Nonequilibrium Quasiparticle Distribution Research Articles

Relaxation and frequency shifts induced by quasiparticles in superconducting qubits

As low-loss nonlinear elements, Josephson junctions are the building blocks of superconducting qubits. The interaction of the qubit degree of freedom with the quasiparticles tunneling through the junction represents an intrinsic relaxation mechanism. We develop a general theory for the qubit decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the qubit properties in devices such as the phase and flux qubits, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and nonequilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible nonequilibrium quasiparticle distribution. We also derive expressions for the shift in qubit frequency in the presence of quasiparticles.

Reversal of Nonlocal Vortex Motion in the Regime of Strong Nonequilibrium

We investigate nonlocal vortex motion in weakly pinning a-NbGe nanostructures, which is driven by a transport current I and remotely detected as a nonlocal voltage V{nl}. At a high I of a given polarity, V{nl} changes sign dramatically. This is followed by V{nl} becoming even in I, with the opposite sign at low and high temperatures T. These findings can be explained by a Nernst-like effect resulting from local electron overheating (low T), and a magnetization enhancement due to a nonequilibrium quasiparticle distribution that leads to a gap enhancement near the vortex core (high T).

Spin Injection and Detection in a Mesoscopic Superconductor at Low Temperatures

We theoretically study nonequilibrium spin transport in a superconducting wire connected by tunnel junctions to two ferromagnetic metal wires, each of which serves as an injector or detector of spin-polarized electron current. We present a set of Boltzmann equations to determine nonequilibrium quasiparticle distributions in this system, and obtain an analytical expression for the nonlocal spin signal in the case of small injection current. It is shown that the quasiparticle distribution in the ferromagnetic metal for detection strongly affects the magnitude of the spin signal. At low temperatures, since nonequilibrium quasiparticles created by the tunneling from the superconductor dominate thermally excited ones, the spin signal becomes independent of temperature. This explains the convergence of the spin signal with decreasing temperature observed in a recent experiment by Poli \textit{et al}.

Theoretical analysis of the operation of the kinetic inductance-based superconducting microwave detector

Nonequilibrium quasiparticle distribution functions that appear in a current-biased thin narrow diffuse superconducting strip under microwave irradiation at a low temperature have been calculated. A change in the kinetic inductance of the strip due to irradiation has been determined. The application of the strip as a microwave detector has been considered and the influence of the nonlinear phonon subsystem of the strip on the magnitude of the response has been found.

Interaction Quench in the Hubbard Model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi-liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is, the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: (i) An initial buildup of correlations where the quasiparticles are formed. (ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. (iii) The long-time limit described by a quantum Boltzmann equation leading to thermalization of the momentum distribution function with a temperature T proportional, variantU.

Rearrangement of the vortex lattice due to instabilities of vortex flow

With increasing applied current, we show that the moving vortex lattice changes its structure from a triangular one to a set of parallel vortex rows in a pinning free superconductor. This effect originates from the change of the shape of the vortex core due to nonequilibrium effects (similar to the mechanism of vortex motion instability in the Larkin-Ovchinnikov theory). The moving vortex creates a deficit of quasiparticles in front of its motion and an excess of quasiparticles behind the core of the moving vortex. This results in the appearance of a wake (region with suppressed order parameter) behind the vortex, which attracts other vortices resulting in an effective direction-dependent interaction between vortices. When the vortex velocity $v$ reaches the critical value ${v}_{c}$, quasiphase slip lines (lines with fast vortex motion) appear, which may coexist with slowly moving vortices between such lines. Our results are found within the framework of the time-dependent Ginzburg-Landau equations and are strictly valid when the coherence length $\ensuremath{\xi}(T)$ is larger or comparable with the decay length ${L}_{\mathit{in}}$ of the nonequilibrium quasiparticle distribution function. We qualitatively explain experiments on the instability of vortex flow at low magnetic fields when the distance between vortices $a⪢{L}_{\mathit{in}}⪢\ensuremath{\xi}(T)$. We speculate that a similar instability of the vortex lattice should exist for $vg{v}_{c}$ even when $al{L}_{\mathit{in}}$.

Symmetric and asymmetric states in a mesoscopic superconducting wire in the voltage-driven regime

The response of a mesoscopic homogeneous superconducting wire, connected with bulk normal metal reservoirs, is theoretically investigated as function of the applied voltage. The finite relaxation length of the nonequilibrium quasiparticle distribution function $\bar{L_E}$ is included where we assumed that our wire is in the dirty limit. We found that {\it both} symmetric and asymmetric states can exist which are characterized by a stationary symmetric and asymmetric distribution of the order parameter with respect to the center of the wire. Current voltage characteristics of the wire with length $L>\bar{L_E}$ being in the symmetric state show a pronounced S-behavior. The asymmetric state may exist only for voltages larger than some critical value and coexist with the symmetric state in a finite voltage interval. For wires with $L \sim \bar{L_E}$ the asymmetric state survives up to higher values of the voltage than the symmetric one and may exist both in the voltage and the current driven regimes. We propose an experiment to observe reversible switching between those stationary symmetric and asymmetric states.

