Nonequilibrium superconductivity

In general, the quasiparticles, phonons, and pair field in a superconductor driven by an external source are out of equilibrium. Here we review briefly the various quasiparticle and phonon lifetimes in real metals and estimate the strengths necessary to induce a strongly nonequilibrium state. Then we investigate the properties of a thin film driven in a spatially uniform steady state by quasiparticle injection, heater phonon pumping, and microwave radiation. This analysis uses a set of coupled kinetic equations for quasiparticle and phonon distributions and the BCS gap equation with the self-consistently determined quasiparticle distribution. Such films can be used to generate phonons with energy near 2 . In addition, the gap enhancement in a thin film due to microwave irradiation is discussed.Work supported by the Office of Naval Research. Preliminary results have been reported at the Applied Superconductivity Conference, Stanford, August 1976 [IEEE Trans. Magn. MAG-13, 747 (1977)] and at the NATO Advanced Study Institute at Lago di Garda, Italy, September 1976 [NATO Adv. Study Inst. Series (B-Physics) 21, 447–486 (1977)].J. S. Guggenheim Foundation Fellow (1976–77).     

Complete Analysis of STJ Detector Performance via Absorption of Phonon Pulses

For the first time a complete analysis of the tunnel and loss parameters of superconducting tunnel junction photon detectors has been made solely by the use of nanosecond phonon pulse excitation. Previously only a partial characterization, requiring supplementary information from photo-excitation measurements, was possible. The present results have been achieved by a more realistic model for the energy spectrum of the phonon pulses and greatly improved (nanosecond) time resolution of the detected signal. The value determined for the tunnel rate is in good agreement with calculations based on the device layer structure. It is believed that the relatively high values of loss time obtained are the result of trap-enhanced recombination due to the high quasiparticle densities attained in the experiments.      

A kinetic theory of the dilute solutions of3He in superfluid4He. I. Thermodynamics and equations of motion

A semimicroscopic kinetic theory of the dilute solutions of³He in superfluid⁴He is presented. The theory considers only phonon and³He quasiparticle excitations and is therefore applicable at temperatures of up to about 0.6 K. The model underlying the theory utilizes a modified Landau-Pomeranchuck³He energy spectrum and a second-order momentum expansion for the effective³He quasiparticle interaction. In addition, it accounts for the effective phonon-³He quasiparticle interaction, to first order in the phonon momentum, by using a renormalized concentration-dependent sound velocity. The simplicity of the model enables the derivation of both a complete equilibrium theory and a complete set of equations of motion for the solutions. The resulting expressions for the thermodynamic properties and the macroscopic currents appearing in the equations of motion represent a useful parametrization of these quantities in terms of the parameters of the model. It is shown that the macroscopic currents can be written in a form which seems to have a simple physical interpretation. As expected, it is found that at local equilibrium the expressions for the currents reduce correctly to the respective phenomenological expressions.     

Phonon excitation of quasiparticles in niobium and tantalum superconducting tunnel junction photon detectors

We report phonon pulse measurements of quasiparticle (qp) self-recombination and trapping by Abrikosov vortices in Nb and Ta superconducting tunnel junctions. The quasiparticle loss times, determined from the shape of the tunnel junction output pulse, were found to be strongly correlated with flux trapping. The measured results were compared with the model of Golubov and Houwman. It was found that qp self-recombination, as measured from the dependence of responsivity on absorbed phonon energy, was also modified by the presence of traps. A process of phonon-mediated de-trapping is proposed to explain the observed effects.     

The field dependence of the thermal conductivity: Evidence for nodes in the gap

The increased thermal conductivity below T_c in YBa₂Cu₃O_7–x (YBCO) is shown to agree with the microwave electrical conductivity, affirming that increase is due to quasiparticle conduction The field dependence, particularly in the conducting plane permits us to separate phonon and quasiparticle contributions for both YBCO and T₂Ba₂CuO₆ single crystals.     

