Sensitivity and linearity of superconducting radio-frequency single-electron transistors: effects of quantum charge fluctuations

We have investigated the effects of quantum fluctuations of quasiparticles on the operation of superconducting radio-frequency single-electron transistors (rf-SETs) for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, subgap rf-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Surprisingly, such rf-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.     

Local density of states and order parameter configurations in layered ferromagnet-superconductor structures

We analyze the local density of states (LDOS) of heterostructures consisting of alternating ferromagnet, F, and superconductor, S, layers. We consider structures of the SFS and SFSFSFS type, with thin nanometer scale F and S layers, within the ballistic regime. The spin-splitting effects of the ferromagnet and the mutual coupling between the S regions, yield several nontrivial stable and metastable pair amplitude configurations, and we find that the details of the spatial behavior of the pair amplitude govern the calculated electronic spectra. These are reflected in discernible signatures of the LDOS. The roles that the magnetic exchange energy, interface scattering strength, and the Fermi wavevector mismatch each have on the LDOS for the different allowed junction configurations, are systematically investigated.     

Supersymmetric representation of order parameter fluctuations

We consider the representation of homogeneous and heterophase fluctuations based on the supersymmetric theory of fields. It is shown that the problem reduces to a mixture of noninteracting Fermi and Bose gases. The thermodynamic features resulting from each type of fluctuations are determined, as well as the correlation functions of the spatial distributions of the order parameter and interphase boundaries.Suma Physicotechnical Institute. RETO Scientific-Industrial Complex. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 49–53, April, 1994.     

Density of states of narrow superconducting channels in the regime of quantum fluctuations of the order parameter

The current–voltage characteristics of superconductor–insulator–semiconductor (S1–I–S2) tunnel junctions, where superconducting electrode S2 is a thin nanowire, are studied experimentally. The observed blurring of the gap singularities is interpreted as a manifestation of the order parameter quantum fluctuations. We propose a model taking into account the broadening of the density of states due to the interaction of electrons with the Mooij–Schön plasmon mode emerging in a quasi-one-dimensional superconducting channel in the regime of quantum fluctuations of the order parameter. The model gives results that are in a reasonable qualitative agreement with the experimental data.     

Excess electrical conductivity in polycrystalline Bi-Ca-Sr-Cu-O compounds and thermodynamic fluctuations of the amplitude of the superconducting order parameter

Measurements of the rounding effects on the electrical resistivity above the superconducting transition in Bi-Ca-Sr-Cu-O polycrystalline compounds are reported, to our knowledge for the first time in this HTSC system. These effects are analyzed in terms of thermodynamic fluctuations of the amplitude of the superconducting order parameter (SCOPF). In the mean-field-like region, the experimental critical exponent seems to be compatible with an order parameter of two components (2d) fluctuating in two dimensions (2D). This contrasts with previous results for A-Ba-Cu-O (A=Y, Ln) and Ln-M-Cu-O (M=Ba, Sr) superconductors, where SCOPF seem to be 2d-3D in all the different dynamic critical regions.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Oscillations of superconducting transition temperature in strong ferromagnet-superconductor bilayers

The superconducting transition temperature T _c of a “clean ferromagnet-dirty superconductor” bilayer is calculated using boundary conditions derived for the quasiclassical Green’s function. This combination corresponds to the majority of experiments, in which Fe, Ni, Co, or Gd are used as a material for the ferromagnetic layer. It is shown that T _c oscillates upon changing thickness of the ferromagnetic layer, in accordance with the experimental observations.     

Relaxation of the superconducting order parameter under microwave irradiation

In superconducting aluminium we measured the influence of microwave irradiation on the time delay between the start of a supercritical current pulse and onset of the corresponding voltage response. We observed a shortening of the delay times due to the microwaves. This reflects the redistribution of the quasiparticles and the enhancement of the superconducting energy gap.     

Resonance tunneling in superconducting junctions with different order parameter symmetries

Resonance tunneling in superconducting junctions with electrode order parameters of s and d symmetry was studied. The Green function formalism was used to derive an equation for the resonance current in junctions of arbitrary dimensionality and order parameter symmetry. A universal equation for resonance super-current was obtained for junctions of arbitrary dimensionality with isotropic electrode order parameters. A numerical analysis of resonance current transport in junctions of various types was performed for the two-dimensional model.     

Spin-dependent quasiparticle transport in aluminum single-electron transistors

We investigate the effect of Zeeman splitting on quasiparticle transport in normal-superconducting-normal (NSN) aluminum single-electron transistors (SETs). In the above-gap transport, the interplay of Coulomb blockade and Zeeman splitting leads to spin-dependence of the sequential tunneling. This creates regimes where either one or both spin species can tunnel onto or off the island. At lower biases, spin-dependence of the single quasiparticle state is studied, and operation of the device as a bipolar spin filter is suggested.     

