arXiv subjects

M. V. Feigel'man

Publications and source records attributed to M. V. Feigel'man.

At least 37 records · Page 2Linked to original sources

arXiv2013

Subgap states in disordered superconductors

We revise the problem of the density of states in disordered superconductors. Randomness of local sample characteristics translates to the quenched spatial inhomogeneity of the spectral gap, smearing the BCS coherence peak. We show that various microscopic models of potential and magnetic disorder can be reduced to a universal phenomenological random order parameter model, whereas the details of the microscopic description are encoded in the correlation function of the order parameter fluctuations. The resulting form of the density of states is generally described by two parameters: the width Gamma measuring the broadening of the BCS peak, and the energy scale Gamma_{tail} which controls the exponential decay of the density of the subgap states. We refine the existing instanton approaches for determination of Gamma_{tail} and show that they appear as limiting cases of a unified theory of optimal fluctuations in a nonlinear system. Application to various types of disorder is discussed.

cond-mat.supr-con↗

arXiv2012

Tunneling conductance due to discrete spectrum of Andreev states

We study tunneling spectroscopy of discrete subgap Andreev states in a superconducting system. If the tunneling coupling is weak, individual levels are resolved and the conductance $G(V)$ at small temperatures is composed of a set of resonant Lorentz peaks which cannot be described within perturbation theory over tunnelling strength. We establish a general formula for their widths and heights and show that the width of any peak scales as normal-state tunnel conductance, while its height is $\lesssim 2e^2/h$ and depends only on contact geometry and the spatial profile of the resonant Andreev level. We also establish an exact formula for the single-channel conductance that takes the whole Andreev spectrum into account. We use it to study the interference of Andreev reflection processes through different levels. The effect is most pronounced at low voltages, where an Andreev level at $E_j$ and its conjugate at $-E_j$ interfere destructively. This interference leads to the quantization of the zero-bias conductance: G(0) equals $2e^2/h$ (or 0) if there is (there is not) a Majorana fermion in the spectrum, in agreement with previous results from $S$-matrix theory. We also study $G(eV>0)$ for a system with a pair of almost decoupled Majorana fermions with splitting $E_0$ and show that at lowest $E_0$ there is a zero-bias Lorentz peak of width $W$ as expected for a single Majorana fermion (a topological NS-junction) with a narrow dip of width $E_0^2/W$ at zero bias, which ensures $G(0)=0$ (the NS-junction remains trivial on a very small energy scale). As the coupling $W$ gets stronger, the dip becomes narrower, which can be understood as enhanced decoupling of the remote Majorana fermion. Then the zero-bias dip requires extremely low temperatures $T\lesssim E_0^2/W$ to be observed.

cond-mat.mes-hall↗

arXiv2012

Universal Broadening of the Bardeen-Cooper-Schrieffer Coherence Peak of Disordered Superconducting Films

In disordered superconductors, the local pairing field fluctuates in space, leading to the smearing of the BCS peak in the density of states and appearance of the subgap tail states. We analyze the universal mesoscopic contributions to these effects and show that they are enhanced by the Coulomb repulsion. In the vicinity of the quantum critical point, where superconductivity is suppressed by the "fermionic mechanism", strong smearing of the peak due to mesoscopic fluctuations is predicted.

cond-mat.supr-con↗

arXiv2012

Majorana state on the surface of a disordered 3D topological insulator

We study low-lying electron levels in an "antidot" capturing a coreless vortex on the surface of a three-dimensional topological insulator in the presence of disorder. The surface is covered with a superconductor film with a hole of size R larger than coherence length, which induces superconductivity via proximity effect. Spectrum of electron states inside the hole is sensitive to disorder, however, topological properties of the system give rise to a robust Majorana bound state at zero energy. We calculate the subgap density of states with both energy and spatial resolution using the supersymmetric sigma model method. Tunneling into the hole region is sensitive to the Majorana level and exhibits resonant Andreev reflection at zero energy.

cond-mat.mes-hall↗

arXiv2010

Excitation spectrum of a 2D long-range Bose-liquid with a supersymmetry

We have studied excitation spectrum of the specfic 2D model of strongly interacting Bose particles via mapping of the many-body Schrodinger equation in imaginary time to the classical stochastic dynamics. In a broad range of coupling strength $α$ a roton-like spectrum is found, with the roton gap being extremely small in natural units. A single quantum phase transition between strongly correlated supefluid and quantum Berezinsky crystal is found.