Phonon Noise in Thin Metal Films in an Advanced Energy Down-Conversion Stage

We have identified an important, new source of line broadening in single photon detectors that work on the principle of absorption in a thin metal film. Phonon down-conversion noise arises through the loss of high energy phonons into the substrate during the initial photon energy down-conversion stage. Because of the relatively small number of phonons initially involved in this process, the loss rate is subject to large fluctuations due to the statistical nature of the energy exchange processes. We have modelled the phonon down-conversion noise that arises in the final stage of the down-conversion cascade, during which the deposited energy is converted into predominantly electronic excitations. At this stage of down-conversion in thin films the cascade phonon energy is sufficiently small that the escape interfaces are accessible for all phonons. Solving the system of coupled integral equations for the interacting electron and phonon systems, we have derived explicit expressions for the variance of the deposited energy. We have compared the results with other known noise contributions for the two foremost types of single optical photon detectors, based on superconducting tunnel junctions and transition edge sensors.      

Quasiparticle Kinetic Equation in a Trapped Bose Gas at Low Temperatures

Recently the authors used the Kadanoff–Baym non-equilibrium Green's function formalism to derive kinetic equation for the non-condensate atoms, in conjunction with a consistent generalization of the Gross–Pitaevskii equation for the Bose condensate wavefunction. This work was limited to high temperatures, where the excited atoms could be described by a Hartree–Fock particle-like spectrum. Following the approach of Kane and Kadanoff in 1965, we present the generalization of our recent work which is valid at low temperatures, where the input single-particle spectrum is now described by the Bogoliubov–Popov approximation. We derive a kinetic equation for the quasiparticle distribution function with collision integrals describing scattering between quasiparticles and the condensate atoms. From the general expression for the collision integral for the scattering between quasiparticle excitations, we find the quasiparticle distribution function corresponding to local equilibrium. This expression includes a quasiparticle chemical potential that controls the non-diffusive equilibrium between condensate atoms and the quasiparticle excitations. We derive a generalized Gross–Pitaevskii equation for the condensate wavefunction that also includes the damping effects due to collisions between atoms in the condensate and the thermally excited quasiparticles. For a uniform Bose gas, our kinetic equation for the thermally excited quasiparticles reduces to that found by Eckern, as well as by Kirkpatrick and Dorfman.     

Quasiparticle Edge Losses in Double STJs Strip X-Rays Detectors

The 2D diffusion model of the strip X-ray detector was developed. The detector consists of a long superconducting strip, which is ended by the trapping layers and superconducting tunnel junctions at each end. The model takes into account the diffusion of the excess quasiparticles, quasiparticle trapping at the tunnel junctions and quasiparticle losses in the volume of the strip and at the strip boundaries. The analytical solution was obtained. It has been shown that quasiparticle losses at the strip boundaries caused the dependence of the signals on the photon absorption site in transverse direction. The latter worsens the energy resolution and transforms the spectral line of the detector to nongaussian shape.      

Phonon Interactions in an Anisotropic Phonon System Leading to a Suprathermal Distribution in Liquid 4He

The relaxation rates of high energy phonons are calculated for a highly anisotropic phonon system which can be realised by phonon pulses in liquid ⁴He. We find that the creation rate for these phonons is very much greater than the decay rate over almost all of the momentum range. As a consequence, we have the unusual behaviour of the distribution function, for the high energy phonons, not being the Bose–Einstein distribution function. From our results we expect that the distribution function will be very much greater than the Bose–Einstein one and also to have a quite different momentum dependence. The analytic expressions which are derived, enable us to explain the physical reasons for a suprathermal distribution of high energy phonons which are predicted to occur in highly anisotropic phonon systems.     

The effect of hotspot formation on quasiparticle yields in superconducting aluminium films

Existing models show that any hotspot created in an Al film following a particle interaction is rapidly diluted. Quasiparticles and phonons decouple at high energies so that on short time-scales quasiparticle diffusion determines the energy transport. Few quasiparticles have energies near the energy gap and there is little gap suppression. We have measured the initial quasiparticle yields in very thin Al films and find somewhat surprisingly that this yield is reduced. It appears that a short time-scale quasiparticle loss mechanism, probably associated with localised over-injection, exists as quasiparticles scatter to low energies within the phonon hotspot.     

