[Show abstract][Hide abstract] ABSTRACT: The Kondo effect in a quantum dot is discussed. In the standard Coulomb blockade setting, tunneling between the dot and the leads is weak, the number of electrons in the dot is well-defined and discrete; the Kondo effect may be considered in the framework of the conventional one-level Anderson impurity model. It turns out however, that the Kondo temperature TK in the case of weak tunneling is extremely low. In the opposite case of almost reflectionless single-mode junctions connecting the dot to the leads, the average charge of the dot is not discrete. Surprisingly, its spin may remain quantized: s=1/2 or s=0, depending (periodically) on the gate voltage. Such a "spin-charge separation" occurs because, unlike an Anderson impurity, a quantum dot carries a broad-band, dense spectrum of discrete levels. In the doublet state, the Kondo effect develops with a significantly enhanced TK. Like in the weak-tunneling regime, the enhanced TK exhibits strong mesoscopic fluctuations. The statistics of the fluctuations is universal, and related to the Porter-Thomas statistics of the wave function fluctuations.
International Journal of Modern Physics B 01/2012; 15(10n11). DOI:10.1142/S0217979201005921 · 0.94 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Local vortex dynamics in Bi2Sr2CaCu2O8 single crystals was studied using novel microscopic GaAs/AlGaAs Hall-sensor arrays. The irreversibility line (IL) is found to exist in the absence of bulk pinning. At high temperatures the IL is due to geometrical barriers whereas at intermediate temperatures the irreversible behavior is determined by surface barriers. Bulk pinning governs the IL only at T < 22 K.
[Show abstract][Hide abstract] ABSTRACT: We investigate the energy and phase relaxation of a superconducting qubit caused by a single quasiparticle. In our model, the qubit is an isolated system consisting of a small island (Cooper-pair box) and a larger superconductor (reservoir) connected with each other by a tunable Josephson junction. If such system contains an odd number of electrons, then even at lowest temperatures a single quasiparticle is present in the qubit. Tunneling of a quasiparticle between the reservoir and the Cooper-pair box results in the relaxation of the qubit. We derive master equations governing the evolution of the qubit coherences and populations. We find that the kinetics of the qubit can be characterized by two time scales - quasiparticle escape time from reservoir to the box, $\Gamma^{-1}_{in}$, and quasiparticle relaxation time $\tau$. The former is determined by the dimensionless normal-state conductance $g_T$ of the Josephson junction and one-electron level spacing $\delta_r$ in the reservoir ($\Gamma_{in}\sim g_T\delta_r$), and the latter is due to electron-phonon interaction. We find that phase coherence is damped on the time scale of $\Gamma^{-1}_{in}$. The qubit energy relaxation depends on the ratio of the two characteristic times, $\tau$ and $\Gamma^{-1}_{in}$, and also on the ratio of temperature $T$ to the Josephson energy $E_J$.
Physical Review B 06/2007; 75(22). DOI:10.1103/PhysRevB.75.229903 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Upon increasing the electron density in a quantum wire, the one-dimensional electron system undergoes a transition to a quasi-one-dimensional state. In the absence of interactions between electrons, this corresponds to filling up the second subband of transverse quantization, and there are two gapless excitation modes above the transition. On the other hand, strongly interacting one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains (zigzag crystal). We show that the soft mode driving the transition to the zigzag state is gapped, and only one gapless mode exists above the transition. Furthermore, we establish that in the vicinity of the transition already arbitrarily weak interactions open a gap in the second mode. We then argue that only one gapless mode exists near the transition at any interaction strength.
[Show abstract][Hide abstract] ABSTRACT: We investigate the energy and phase relaxation of a superconducting
qubit caused by a single quasiparticle. In our model, the qubit is an
isolated system consisting of a small island (Cooper-pair box) and a
larger superconductor (reservoir) connected with each other by a tunable
Josephson junction. If such a system contains an odd number of
electrons, then even at lowest temperatures a single quasiparticle is
present in the qubit. Tunneling of a quasiparticle between the reservoir
and the Cooper-pair box results in the relaxation of the qubit. We
derive master equations governing the evolution of the qubit coherences
and populations. We find that the kinetics of the qubit can be
characterized by two time scales—quasiparticle escape time from
the reservoir to the box Γin-1 and
quasiparticle relaxation time τ . The former is determined by the
dimensionless normal-state conductance gT of the Josephson
junction and one-electron level spacing δr in the
reservoir (Γin˜gTδr)
, and the latter is due to the electron-phonon interaction. We find that
phase coherence is damped on the time scale of
Γin-1 . The qubit energy relaxation depends
on the ratio of the two characteristic times τ and
Γin-1 and also on the ratio of temperature
T to the Josephson energy EJ .
[Show abstract][Hide abstract] ABSTRACT: We review a novel approach to the superconductive proximity effect in disordered normal-superconducting (N-S) structures.
