsuperconducting channels with phase slip centers and, to some extent, for theShapiro steps in Josephson junctions. This provides evidence for the Josephsonproperties of the phase slip lines in wide superconducting films and supports theassumption about the similarity between the processes of phase slip in wide and narrowfilms.

Negative magnetoresistance and phase slip process in superconducting nanowires

We argue that the negative magnetoresistance of superconducting nanowires, which was observed in recent experiments, can be explained by the influence of the external magnetic field on the critical current of the phase slip process. We show that the suppression of the order parameter in the bulk superconductors made by an external magnetic field can lead to an enhancement of both the first $I_{c1}$ and the second $I_{c2}$ critical currents of the phase slip process in nanowires. Another mechanism of an enhancement of $I_{c1}$ can come from decreasing the decay length of the charge imbalance $\lambda_Q$ at weak magnetic fields because $I_{c1}$ is inversely proportional to $\lambda_Q$. The enhancement of the first critical current leads to a larger intrinsic dissipation of the phase slip process. It suppresses the rate of both the thermo-activated and/or quantum fluctuated phase slips and results in decreasing the fluctuated resistance.

Critical currents of the phase slip process in the presence of electromagnetic radiation: Rectification for time asymmetric ac signal

We studied theoretically the effect of time symmetric and asymmetric electromagnetic (e.m.) radiation on the phase-slip process in superconducting wires in the regime where there is no stimulation of superconductivity. We found that for large amplitudes ${j}^{\mathit{ac}}$ of the symmetric ac signal the value of the lower critical current ${j}_{c1}({j}^{\mathit{ac}})$ at which the voltage vanishes in the sample oscillates as a function of ${j}^{\mathit{ac}}$. The amplitude of these oscillations decays with increasing power of the ac signal, and we explain it either by the existence of a maximal current ${j}_{c3}$ beyond which no phase slips can be created or by a weak heat removal from the sample. Applying an asymmetric in time signal (with zero dc current) we show that it may lead to a finite voltage in the system (i.e., ratchet effect). At high enough frequencies the rectified voltage is directly proportional to the frequency of the applied e.m. radiation. These properties resemble in many aspects the behavior of a Josephson junction under e.m. radiation. The differences are mainly connected to the effect of the transport current on the magnitude of the order parameter.

Dynamical Phase Slipping in Superconducting Nanowires

In the present work a study of resist state dynamics of superconducting nanowires on the basis of simulation of the one-dimensional time-dependent Ginzburg-Landau equation is carried out. The parameter u characterizing the “purity” of a superconducting substance was introduced in this equation. It was found out that an area of the current density, in which a dynamical phase slip process is observed, exists at u > 1. This process depends on the length of the nanowires and is not defined by thermodynamic fluctuations of conductivity and order parameter in contrast to thermal activated phase slips and quantum phase slip mechanisms. Also their arising does not depend on heterogeneity of nanowire substances.

Dissipation in quasi-one-dimensional superconducting single-crystalSnnanowires

Electrical transport measurements were made on single-crystal Sn nanowires to understand the intrinsic dissipation mechanisms of a one-dimensional superconductor. While the resistance of wires of diameter larger than 70 nm drops precipitately to zero at Tc near 3.7 K, a residual resistive tail extending down to low temperature is found for wires with diameters of 20 and 40 nm. As a function of temperature, the logarithm of the residual resistance appears as two linear sections, one within a few tenths of a degree below Tc and the other extending down to at least 0.47 K, the minimum temperature of the measurements. The residual resistance is found to be ohmic at all temperatures below Tc of Sn. These findings are suggestive of a thermally activated phase slip process near Tc and quantum fluctuation-induced phase slip process in the low temperature regime. When the excitation current exceeds a critical value, the voltage-current (V-I) curves show a series of discrete steps in approaching the normal state. These steps cannot be fully understood with the classical Skocpol-Beasley-Tinkham phase slip center model (PSC), but can be qualitatively accounted for partly by the PSC model modified by Michotte et al.