Boltzmann Equations for Spin and Charge Relaxations in Superconductors

In a superconductor coupled with a ferromagnetic metal, spin and charge imbalances can be induced by injecting spin-polarized electron current from the ferromagnetic metal. We theoretically study a nonequilibrium distribution of quasiparticles in the presence of spin and charge imbalances. We show that four distribution functions are needed to characterize such a nonequilibrium situation, and derive a set of linearized Boltzmann equations for them by extending the argument by Schmid and Sch\"{o}n based on the quasiclassical Green's function method. Using the Boltzmann equations, we analyze the spin imbalance in a thin superconducting wire weakly coupled with a ferromagnetic electrode. The spin imbalance induces a shift $\delta\mu$ ($- \delta \mu$) of the chemical potential for up-spin (down-spin) quasiparticles. We discuss how $\delta \mu$ is relaxed by spin-orbit impurity scattering.

A Particle Detector Based on a Double Barrier Josephson Junction

We analyze the performance of a particle detector based on a double-barrier Nb/Al/AlOx/Al/AlOx/Al/Nb junction where the Al trapping layer is embedded between two insulating AlO/sub x/ barriers. Within this layer, a very sharp Andreev bound state (ABS) level E/sub 0/ is formed. Because of a very long recombination time, the charge amplification factor is expected to be 10-100 times larger in the double-barrier detector compared to ordinary single-barrier devices. The double barrier detector also has much higher idle-state subgap resistance at low temperatures. Because the middle Al quasiparticle trap layer is separated from the adjacent layers by two insulating tunneling barriers, the proximity effect is minimized. This provides much better alignment between the maximum of nonequilibrium quasiparticle distribution function and the maximum in the electron density of states. All the factors listed result in much higher sensitivity and the energy resolution of the double barrier Nb-based STJ as compared to their single-barrier analogs.

Optical conductivity in nonequilibriumd-wave superconductors

We consider the optical conductivity of a $d$-wave BCS superconductor in the presence of a nonequilibrium distribution of excess quasiparticles. Two different simplified models used in the past for the $s$-wave case are considered and results compared. In the ${T\phantom{\rule{0.1em}{0ex}}}^{*}$ model of Parker the excess quasiparticles are assumed to be in a thermal distribution at some temperature ${T\phantom{\rule{0.1em}{0ex}}}^{*}$ larger than the equilibrium sample temperature. In the ${\ensuremath{\mu}}^{*}$ model of Owen and Scalapino a chemical potential is introduced to accommodate the excess quasiparticles. Some of the results obtained are specific to the model; most are qualitatively similar in both.

Evidence for an excited nonequilibrium quasiparticle distribution in superconducting tunnel junctions resulting from energy accumulation via sequential tunneling

We have observed experimentally and modeled theoretically a previously unidentified nonequilibrium state in superconducting tunnel junctions. The state occurs in small gap, multiple tunneling junctions, and is caused by the raising in energy of the quasiparticle distribution through multiple cycles of sequential forward- and back-tunneling events. Because of the low-energy gap, quasiparticles may survive in the higher-energy states until they reach the energy threshold for emission of Cooper pair-breaking phonons, leading to generation of further quasiparticles. We modeled the process by solving the coupled system of kinetic equations for interacting quasiparticles and phonons, and studied the effect experimentally in high quality Al and Ta/Al superconducting tunnel junctions in the temperature range 40–300 mK. The distinctive features are large subgap currents exceeding that due to thermal excitations by several orders of magnitude at low temperatures, together with a very sharp onset of current with bias voltage

Relaxation of high-energy quasiparticle distributions: Electron-electron scattering in a two-dimensional electron gas

A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for high-energy quasiparticle distributions. This method is used to explain novel measurements of the non-monotonic energy dependence of the signal of scattered electrons in a 2D system. The observed effect is related to a crossover from the ballistic to the hydrodynamic regime of electron flow.

Supercurrent-induced Peltier-like effect in superconductor/normal-metal weak links

The local nonequilibrium quasiparticle distribution function in a normal-metal wire depends on the applied voltage over the wire and the type and strength of different scattering mechanisms. We show that in a setup with superconducting reservoirs, in which the supercurrent and the dissipative current flow (anti) parallel, the distribution function can also be tuned by applying a supercurrent between the contacts. Unlike the usual control by voltage or temperature, this leads to a Peltier-like effect: the supercurrent converts an externally applied voltage into a difference in the effective temperature between two parts of the system maintained at the same potential. We suggest an experimental setup for probing this phenomenon and mapping out the controlled distribution function.