The method is based on the multicharge Keldysh action and is suitable for the treatment of interaction and fluctuation effects.
As an application of the formalism, we study the subgap conductance and noise in two-dimensional N-S systems in the presence
of the electron-electron interaction in the Cooper channel. It is shown that singular nature of the interaction correction
at large scales leads to a nonmonotonuos temperature, voltage and magnetic field dependence of the Andreev conductance.
[Show abstract][Hide abstract] ABSTRACT: We analyze the decay of Rabi oscillations in a charge qubit consisting of a Cooper pair box connected to a finite-size superconductor by a Josephson junction. We concentrate on the contribution of quasiparticles in the superconductors to the decay rate. Passing of a quasiparticle through the Josephson junction tunes the qubit away from the charge degeneracy, thus spoiling the Rabi oscillations. We find the temperature dependence of the quasiparticle contribution to the decay rate for open and isolated systems. The former case is realized if a normal-state trap is included in the circuit, or if just one vortex resides in the qubit; the decay rate has an activational temperature dependence with the activation energy equal to the superconducting gap $\Delta$. In a superconducting qubit isolated from the environment, the activation energy equals $2\Delta$ if the number of electrons is even, while for an odd number of electrons the decay rate of an excited qubit state remains finite in the limit of zero temperature. We estimate the decay rate for realistic parameters of a qubit.
[Show abstract][Hide abstract] ABSTRACT: We consider a class of systems where, due to the large mismatch of dielectric
constants, the Coulomb interaction is approximately one-dimensional. Examples
include ion channels in lipid membranes and water filled nanopores in silicon
or cellulose acetate films. Charge transport across such systems possesses the
activation behavior associated with the large electrostatic self-energy of a
charge placed inside the channel. We show here that the activation barrier
exhibits non-trivial dependence on the salt concentration in the surrounding
water solution and on the length and radius of the channel.
Physica A: Statistical Mechanics and its Applications 04/2005; 359(1-359):129-161. DOI:10.1016/j.physa.2005.05.097 · 1.73 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The temperature dependence of electron dephasing time tau(phi)(T) is calculated for a disordered metal with a small concentration of superconductive grains. Above the macroscopic superconducting transition line, when electrons in the metal are normal, Andreev reflection from the grains leads to a nearly temperature-independent contribution to the dephasing rate. In a broad temperature range tau(-1)(phi)(T) strongly exceeds the prediction of the classical theory of dephasing in normal disordered conductors, whereas magnetoresistance is dominated (in two dimensions) by the Maki-Tompson correction and is positive.
[Show abstract][Hide abstract] ABSTRACT: We consider the classical-quantum behavior crossover in a small,
externally driven Josephson junction. Charge of a small superconducting
grain fluctuates strongly if its critical current J_c(t) is modulated
(kicked) by short periodic pulses (e.g. by changing the tunneling
strength). The system may be mapped onto the model of quantum kicked
rotator [1]. For large amplitudes of J_c(t) and short enough times, the
grain charge, Q(t), diffuses in time. That is, the charge correlation
function K(t) = <(Q(t)-Q(0))^2> = 2Dt, where the classical
diffusion coefficient, D, may be expressed through the microscopical
parameters of the model. Quantum corrections develop at times longer
than the Ehrenfest time of the corresponding dynamical system, t_E
˜ ln D/(2e)^2. We have calculated weak-localization one-loop
renormalization of the diffusion coefficient, δ D(ω), and
found δ K(t)= -4/3√ π 2e√ D (t-2t_E)^3/2 for
2tE ˜ t≪ t_L, where t_L ˜ D/(2e)^2 is the
time to develop the strong localization [1,2]. The predicted
classical-quantum crossover may be observed by performing time-resolved
potentiometry on the kicked Josephson grain. Alternatively, the effect
may be detected by driving a periodic current of a large amplitude,
J≫ J_c, across the grain and monitoring fluctuations of voltage. We
believe that such a crossover applies to other periodic driven systems.
[1] G. Casati et. al., Lect. Notes Phys.93, 334 (1979). [2] S.Fishman
et. al. Phys. Rev. Lett. 49, 509 (1982); A.Altland, ibid. 71, 69 (1993).