cond-mat.supr-con↗

arXiv2010

Anomalous Josephson current via Majorana bound states in topological insulators

We propose a setup involving Majorana bound states (MBS) hosted by a vortex on a superconducting surface of a 3D Topological Insulator (TI). We consider a narrow channel drilled across a TI slab with both sides covered by s-wave superconductor. In the presence of a vortex pinned to such a channel, it acts as a ballistic nanowire connecting the superconducting surfaces, with a pair of MBS localized in it. The energies of the MBS possess a 4π-periodic dependence on the superconductive phase difference ϕbetween the surfaces. It results in the appearence of an anomalous term in the current-phase relation, I_a(ϕ) for the supercurrent flowing along the channel between the superconductive surfaces. We have calculated the shape of the 4π-periodic function I_a(ϕ), as well as the dependence of its amplitude on temperature and system parameters.

cond-mat.mes-hall↗

arXiv2010

Superconductor-Insulator transition and energy localization

We develop an analytical theory for generic disorder-driven quantum phase transitions. We apply this formalism to the superconductor-insulator transition and we briefly discuss the applications to the order-disorder transition in quantum magnets. The effective spin-1/2 models for these transitions are solved in the cavity approximation which becomes exact on a Bethe lattice with large branching number K >> 1 and weak dimensionless coupling g << 1. The characteristic features of the low temperature phase is a large self-formed inhomogeneity of the order-parameter distribution near the critical point K_{c}(g) where the critical temperature T_{c} of the ordering transition vanishes. Near the quantum critical point, the typical value of the order parameter vanishes exponentially, B_{0}\propto e^{-C/(K-K_{c}(g))}. In the disordered regime, realized at K ω_{d} the level acquire a non-zero width which is self-generated by the many-body interactions. In this phase the spin model provides by itself an intrinsic thermal bath. Another phase is obtained at smaller K<K^{*}(g), where all the eigenstates are discrete, corresponding to full many-body localization. These results provide an explanation for the activated behavior of the resistivity in amorphous materials on the insulating side near the SI transition and a semi-quantitative description of the scanning tunneling data on its superconductive side.

cond-mat.supr-con↗

arXiv2010

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at $E_F=E_c$, superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at $E_F$ still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap $Δ$, that is due to many-body correlations and a new "pseudogap" energy scale $Δ_P$ which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive $T_c$. Two gap nature of the "pseudo-gaped superconductor" is shown to lead to a number of unusual physical properties.

cond-mat.supr-con↗

arXiv2010

Quantum spin metal state on a decorated honeycomb lattice

We present a modification of exactly solvable spin-(1/2) Kitaev model on the decorated honeycomb lattice, with a ground state of "spin metal" type. The model is diagonalized in terms of Majorana fermions; the latter form a 2D gapless state with a Fermi-circle those size depends on the ratio of exchange couplings. Low-temperature heat capacity C(T) and dynamic spin susceptibility χ(ω,T) are calculated in the case of small Fermi-circle. Whereas C(T)\sim T at low temperatures as it is expected for a Fermi-liquid, spin excitations are gapful and χ(ω,T) demonstrate unusual behaviour with a power-law peak near the resonance frequency. The corresponding exponent as well as the peak shape are calculated.

cond-mat.str-el↗

arXiv2009

AC Josephson effect in the long voltage-biased SINIS junction

Theory of non-stationary coherent effects is developed for superconductor-normal-superconductor (SNS) structures with relatively strong normal scattering on S/N interfaces (interface resistance is large compared to intrinsic resistance of N metal). Analitical expressions are found for the time-dependent anomalous Green functions induced in the N region under the fixed-voltage-bias. The amplitude of the current oscillations is determined in non-equilibrium conditions. Non-stationary correction to the distribution function is calculated in high-temperature limit and found to be slowly decreasing with the temperature, leading to the dominance of the second-harmonic term in the Josepshon current at high temperatures and low voltage.

cond-mat.supr-con↗

arXiv2008

Proximity-induced superconductivity in graphene

We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, T_c, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T<<T_c, and zero magnetic field, the density of states is characterized by a small gap E_g<T_c resulting from the collective proximity effect. Transverse magnetic field H_g(T) E_g is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field H_{g2}(T).

cond-mat.mes-hall↗

arXiv2008

Comment on "Superinsulator and Quantum Synchronization"

We show that the "theory" of "superinsulating" state presented by V.Vinokur et al (Nature vol. 452, p. 613, 2008) and Fistul et al (Phys. Rev. Lett. vol. 100, 086805, 2008) is essentially incorrect due to a sequence of errors in the theoretical analysis of the standard model of Josephson arrays which properties have been carefully studied and described in the literature. The line of calculations suggested in these articles lead to unphysical results. In particular, the calculations predict a direct current flowing through a capacitor. Moreover, this current may flow even in the absence of voltage - a sort of supercurrent flowing in the "superinsulating" state. We also question that the theoretical model employed in these works, even if treated correctly, is applicable to the analysis of experimental data on homogeneously disordered superconductive films.