Peierls transition as spatially inhomogeneous gap suppression

We propose a model of the Peierls transition (PT) taking into account amplitude fluctuations of the charge-density waves and spontaneous thermally activated suppression of the Peierls gap, akin to the phase slip process. The activation results in the exponential growth of the normal phase with increasing temperature. The model fairly describes the behavior of resistance, thermal expansion, Young modulus and specific heat both below and above the PT temperature $T_P$. The PT appears to have a unique nature: it does not comprise $T_P$ as a parameter, and at the same time it has features of the 1st order transition. The possible basis for the model is activation of non-interacting amplitude solitons perturbing large volumes around them.

Condition for the occurrence of phase slip centers in superconducting nanowires under applied current or voltage

Experimental results on the phase slip process in superconducting lead nanowires are presented under two different experimental conditions: constant applied current or constant voltage. Based on these experiments we established a simple model which gives us the condition of the appearance of phase slip centers in a quasi-one-dimensional wire. The competition between two relaxations times (relaxation time of the absolute value of the order parameter ${\ensuremath{\tau}}_{|\ensuremath{\psi}|}$ and relaxation time of the phase of the order parameter in the phase slip center ${\ensuremath{\tau}}_{\ensuremath{\varphi}})$ governs the phase slip process. Phase slips, as periodic oscillations in time of the order parameter, are only possible if the gradient of the phase grows faster than the value of the order parameter in the phase slip center, or equivalently if ${\ensuremath{\tau}}_{\ensuremath{\varphi}}<{\ensuremath{\tau}}_{|\ensuremath{\psi}|}.$

Coulomb blockade of phase slip in mesoscopic charge-density-wave systems

Thermally activated phase-slip processes near electrical contacts are responsible for the nonlinear current–voltage characteristic in clean mesoscopic charge-density-wave systems. We calculate the phase-slip rate for a dislocation-loop nucleation and that for a dislocation-pair nucleation, by taking account of the influence of long-range Coulomb interactions. It is shown that due to a large charging energy associated with dislocation lines, the phase-slip rate is greatly reduced for both the nucleation processes when the applied voltage is smaller than a threshold voltage. This indicates that the collective current below the threshold voltage is strongly suppressed by the Coulomb blockade of the phase slip.

Quantum Nucleation of Phase Slip in Charge-Density-Wave Systems: Role of Long-Range Coulomb Interactions

Phase-slip processes near electrical contacts are responsible for the nonlinear current–voltage characteristic in clean charge-density-wave systems. In the low-temperature regime near absolute zero, the phase slip is induced by dislocation-loop (DL) nucleation due to quantum tunneling. The quantum nucleation rate of the phase slip is calculated at zero temperature by taking account of the Coulomb interaction effect on the DL. It is shown that a large charging energy associated with the DL greatly reduces the nucleation rate in the low-bias regime. Consequently, the current-voltage characteristic, which is determined by the nucleation rate, is shifted to higher voltages compared with that in the absence of the Coulomb interaction. The voltage shift is of the order of \(V_{\text{th}} \sim \gamma \hbar \omega_{\text{p}}/e\) (γ: anisotropy constant, ω p : plasma frequency in the normal state).

Coulomb Blockade of the Collective Current in Charge-Density-Wave Systems

The Coulomb-interaction effect on the phase slip in charge-density-wave (CDW) systems is studied theoretically. Sliding motion of the CDW is accompanied by thermally activated phase-slip processes near electrical contacts. We calculate the thermal nucleation rate of the phase slip taking account of the Coulomb-interaction effect on dislocation loops. We find that the effect manifests itself when the quasiparticle screening length λ qp is much longer than the longitudinal phason screening length λ ph . It is shown that due to a large charging energy associated with the dislocation-loop nucleation, the phase-slip rate is greatly reduced when the applied voltage is smaller than the threshold voltage \(V_{\text{th}} \sim \gamma \hbar v_{\text{F}}/(e \lambda_{\text{ph}})\) (γ: anisotropy constant, v F : Fermi velocity). This indicates that the collective CDW current below the threshold voltage is strongly suppressed by the Coulomb blockade of the phase slip.