[Show abstract][Hide abstract] ABSTRACT: We study a crossover from classical to quantum picture in the electron energy statistics in a system with broken time-reversal symmetry. The perturbative and nonperturbative parts of the two level correlation function, $R(\omega)$ are analyzed. We find that in the intermediate region, $\Delta\ll\omega\sim t_E^{-1}\ll t_{erg}^{-1}$, where $t_E$ and $t_{erg}$ are the Ehrenfest and ergodic times, respectively, $R(\omega)$ consists of a series of oscillations with the periods depending on $t_E$, deviating from the universal Wigner-Dyson statistics. These Ehrenfest oscillations have the period dependence as $t_E^{-1}$ in the perturbative part. [For systems with time-reversal symmetry, this oscillation in the perturbative part of $R(\omega)$ was studied in an earlier work (I. L. Aleiner and A. I. Larkin, Phys. Rev. E {\bf 55}, R1243 (1997))]. In the nonperturbative part they have the period dependence as $(\Delta^{-1}+\alpha t_E)^{-1}$ with $\alpha$ a universal numerical factor. The amplitude of the leading order Ehrenfest oscillation in the nonperturbative part is larger than that of the perturbative part. Comment: 20 pages, 4 figures, submitted to Phys. Rev. B
Physical Review B 10/2003; 70(3). DOI:10.1103/PhysRevB.70.035305 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider the effect of the RKKY interaction between magnetic impurities on the electron relaxation rates in a normal metal. The interplay between the RKKY interaction and the Kondo effect may result in a non-monotonic temperature dependence of the electron momentum relaxation rate, which determines the Drude conductivity. The electron phase relaxation rate, which determines the magnitude of the weak localization correction to the resistivity, is also a non-monotonic function of temperature. For this function, we find the dependence of the position of its maximum on the concentration of magnetic impurities. We also relate the electron energy relaxation rate to the excitation spectrum of the system of magnetic impurities. The energy relaxation determines the distribution function for the out-of-equilibrium electrons. Measurement of the electron distribution function thus may provide information about the excitations in the spin glass phase. Comment: 15 pages, 5 figures
[Show abstract][Hide abstract] ABSTRACT: What quantity controls the Coulomb blockade oscillations if the dot-lead conductance is essentially frequency dependent? We argue that it is the conductance at the imaginary frequency given by the effective charging energy. The latter may be very different from the bare charging energy due to the interface-induced capacitance (or inductance). These observations are supported by a number of examples, considered from the weak and strong coupling (perturbation theory versus instanton calculus) perspectives.
[Show abstract][Hide abstract] ABSTRACT: We investigate the crossover from the semiclassical to the quantum description of electron energy states in a chaotic metal grain connected to a superconductor. We consider the influence of scattering off point impurities (quantum disorder) and of quantum diffraction (quantum chaos) on the electron density of states. We show that both the quantum disorder and the quantum chaos open a gap near the Fermi energy. The size of the gap is determined by the mean free time in disordered systems and by the Ehrenfest time in clean chaotic systems. Particularly, if both times become infinitely large, the density of states is gapless, and if either of these times becomes shorter than the electron escape time, the density of states is described by random matrix theory. Using the Usadel equation, we also study the density of states in a grain connected to a superconductor by a diffusive contact. Comment: 20 pages, 10 figures
[Show abstract][Hide abstract] ABSTRACT: The superconductivity in very thin rings is suppressed by quantum phase slips. As a result, the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrödinger equation with twisted boundary conditions.
[Show abstract][Hide abstract] ABSTRACT: It is shown that states with phase increments deltaphi > pi can form in superconductor-narrowing (normal metal)-superconductor systems. If the conditions a << l << xi(0), where a is the cross-sectional size of the narrowing, l is the length of narrowing, and xi(0) is the correlation radius at zero temperature, are satisfied, there is a region of parameters (a, l, xi(0), T) in which the critical current is attained in solutions with a phase difference deltaphi > pi. (C) 2002 MAIK "Nauka / Interperiodica".
[Show abstract][Hide abstract] ABSTRACT: A superconductor with interacting paramagnetic impurities is considered. The impurities are coupled via the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. At a temperature Tg, the system of magnetic impurities forms a spin-glass state. We study the effect of the spin-spin interactions on the superconducting transition point at T<Tg. We show that superconducting properties depend on the state of the spin system via spin-spin autocorrelation functions. With the help of the Keldysh technique, a general nonequilibrium Gor’kov equation is derived. Possible aging effects in the superconducting transition point are discussed. The equilibrium superconducting transition point is found explicitly and shown to be shifted towards higher temperatures and impurity concentrations compared to the classical Abrikosov-Gor’kov curve. The corresponding shift of the superconducting quantum critical point is quite small (about 10%). A method of calculating spin-spin correlation function is suggested. The method combines the ideas of random mean-field method and virial expansion. We calculate analytically the first virial term for the spin-spin correlator for the quantum Heisenberg spin glass with the RKKY interactions in the quasiequilibrium regime.
Physical Review B 08/2002; 66(6). DOI:10.1103/PhysRevB.66.064526 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The leading (Gaussian) fluctuation correction to the weak coupling zero temperature BCS superconducting gap equation is computed. We find that the dominant contribution comes from the high energies and momenta (compared to the gap) and gives a correction smaller by the weak-coupling factor $gN_0$ than the mean-field terms. This correction is small due to cancellation of singular contributions from the amplitude and phase mode at high energies and momenta.
Physical Review B 08/2002; 70(21). DOI:10.1103/PhysRevB.70.214531 · 3.74 Impact Factor