Non-equilibrium spin accumulation in ferromagnetic single-electron transistors

We study transport in ferromagnetic single-electron transistors. The non-equilibrium spin accumulation on the island caused by a finite current through the system is described by a generalized theory of the Coulomb blockade. It enhances the tunnel magnetoresistance and has a drastic effect on the time-dependent transport properties. A transient decay of the spin accumulation may reverse the electric current on time scales of the order of the spin-flip relaxation time. This can be used as an experimental signature of the non-equilibrium spin accumulation. Received 6 May 1998     

Nonmonotonic behavior of the superconducting transition temperature in bimetallic ferromagnet-superconductor structures

For layered ferromagnet/superconductor (F/S) structures we develop a theory of the proximity effect. In contrast to previous approaches, this theory allows for a finite transmission coefficient of the interface between the two metals and competition between the diffusion and spin-wave types of quasiparticle motion in the ferromagnet’s strong exchange field. The superconductivity in F/S systems proves to be a superposition of BCS pairing with a constant-sign pair amplitude in the S-layers and Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) pairing with an oscillating wave function in the F-layers. We show that the oscillatory behavior of the superconducting transition temperature T _c is due to oscillations of the Cooper pair flux from the S-layer to the F-layer, which are the result of oscillations of the discontinuity (jump) of the pair amplitude at the F/S boundary as the thickness d _f of the F-layer increases. The presence of nonmagnetic impurities leads to heavy damping of the oscillations of the LOFF pair amplitude and rapid deterioration of the coherent coupling of the boundaries of the F-layer in which the T _s vs. d _f dependence reaches a plateau as d _f increases. In F/S superlattices, in contrast to F/S double-layer junctions, there are two forms of the LOFF state, the 0-phase and the π-phase, which differ in their symmetry with respect to the center of the F layer. This gives rise to additional oscillations in the T _c (d _f ) dependence due to the 0-π transitions. As the most vivid manifestation of LOFF states in F/S-systems, we predict the existence of recurrent and periodically recurrent superconductivities. We give a qualitative explanation of the different behavior of the superconducting transition temperature observed by different groups of experimenters dealing with the same ferromagnet-superconductor structures. Zh. éksp. Teor. Fiz. 113, 1708–1730 (May 1998)     

The order parameter for the superconducting phases of UPt3

I review the principal theories that have been proposed for the superconducting phases of UPt₃. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. Much attention has been given to the Ginzberg-Landau region of the phase diagram where the phase boundaries of three phases appear to meet at a tetracritical point. It has been argued that the existence of a tetracritical point for all field orientations eliminates the two-dimensional (2D) orbital representations coupled to a symmetry-breaking field (SBF) as a viable theory of these phases and favours either a theory based on two primary order parameters belonging to different irreducible representations that are accidentally degenerate, as described by Chen and Garg 1993, or a spin-triplet, orbital one-dimensional representation with non spin-orbit coupling in the pairing channel, as described by Machida and Ozaki 1991. I comment on the limitations of the models proposed so far for the superconducting phases of UPt₃. I also find that a theory in which the order parameter belongs to an orbital 2D representation coupled to a SBF is a viable model for the phases of UPt₃, based on the existing body of experimental data. Specifically, I show that the existing phase diagram (including an apparent tetracritical point for all field orientations), the anisotropy of the upper critical field over the full temperature range, the correlation between superconductivity and basal plane antiferromagnetism and the low-temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd-parity E_2u order parameter with a pair spin projection of zero along the ?c axis. The coupling of an antiferromagnetic moment to the superconducting order parameter acts as a SBF which is responsible for the apparent tetracritical point, in addition to the zero-field double transition. The new results presented here for the E_2u representation are based on an analysis of the material parameters calculated within the Bardeen-Cooper-Schrieffer theory for the 2D representations, and a refinement of the SBF model given by Hess et al. (1989). I also discuss possible experiments to test the symmetry of the order parameter.     

Far-infrared absorption of superconducting films with spatially varying order parameter

We have measured the far-infrared absorption of superconducting films in situations, where the order parameter varies spatially. The variation is induced by a perpendicular magnetic field or with a proximity effect contact. The measurements are analysed on the basis of a local model, combining a spatial variation of the order parameter with the Abrikosov-Gorkov solutions of a homogeneous superconductor under pair-breaking conditions.     

On order parameter fluctuations in Rochelle salt detected by Brillouin scattering

In both of the nonpolar phases of ferroelectric-ferroelastic Rochelle salt frequency and linewidth of the quasilongitudinal acoustic phonon propagating along [011] have been investigated in a high resolution Brillouin- scattering experiment. Softening and damping of this mode can be quantitatively explained by a piezoelectric coupling to the fluctuations of the polarization along the ferroelectric axis, P₁.     

Temperature dependence of the relaxation time of the superconducting order parameter

We have measured the temperature dependences of the relaxation time of the superconducting order parameter and of the equilibrium energy gap close to the transition temperature in very clean films of aluminum. The results are only consistent with the temperature and energy gap dependence predicted by Schmid and Schön. We also show that the magnitude and mean free path dependence of the electron inelastic collision time is in good agreement with calculations.     

Measurements of Kondo and spin splitting in single-electron transistors

We measure the spin splitting in a magnetic field B of localized states in single-electron transistors using a new method, inelastic spin-flip cotunneling. Because it involves only internal excitations, this technique gives the most precise value of the Zeeman energy Delta=/g/mu(B)B. In the same devices we also measure the splitting with B of the Kondo peak in differential conductance. The Kondo splitting appears only above a threshold field as predicted by theory. However, the magnitude of the Kondo splitting at high fields exceeds 2/g/mu(B)B in disagreement with theory.