Phase Slip in Mesoscopic Charge-Density-Wave Systems

Collective electron transport in mesoscopic charge-density-wave (CDW) systems is studied theoretically. Sliding motion of the CDW is accompanied by thermally activated phase-slip processes near electrical contacts. Each phase-slip event gives rise to an addition or removal of a wavefront, resulting in deformation of the overall phase profile. Since the energy barrier for thermal nucleation of phase-slip centers strongly depends on the phase profile, its deformation affects the phase-slip rate, particularly in small samples. We calculate the nonlinear behavior between the CDW current and the phase-slip voltage V ps , taking account of the small-size effect on the phase-slip rate. Using the parameters for NbSe 3 , we find that the small-size effect reduces V ps when the sample length is smaller than a few micrometers. This behavior is consistent with the recent experiment by Mantel et al. : Phys. Rev. Lett. 84 (2000) 538 for mesoscopic NbSe 3 wires.

Current conversion in the sliding charge density wave state of NbSe 3

High spatial resolution (30–100 μm) X-ray measurements of the satellite positional shift q have been carried out in the upper charge-density-wave state of NbSe 3. We determined the spatial distribution of the CDW plastic deformations between electrodes under applied currents. With direct current we observe a steep exponential decrease of q with position x along the sample near the contacts followed by a linear dependence in the central part of the sample. This second regime is attributed to transverse pinning of the CDW dislocations while the first is dominated by phase slip processes. The observed differences between data from direct current and pulsed current measurements indicate a significant, strongly spatially dependent relaxational behaviour of the CDW deformations.

Temperature-dependent conductivity of ultrasmall Josephson junctions

In this paper we analyse the transport properties of Josephson junctions embedded in an electromagnetic environment caused by pads and leads near to the junctions. At sufficiently low temperatures we find that the conductivity of the Josephson junctions at low bias is strongly suppressed due to the Coulomb blockade of Cooper pair tunnelling. At high enough temperatures, the conductivity of the Josephson junctions is also reduced due to thermal activated phase slip processes. As a consequence, transport of supercurrent with maximal conductivity is reached at an intermediate temperature. The dependence of various transport regimes on the Josephson energy and the charging energy is discussed.

Charge density wave phase slip in the quasi-one-dimensional blue bronze compound K 0.3MoO 3

Summary The electric current transported by sliding Charge Density Wave [CDW]converts into single particle current at current terminals. It is widely accepted now that this conversion is provided by phase slip process; i.e by nucleation and motion of topological defects of the CDW, which develops in close vicinity of current terminals. We report here measurements of the phase slip process in the quasi-one dimensional conductor K 0.3 MoO 3 .

Quantum Phase Slips and Transport in Ultrathin Superconducting Wires

We present a microscopic study of the quantum fluctuations of the superconducting order parameter in thin homogeneous superconducting wires at all temperatures below ${T}_{c}$. The rate of quantum phase-slip processes determines the resistance $R(T)$ of the wire, which is observable in very thin wires, even at low temperatures. Furthermore, we predict a new low-temperature metallic phase below a critical wire thickness in the 10-nm range, in which quantum phase slips proliferate.

Quantum decay of supercurrent in thin superconducting wires

Quantum fluctuations cause a decay of the supercurrent in thin superconducting wires making them resistive even at very low temperatures. We derive a microscopic effective action formalism that goes beyond the usual TDGL approach and study quantum fluctuations of the superconducting order parameter at all temperatures belowTC. We calculate the quantum phase slip rate in thin superconducting wires, demonstrate the importance of dissipation in a quantum phase slip process, and evaluate the resistanceR(T) of the wire. In very thin wires the effect is well observable, even at zero temperature.

Phase-slip processes induced by microwave field and direct current in superconducting ceramic YBa 2 Cu 3 O 7−x

Phase-slip processes induced by microwave field and direct current in superconducting ceramic YBa 2 Cu 3 O 7−x