The coupled phonon spectrum in3He-4He solutions

A simple extension of a model previously used for³He-⁴ He solutions is presented, in which the effective vertex functions between³ He and⁴ He density fluctuations are assumed to depend only on the momentum transfer. The possible zero-concentration³ He quasiparticle spectra are divided into two classes, those that do and those that do not intersect the⁴ He phonon spectrum. The present model calculations of the coupled phonon spectrum demonstrate that as the temperature is decreased the behavior of the shifts in the phonon spectrum can be considered as a signature of the class of³ He quasiparticle spectrum used. Comparison with recent scattering experiments, however, indicates that the existing data are not sufficient to distinguish unambiguously between the two classes of³ He spectrum. It is suggested that a low-temperature neutron scattering experiment be performed to settle this question.     

Polaronic Trions at the MoS2/SrTiO3 Interface

The reduced electrical screening in 2D materials provides an ideal platform for realization of exotic quasiparticles, that are robust and whose functionalities can be exploited for future electronic, optoelectronic, and valleytronic applications. Recent examples include an interlayer exciton, where an electron from one layer binds with a hole from another, and a Holstein polaron, formed by an electron dressed by a sea of phonons. Here, a new quasiparticle is reported, “polaronic trion” in a heterostructure of MoS₂/SrTiO₃ (STO). This emerges as the Fröhlich bound state of the trion in the atomically thin monolayer of MoS₂ and the very unique low energy soft phonon mode (≤7 meV, which is temperature and field tunable) in the quantum paraelectric substrate STO, arising below its structural antiferrodistortive (AFD) phase transition temperature. This dressing of the trion with soft phonons manifests in an anomalous temperature dependence of photoluminescence emission leading to a huge enhancement of the trion binding energy (≈70 meV). The soft phonons in STO are sensitive to electric field, which enables field control of the interfacial trion–phonon coupling and resultant polaronic trion binding energy. Polaronic trions could provide a platform to realize quasiparticle‐based tunable optoelectronic applications driven by many body effects.     

Graphene Microbolometers with Superconducting Contacts for Terahertz Photon Detection

We report on noise and thermal conductance measurements taken in order to determine an upper bound on the performance of graphene as a terahertz photon detector. The main mechanism for sensitive terahertz detection in graphene is bolometric heating of the electron system. To study the properties of a device using this mechanism to detect terahertz photons, we perform Johnson noise thermometry measurements on graphene samples. These measurements probe the electron–phonon behavior of graphene on silicon dioxide at low temperatures. Because the electron–phonon coupling is weak in graphene, superconducting contacts with large gap are used to confine the hot electrons and prevent their out-diffusion. We use niobium nitride leads with a \(T_\mathrm {c}\approx 10\)  K to contact the graphene. We find these leads make good ohmic contact with very low contact resistance. Our measurements find an electron–phonon thermal conductance that depends quadratically on temperature above 4 K and is compatible with single terahertz photon detection.     

Giant cross section of resonant electromagnetic wave scattering by electron in metal and semiconductor clusters

A new formula is obtained for the cross section of light scattering by electron under conditions where the damping of its oscillations is related entirely to the spontaneous re-radiation of photon. The cross section for resonant light scattering can become macroscopic, which is only possible in a nanocluster where the phonon energy is greater than the photon energy.     