cond-mat.supr-con↗

arXiv2007

Superconductor-insulator duality for the array of Josephson wires

We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N \gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions's Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter $q \approx N^2 \exp(-\sqrt{8E_J/E_C})$, with superconductive state corresponding to small $q < q_c $. The values of $q_c$ are calculated for magnetic frustrations $f= 0$ and $f= \frac12$. Temperature of superconductive transition $T_c(q)$ and $q < q_c$ is estimated for the same values of $f$. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter $\bar{q} = q/\sqrt{N}$; we estimated critical value $\bar{q}_c$.

cond-mat.supr-con↗

arXiv2007

Theory of 2D superconductor with broken inversion symmetry

A detailed theory of a phase diagram of a 2D surface superconductor in a parallel magnetic field is presented. A spin-orbital interaction of the Rashba type is known to produce at a high magnetic field $h$ (and in the absence of impurities) an inhomogeneous superconductive phase similar to the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state with an order parameter $Δ(r) \propto \cos(Qr)$. We consider the case of a strong Rashba interaction with the spin-orbital splitting much larger than the superconductive gap $Δ$, and show that at low temperatures $T\leq 0.4 T_{c0}$ the LOFF-type state is separated from the usual homogeneous state by a first-order phase transition line. At higher temperatures another inhomogeneous state with $Δ(r) \propto \exp(i Qr)$ intervenes between the uniform BCS state and the LOFF-like state at $gμ_B h \approx 1.5 T_{c0}$. The modulation vector $Q$ in both phases is of the order of $gμ_B h/v_F$. The superfluid density $n_s^{yy}$ vanishes in the region around the second-order transition line between the BCS state and the new ``helical'' state. Non-magnetic impurities suppress both inhomogeneous states, and eliminate them completely at $T_{c0}τ\leq 0.11$. However, once an account is made of the next-order term over the small parameter $α/v_F \ll 1$, a relatively long-wave helical modulation with $Q \sim gμ_B hα/v_F^2$ is found to develop from the BCS state. This long-wave modulation is stable with respect to disorder. In addition, we predict that unusual vortex defects with a continuous core exist near the phase boundary between the helical and the LOFF-like states. In particular, in the LOFF-like state these defects may carry a half-integer flux.

cond-mat.supr-con↗

arXiv2006

Eigenfunction fractality and pseudogap state near superconductor-insulator transition

We develop a theory of a pseudogap state appearing near the superconductor-insulator transition in strongly disordered metals with attractive interaction. We show that such an interaction combined with the fractal nature of the single particle wave functions near the mobility edge leads to an anomalously large single particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

cond-mat.supr-con↗

arXiv2006

Proximity effect in the presence of Coulomb interaction and magnetic field

We consider a small metallic grain coupled to a superconductor by a tunnel contact. We study the interplay between proximity and charging effects in the presence of the external magnetic field. Employing the adiabatic approximation we develop a self-consistent theory valid for an arbitrary ratio of proximity and Coulomb strength. The magnetic field suppresses the proximity-induced minigap in an unusual way. We find the phase diagram of the grain in the charging energy - magnetic field plane. Two distinct states exist with different values and magnetic field dependences of the minigap. The first-order phase transition occurs between these two minigapped states. The transition to the gapless state may occur by the first- or second-order mechanism depending on the charging energy. We also calculate the tunneling density of states in the grain. The energy dependence of this quantity demonstrates two different gaps corresponding to the Coulomb and proximity effects. These gaps may be separated in sufficiently high magnetic field.

cond-mat.supr-con↗

arXiv2005

Josephson Effect in a Coulomb-blockaded SINIS Junction

The problem of Josephson current through Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as phase bias changes from 0 to pi. In the broad range of Coulomb strength the current-phase relation is substantially non-sinusoidal and qualitatively different from the case of semi-ballistic SNS junctions. Coulomb interaction leads to appearance of a local minimum in the current at some intermediate value of phase difference applied to the junction.

cond-mat.mes-hall↗

arXiv2005

2D SNS junction with Rashba spin-orbit interaction

The effect of Rashba spin-orbital interaction upon supercurrent in S-2DEG-S proximity junctions is investigated in the clean limit. Generalization of Beenakker's formula for Andreev levels to the case of spin-orbital scattering is presented. Spin-orbit - induced splitting of Andreev bound-states is predicted for a junction of infinite width, and with non-vanishing normal backscattering at S/N interfaces. Semiclassical average of the Josephson current is however insensitive to the Rashba coupling as long as electron-electron interaction in 2DEG is neglected.

cond-mat.mes-hall↗