Electrons In Normal Metals Research Articles

Unconventional superconductivity after the BCS paradigm and empirical rules for the exploration of high temperature superconductors

Superconducting state is achieved through quantum condensation of Cooper pairs which are new types of charge carriers other than single electrons in normal metals. The theory established by Bardeen-Cooper-Schrieffer (BCS) in 1957 can successfully explain the phenomenon of superconductivity in many single-element and alloy superconductors. Within the BCS scheme, the Cooper pairs are formed by exchanging the virtual vibrations of lattice (phonons) between two electrons with opposite momentum near the Fermi surface. The BCS theory has dominated the field of superconductivity over 64 years. Many superconductors discovered in past four decades, such as the heavy Fermion superconductors, cuprates, iron pnictide/chalcogenide and nickelates seem, however, to strongly violate the BCS picture. The most important issue is that, perhaps the BCS picture based on electron-phonon coupling are the special case for superconductivity, there are a lot of other reasons or routes for the Cooper pairing and superconductivity. In this short overview paper, we will summarize part of these progresses and try to guide readers to some new possible schemes of superconductivity after the BCS paradigm. We also propose several empirical rules for the exploration of high-temperature unconventional superconductors.

Tunneling in Fermi systems with quadratic band crossing points

We investigate the tunneling of quasiparticles through a rectangular potential barrier of finite height and width, in 2d and 3d semimetals with band structures consisting of a quadratic band crossing point. We compute the transmission coefficient at various incident angles, and also the conductivity and the Fano factor. We discuss the distinguishing signatures of these transport properties in comparison with other semimetals, as well as electrons in normal metals.

Measurement and modeling of a large-area normal-metal/insulator/superconductor refrigerator with improved cooling

In a normal-metal/insulator/superconductor (NIS) tunnel junction refrigerator, the normal-metal electrons are cooled and the dissipated power heats the superconducting electrode. This paper presents a review of the mechanisms by which heat leaves the superconductor and introduces overlayer quasiparticle traps for more effective heatsinking. A comprehensive thermal model is presented that accounts for the described physics, including the behavior of athermal phonons generated by both quasiparticle recombination and trapped quasiparticles. We compare the model to measurements of a large area (>400 um^2) NIS refrigerator with overlayer quasiparticle traps, and demonstrate that the model is in good agreement experiment. The refrigerator IV curve at a bath temperature of 300 mK is consistent with an electron temperature of 82 mK. However, evidence from independent thermometer junctions suggests that the refrigerator junction is creating an athermal electron distribution whose total excitation energy corresponds to a higher temperature than is indicated by the refrigerator IV curve.

Single-charge escape processes through a hybrid turnstile in a dissipative environment

We have investigated the static, charge-trapping properties of a hybrid superconductor–normal metal electron turnstile embedded in a high-ohmic environment. The device includes a local Cr resistor on one side of the turnstile, and a superconducting trapping island on the other side. The electron hold times, τ∼2–20 s, in our two-junction circuit are comparable with those of typical multi-junction, N⩾4, normal-metal single-electron tunneling devices. A semi-phenomenological model of the environmental activation of tunneling is applied for the analysis of the switching statistics. The experimental results are promising for electrical metrology applications.

Origin of Hysteresis in a Proximity Josephson Junction

We investigate hysteresis in the transport properties of superconductor-normal-metal-superconductor (S-N-S) junctions at low temperatures by measuring directly the electron temperature in the normal metal. Our results demonstrate unambiguously that the hysteresis results from an increase of the normal-metal electron temperature once the junction switches to the resistive state. In our geometry, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction.

Toward the optimization of electronic refrigerators

Normal metal–insulator–superconductor (NIS) junction can act as refrigerator of electron gas in a normal metal electrode under certain conditions. If majority of high energy electrons in a normal metal is moved with a bias voltage to energy levels above the superconductor's energy gap, their extraction from a normal metal is enabled by tunnelling. Their substitution with lower energy electrons results in lowering of the normal metal electron gas energy. Due to excess quasiparticle density in the superconductive electrode in vicinity of the junction, which is a result of tunnelling of quasiparticles from the normal metal and low capability of removal of these particles from the junction area the cooling capability of junctions deteriorates at lower environment temperatures. This is mainly the results of back tunnelling of excess quasiparticles to a normal metal and of dissipated energy, released by Coooper pair formation in proximity of the junction. Quantitative description of quasiparticle behavior in the superconductive electrode of the NIS junction is given. Energy dependent diffusion of quasiparticles in superconductor, their consumption due to Cooper pair creation and inflow of additional quasiparticles from a normal metal are considered. The model results in position dependence of quasiparticles' density in the junction proximity.

Electron and Phonon Cooling in a Superconductor–Normal-Metal–Superconductor Tunnel Junction

We present evidence for the cooling of normal-metal phonons, in addition to the well-known electron cooling, by electron tunneling in a superconductor-normal-metal-superconductor tunnel junction. The normal-metal electron temperature is extracted by comparing the device current-voltage characteristics to the theoretical prediction. We use a quantitative model for the heat transfer that includes the electron-phonon coupling in the normal metal and the Kapitza resistance between the substrate and the metal. It gives a very good fit to the data and enables us to extract an effective phonon temperature in the normal metal.