Energy transfer through the interface into a quantum fluid with nonlinear dispersion relation

No Heading In this work the problem is solved of the creation of a quasiparticle of a quantum fluid with anomalous dispersion on the boundary with a heated solid. The generalization is offered of the model of Kapitzas temperature discontinuity on the interface between two continuous mediums to the case of nonlinear dispersion relation of one of them. The quantum fluid with nonlinear dispersion is described within the framework of the new approach, in which it is considered as a continuous medium at all length scales. It is shown that in such medium there is a standing wave near the boundary, that is damped with distance. The probability of quasiparticle creation is obtained and is shown to be always less than the creation probability of a quasiparticle of an ordinary continuous medium with the same phase velocity. The correction to the creation probability of a phonon of superfluid ⁴He by a heated solid is found at small wave vectors.PACS numbers: 67.40 Bz, 67.40 Db, 67.40 Pm.     

Towards X-ray Thermal Kinetic Inductance Detectors

Traditionally, kinetic inductance detectors (KIDs) have been thought of as non-equilibrium detectors, which detect the excess of quasiparticles from the absorbed photon. In this case, recombination of quasiparticles is the bottleneck that limits the quasiparticle lifetime. However, the response of a KID to an excess of quasiparticles from photon absorption gives a nearly identical response to the increase in quasiparticle density due to a temperature change. Thus, KIDs can be used as thermometers to detect the temperature rise in an absorber due to a thermalized X-ray photon. In this work, we present a working prototype of an X-ray thermal KID (i.e., TKID) using a tungsten silicide resonator with superconducting tantalum absorber on a silicon nitride membrane. Finally, we outline improvements for future designs.     

Comparison of thermal conductivity data for partially stabilized zirconia with values derived from thermal diffusivity results

The thermal conductivity of partially stabilized zirconia was measured over the temperature range 320–1273 K using the radial heat flow method. The data have an absolute uncertainty of about ±2% and repeat measurements showed no evidence of changes in the thermal conductivity at high temperatures. This also was true for the thermal diffusivity data, which were obtained in vacuum over the temperature range 300–1473 K. Both sets of thermal conductivity data pass through minima at high temperatures. Quantitative differences were observed in the temperatures and thermal conductivities of the two minima. The results were analyzed by assuming parallel conduction by phonons and photons, and the phonon component was identified by fitting lower-temperature data. Extrapolating this curve allowed identification of the photon contribution to the thermal conductivity at high temperatures. The photon contribution approached a T ³ function and was larger in the thermal conductivity specimens. The difference in the photon contributions correlates with changes in the optical properties of the samples produced during the high temperature measurments.     

Influence of the Quasiparticle and Phonon Subsystem Coupling on the Multitunneling in STJ Detectors

The scope of this work is to account for the phonon exchange in the process of multitunneling in superconducting tunnel junction (STJ) detector. The theory of branching cascade processes was applied to the process of multitunneling in STJ. The duality nature of quasiparticles and the coupling of the quasiparticle and phonon subsystems were taken into account. The extreme cases of the general formula were analyzed. It was shown that the general formula encloses all specific cases published in literature.     

Quasiparticle Dynamics in FeSe Superconductors Studied by Femtosecond Spectroscopy

The ultrafast quasiparticle dynamics in FeSe single crystals were measured by using dual-color transient reflectivity measurements (ΔR/R) from 4.4 to 290 K. In general, the typical ΔR/R of FeSe includes two significant components. One is the relaxation of photoinduced quasiparticles, which has been used to estimate the electron–phonon coupling strength (λ=0.16). The other is the oscillation component due to the acoustic phonon. Moreover, the acoustic phonon’s energy estimated from the period of oscillation in ΔR/R markedly shrinks around 90 K, which is the so-called phonon softening.     

Generation of motional entangled coherent state in an optomechanical system in the single photon strong coupling regime

The single-photon strong coupling in the deep-resolved sideband of the optomechanical system induces photon blockade (PB) effect. For the PB cavity, an initial mechanical coherent state evolves into superposition of phonon cat states entangled with the cavity Fock states. Measurement of the cavity photon number states produces phonon even and odd cat states. The information leakage effect of two photon states on the fidelity of cat states is calculated, it is shown that for low average phonon number this effect is negligible and decreases by increasing the two photon cavity state. The Lindblad equation is solved numerically to obtain the environmental effects on the fidelity of cat states.