Nonequilibrium quasiparticle distribution induced by Kondo defects.

It is shown that in resistive nanowires out of equilibrium containing either single- or two-channel Kondo impurities the distribution function f(E,U) obeys scaling behavior in terms of the quasiparticle energy E and the bias voltage U. The numerically calculated f(E,U) curves explain quantitatively recent experiments on Cu and Au nanowires. The systematics of the impurity concentration c(imp) extracted from the comparison between theory and results on various Cu and Au samples strongly suggests that in these systems the scaling arises from magnetic Kondo impurities.

Flux-flow resistance in the cuprate superconductors: effect of the nonequilibrium quasiparticle distribution

In the low temperature limit T≪ T c in the cuprate superconductors the quasiparticle scattering associated with the flux-flow resistance can become sensitively dependent on the electric field. This dependence results from the shift of the quasiparticle energy distribution away from equilibrium, in combination with the energy dependence of the density of states near the Fermi energy providing the phase space available for scattering. These concepts are used for explaining the recently observed highly nonlinear flux-flow-resistance behavior in the cuprate superconductor Nd 2− x Ce x CuO y .

Magnetic-field effect on the supercurrent of an SNS junction

In this paper we study the effect of a Zeeman field on the supercurrent of a mesoscopic SNS junction. It is shown that the supercurrent suppression is due to a redistribution of current-carrying states in energy space. A dramatic consequence is that (part of the) the suppressed supercurrent can be recovered with a suitable non-equilibrium distribution of quasiparticles.

Tunneling spectroscopy study of spin-polarized quasiparticle injection effects in cuprate/manganite heterostructures

Scanning tunneling spectroscopy was performed at 4.2 K on epitaxial thin-film heterostructures comprising YBa2Cu3O7−δ and La0.7Ca0.3MnO3, to study the microscopic effects of spin-polarized quasiparticle injection from the half-metallic ferromagnetic manganite on the high Tc cuprate superconductor. The quasiparticle tunneling characteristics observed were consistent with d-wave pairing symmetry, with a gap-maximum Δ0≈22 meV, up to at least 35 mA (7×103 A/cm2) injection. Spectral smearing observed at higher injections could be fitted to elevated effective quasiparticle temperatures, even though negligible sample heating was detected by in situ thermometry. The overall spectral evolution with the injection current also appears to be nonthermal in character, showing a nonmonotonic change in both the zero-bias tunneling conductance and the area under the conductance spectrum. We discuss general implications of these results for the scenario of dynamic pair breaking by a nonequilibrium distribution of spin-polarized quasiparticles.

Quasiparticle dynamics and phase locking in a S-I-S multilayer Josephson junction

New dynamical equations describing the Josephson effect and nonequilibrium quasiparticle distribution in a multilayer Josephson tunnel structure at T∼Tc are obtained, starting from the microscopic theory. It is shown that quasiparticle dynamics has a strong influence on the Josephson effect. Novel regimes with giant charge-imbalance oscillations are found. A new type of hysteresis on the current-voltage characteristic is predicted.

Time evolution of nonequilibrium quasiparticle and phonon distributions in superconducting films

Superconducting tunneling junctions are promising candidates for low energy X-ray detectors. To fully exploit the possibilities of the high energy resolution it is necessary to understand the microscopic processes and to get a clear insight into the importance of the different loss mechanisms. The linearized coupled kinetic equations for the nonequilibrium quasiparticle f(ω, t) and phonon n(Ω, t) distributions were solved by Chang and Scalapino for the stationary case. The time evolution of the full set of equations was investigated later by Zehnder. In this work we report results of calculations for the time dependence of f(ω, t) and n(Ω, t) which were obtained in a more general approach. In particular, the volume expansion of the initial distribution created by the absorption process was considered by making the distribution functions space dependent and adding a diffusion term to the equations. Results for Nb are discussed in detail.

Electronic instability during vortex motion in cuprate superconductors Regime of low and high magnetic fields

The critical velocity ν ϕ ∗ associated with the electronic instability predicted by Larkin and Ovchinnikov displays a cross-over effect from magnetic-field independent behavior at high fields to the proportionality ν ϕ ∗ ∼B − 1 2 at low fields. This low-field behavior results from the fact that ν ϕ ∗ multiplied with the inelastic quasiparticle scattering time τ in must reach at least the intervortex distance, thereby ensuring spatial homogeneity of the nonequilibrium quasiparticle distribution. At high magnetic fields the flux-flow instability becomes unobservable due to the onset of fluctuation effects contributing to the resistivity.