Dispersionless modes and the superconductivity of ultrathin films

A self-consistent analytical solution of the problem of the superconductivity of ultrathin metal films is found within the tight-binding model for normal-metal electrons with a simple example of a film of three atomic layers. Superconductivity is not destroyed in atomically thin films if the energies of the electron subsystem lie near the Fermi surface at least for some values of the quasimomentum component along the film. A substantial increase in the critical temperature of an ultrathin metal film as compared to its bulk value is possible if the electron excitation spectrum contains low-energy modes with an anomalously weak dispersion.

Proximity effect in ultrathin Pb/Ag multilayers within the Cooper limit

We report on transport and tunneling measurements performed on ultrathin Pb/Ag (strong-coupled superconductor/normal metal) multilayers evaporated by quench condensation. The critical temperature and energy gap of the heterostructures oscillate with addition of each layer, demonstrating the validity of the Cooper limit model in the case of multilayers. We observe excellent agreement with a simple theory for samples with layer thickness larger than $30\mathrm{\AA{}}.$ Samples with single layers thinner than $30\mathrm{\AA{}}$ deviate from the Cooper limit theory. We suggest that this is due to the ``inverse proximity effect'' where the normal-metal electrons improve screening in the superconducting ultrathin layer and thus enhance the critical temperature.

Shapiro effect in mesoscopic LC circuit

In this paper we consider the movement of an electron in the single electron tunnel process through a mesoscopic capacitor. The results show that, due to the Coulomb force, there is a threshold voltage Vt in the mesoscopic LC circuit. When the external voltage is lower than the threshold voltage, the tunnel current value is zero and the Coulomb blockade phenomenon arises. Furthermore, considering that the mesoscopic dimension is comparable to the coherence length in which charge carriers retain the phase remembrance, a weak coupling can be produced through the proximity effect of the normal metal electrons of both electrodes of a mesoscopic capacitor. By varying the external voltage, we can observe the Shapiro current step on the current-voltage characteristic curve of a mesoscopic LC circuit.

Heat sources in electronic refrigerators

Tunneling electric current through the normal metal-insulator-superconductor junction is accompanied with heat flow out of normal metal when properly voltage biased. The phenomenon enables cooling of electrons and phonons (under special conditions) in the region below 1 K. At lower bath temperatures two parasitic heat sources decrease refrigerator performance. (i) Due to tunneling of hot electrons from a normal metal electrode to a superconductive one an excess quasiparticle density appears in the superconductor which results in tunneling of electrons back to the normal metal and consequently the normal metal electron temperature increases. This phenomenon is called back tunneling. (ii) Second heat source is the Cooper pair formation: the part of energy released by the formation of Cooper pairs in a superconductor is dissipated in a normal metal. Both contributions are calculated-by considering quasiparticle behavior in the junction region and no free parameters are introduced. Diffusion, tunneling and back tunneling of quasiparticles in the superconductor in equilibrium are considered to calculate temperatures of electrons and phonons in the normal metal electrode. This detailed model explains the increase of normal metal electron temperatures above the bath temperature at lower bath temperatures.

CESR in superconductors: Relevance of highT c copper oxide systems

CESR is a highly effective tool to study the interaction among conduction electrons in normal metals. In superconductors belowT c it can reveal vital information concerning the pairing interactions. A comparative study of highT c and conventional superconductors is presented and it is shown that the disappearance of CESR in the superconducting state is a feature common to both conventional and highT c superconductors and establishes the importance of exchange interactions in pairing. This is supported by experimental observations.

Specific heat discontinuity of a proximity-effect sandwich system containing Kondo impurities

The theoretical work of Matsuura, Ichinose, and Nagaoka on the Kondo effect in superconductors and McMillan's tunneling model are applied to a proximity-effect sandwich system containing Kondo impurities. Analytic expressions for the renormalized Green's functions of superconducting and normal-metal electrons are given as functions of the system composition. It is found that as the thicknesses become large, the specific heat discontinuity changes continuously from the Muller-Hartmann-Zittartz value for the magnetic cases to the Ichinose value for the nonmagnetic ones. For small values of the layer thickness, and with the films in proximity, our results can be used to calculate the specific heat jump at the transition temperature numerically.

Hot electrons in metals at low temperatures

Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density (≲ 106 A/cm2) through thin, narrow (~1 Μm wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when θ ≪ θD, where θ is the average electron energy and θ D is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S(Ω) ≡ α2 F(Ω) and g(Ω) ≡ αtr 2 F(Ω). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.

Magnetic Field Splitting of the Density of States of Thin Superconductors

Using Green's-function techniques, we present a theoretical calculation of the behavior of the density of states, free energy, and order parameter of very thin superconductors in a high magnetic field as a function of spin-orbit and spin-flip impurity scattering. In very thin superconducting films without spin scattering, the upper critical field is determined by the Pauli paramagnetism of the normal-metal electrons. Tunneling measurements by Meservey and Tedrow have shown a spin splitting by $2{\ensuremath{\mu}}_{B}H$ in energy space of the BCS peak in the density of states. Zero-temperature calculations of the separate up- and down-spin Green's function for a superconductor show that spin-orbit impurities destroy the magnetic field separation of the peaks in the density of states but do not destroy the energy gap. Spin-flip scattering is much more destructive and destroys both the separation of the peaks and the energy gap. We generalize the calculation to $T\ensuremath{\ne}0$ and calculate and plot the critical field versus temperature and the magnetic field dependence of the free energy and order parameter for the various values of the spin-orbit and spin-flip parameter. We also use the theoretical calculations to obtain a fit to the low-temperature tunneling data of Meservey and Tedrow between thin Al and a normal metal and the spin-polarized tunneling between thin Al and ferromagnetic metals.