A. I. Larkin

Institute for Theoretical and Experimental Physics, Moskva, Moscow, Russia

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Publications (194)434.22 Total impact

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    ABSTRACT: The phase transition into a spin glass-like state is predicted for the system of superconductive wires connected by Josephson links and placed into the magnetic field. History-dependent equations of state for T<Tc are derived and diamagnetic response to the variation of the magnetic field is predicted. The experiments that can solve the discrepancy between the analytical theory and the numerical simulations on the existence of the phase transition in the vector spin glasses are discussed.
    Modern Physics Letters B 01/2012; 01(01n02). · 0.48 Impact Factor
  • L.b.ioffe, A.i.larkin
    International Journal of Modern Physics B 01/2012; 01(03n04). · 0.46 Impact Factor
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    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). · 0.46 Impact Factor
  • L. B.ioffe, A. I.larkin
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    ABSTRACT: In the limit of weak quantum fluctuations an effective long-wave action of the Heisenberg quantum antiferromagnet is obtained which allows one to get a spectrum, spin, and statistics of long-wave fluctuations. In the vicinity of the point of instability of an antiferromagnetic state quantum fluctuations result (at zero temperature as well) in a paramagnetic phase of a spin liquid.
    International Journal of Modern Physics B 01/2012; 02(02). · 0.46 Impact Factor
  • Roman Lutchyn, Leonid Glazman, Anatoly Larkin
    Physical Review B. 08/2007; 76(6).
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    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.
    EPL (Europhysics Letters) 07/2007; 30(6):367. · 2.26 Impact Factor
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    R. M. Lutchyn, L. I. Glazman, A. I. Larkin
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    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).
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    Julia S Meyer, K A Matveev, A I Larkin
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    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.
    Physical Review Letters 04/2007; 98(12):126404. · 7.73 Impact Factor
  • R. M. Lutchyn, L. I. Glazman, A. I. Larkin
    [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 .
    Physical review. B, Condensed matter 08/2006; · 3.66 Impact Factor
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    Roman Lutchyn, Leonid Glazman, Anatoly Larkin
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    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.
    Physical review. B, Condensed matter 04/2005; · 3.66 Impact Factor
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    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 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; · 1.68 Impact Factor
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    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.
    Physical Review Letters 07/2004; 92(24):247002. · 7.73 Impact Factor
  • C. S. Tian, A. Kamenev, A. I. Larkin
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    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).
    02/2004; -1:22004.
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    Chushun Tian, Anatoly I. Larkin
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    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; · 3.66 Impact Factor
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    M. G. Vavilov, L. I. Glazman, A. I. Larkin
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    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
    Physical review. B, Condensed matter 05/2003; · 3.66 Impact Factor
  • Yu. N. Ovchinnikov, A. I. Larkin
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    ABSTRACT: Without Abstract
    JETP Letters 01/2003; 77(2):118-118. · 1.52 Impact Factor
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    A Kamenev, A I Larkin
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    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.
    Physical Review Letters 01/2003; 89(23):236801. · 7.73 Impact Factor
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    M. G. Vavilov, A. I. Larkin
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    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
    Physical review. B, Condensed matter 10/2002; · 3.66 Impact Factor
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    K A Matveev, A I Larkin, L I Glazman
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    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.
    Physical Review Letters 09/2002; 89(9):096802. · 7.73 Impact Factor
  • Y. N. Ovchinnikov, A. I. Larkin
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    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".
    JETP Letters 09/2002; · 1.52 Impact Factor

Publication Stats

9k Citations
434.22 Total Impact Points

Institutions

  • 1980–2012
    • Institute for Theoretical and Experimental Physics
      Moskva, Moscow, Russia
  • 1973–2012
    • Russian Academy of Sciences
      • L. D. Landau Institute for Theoretical Physics
      Moskva, Moscow, Russia
  • 2007
    • The Ohio State University
      • Department of Physics
      Columbus, OH, United States
  • 1996–2007
    • University of Minnesota Duluth
      • Department of Physics
      Duluth, Minnesota, United States
    • Argonne National Laboratory
      Lemont, Illinois, United States
  • 1993–2007
    • Weizmann Institute of Science
      • Department of Physics of Condensed Matter
      Tel Aviv, Tel Aviv, Israel
  • 2000
    • Duke University
      • Department of Physics
      Durham, NC, United States
  • 1999–2000
    • Ruhr-Universität Bochum
      • Institut für Theoretische Physik III
      Bochum, North Rhine-Westphalia, Germany
  • 1994
    • Bar Ilan University
      • Department of Physics
      Ramat Gan, Tel Aviv, Israel
  • 1991
    • The University of Tokyo
      • Department of Applied Life Sciences
      Tokyo, Tokyo-to, Japan
  • 1988
    • Karlsruhe Institute of Technology
      • Institute of Theoretical Condensed Matter Physics
      Karlsruhe, Baden-Wuerttemberg, Germany
  • 1962
    • Kurchatov Institute
      Moskva, Moscow, Russia