arXiv subjects

V. B. Geshkenbein

Publications and source records attributed to V. B. Geshkenbein.

At least 19 recordsLinked to original sources

arXiv2017

Vortex dynamics in type II superconductors under strong pinning conditions

We study effects of pinning on the dynamics of a vortex lattice in a type II superconductor in the strong-pinning situation and determine the force--velocity (or current--voltage) characteristic combining analytical and numerical methods. Our analysis deals with a small density $n_p$ of defects that act with a large force $f_p$ on the vortices, thereby inducing bistable configurations that are a characteristic feature of strong pinning theory. We determine the velocity-dependent average pinning-force density $\langle F_p(v)\rangle$ and find that it changes on the velocity scale $v_p \sim f_p/ηa_0^3$, where $η$ is the viscosity of vortex motion and $a_0$ the distance between vortices. In the small pin-density limit, this velocity is much larger than the typical flow velocity $v_c \sim F_c/η$ of the free vortex system at drives near the critical force-density $F_c = \langle F_p(v=0)\rangle \propto n_p f_p$. As a result, we find a generic excess-force characteristic, a nearly linear force--velocity characteristic shifted by the critical force-density $F_c$; the linear flux-flow regime is approached only at large drives. Our analysis provides a derivation of Coulomb's law of dry friction for the case of strong vortex pinning.

cond-mat.supr-con↗

arXiv2016

Probing the pinning landscape in type-II superconductors via Campbell penetration depth

Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $λ_{\rm \scriptscriptstyle C}$ defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth $λ_{\rm \scriptscriptstyle C}$ using strong pinning theory. Our results explain the dependence of $λ_{\rm \scriptscriptstyle C}$ on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions as well as $δT_c$- and $δ\ell$-pinning, we discuss the behavior of the Campbell length for different vortex state preparations within the phenomenological $H$-$T$ phase diagram and compare our results with recent experiments.

cond-mat.supr-con↗

arXiv2015

Campbell penetration in the critical state of type-II superconductors

The penetration of an $ac$ magnetic signal into a type II superconductor residing in the Shubnikov phase depends on the pinning properties of Abrikosov vortices. Within a phenomenological theory, the so-called Campbell penetration depth $λ_{\rm \scriptscriptstyle C}$ is determined by the curvature $α$ at the bottom of the effective pinning potential. Preparing the sample into a Bean critical state, this curvature vanishes and the Campbell length formally diverges. We make use of the microscopic expression for the pinning force density derived within strong pinning theory and show how flux penetration on top of a critical state proceeds in a regular way.

cond-mat.supr-con↗

arXiv2015

Campbell response in type II superconductors under strong pinning conditions

Measuring the $ac$ magnetic response of a type II superconductor provides valuable information on the pinning landscape (pinscape) of the material. We use strong pinning theory to derive a microscopic expression for the Campbell length $λ_{\rm \scriptscriptstyle C}$, the penetration depth of the $ac$ signal. We show that $λ_{\rm \scriptscriptstyle C}$ is determined by the jump in the pinning force, in contrast to the critical current $j_c$ which involves the jump in pinning energy. We demonstrate that the Campbell lengths generically differ for zero-field-cooled and field-cooled samples and predict that hysteretic behavior can appear in the latter situation. We compare our findings with new experimental data and show the potential of this technique in providing information on the material's pinscape.

cond-mat.supr-con↗

arXiv2014

Suppression of Geometric Barrier in Type II Superconducting Strips

We study the magnetic response of a superconducting double strip, i.e., two parallel coplanar thin strips of width $2w$, thickness $d \ll w$ and of infinite length, separated by a gap of width $2s$ and subject to a perpendicular magnetic field $H$. The magnetic properties of this system are governed by the presence of a geometric energy barrier for vortex penetration which we investigate as a function of applied field $H$ and gap parameter $s$. The new results deal with the case of a narrow gap $s \ll w$, where the field penetration from the inner edges is facilitated by large flux focusing. Upon reducing the gap width $2s$, we observe a considerable rearrangement of the screening currents, leading to a strong reduction of the penetration field and the overall magnetization loop, with a suppression factor reaching $\sim (d/w)^{1/2}$ as the gap drops below the sample thickness, $2s < d$. We compare our results with similar systems of different shapes (elliptic, rectangular platelet) and include effects of surface barriers as well. Furthermore, we verify that corrections arising from the magnetic response of the Shubnikov phase in the penetrated state are small and can be omitted. Extending the analysis to multiple strips, we determine the specific sequence of flux penetrations into the different strips. Our studies are relevant for the understanding of platelet shaped samples with cracks or the penetration into layered superconductors at oblique magnetic fields.

cond-mat.supr-con↗

arXiv2011

Dynamic Aspects of Strong Pinning

We determine the current--voltage characteristic of type II superconductors in the presence of strong pinning centers. Focusing on a small density of defects, we derive a generic form for the characteristic with a linear flux-flow branch shifted by the critical current (excess-current characteristic). The details near onset, a hysteretic jump (for $κ\gg 1$) or a smooth velocity turn-on ($κ\to 1$), depend on the Labusch parameter $κ$ characterising the pinning centers. Pushing the single-pin analysis into the weak pinning domain, we reproduce the collective pinning results for the critical current.

cond-mat.supr-con↗

arXiv2010

Free-energy distribution functions for the randomly forced directed polymer

We study the $1+1$-dimensional random directed polymer problem, i.e., an elastic string $ϕ(x)$ subject to a Gaussian random potential $V(ϕ,x)$ and confined within a plane. We mainly concentrate on the short-scale and finite-temperature behavior of this problem described by a short- but finite-ranged disorder correlator $U(ϕ)$ and introduce two types of approximations amenable to exact solutions. Expanding the disorder potential $V(ϕ,x) \approx V_0(x) + f(x) ϕ(x)$ at short distances, we study the random force (or Larkin) problem with $V_0(x) = 0$ as well as the shifted random force problem including the random offset $V_0(x)$; as such, these models remain well defined at all scales. Alternatively, we analyze the harmonic approximation to the correlator $U(ϕ)$ in a consistent manner. Using direct averaging as well as the replica technique, we derive the distribution functions ${\cal P}_{L,y}(F)$ and ${\cal P}_L(F)$ of free energies $F$ of a polymer of length $L$ for both fixed ($ϕ(L) = y$) and free boundary conditions on the displacement field $ϕ(x)$ and determine the mean displacement correlators on the distance $L$. The inconsistencies encountered in the analysis of the harmonic approximation to the correlator are traced back to its non-spectral correlator; we discuss how to implement this approximation in a proper way and present a general criterion for physically admissible disorder correlators $U(ϕ)$.

cond-mat.dis-nn↗

arXiv2008

Quantum instability in a dc-SQUID with strongly asymmetric dynamical parameters

A classical system cannot escape out of a metastable state at zero temperature. However, a composite system made from both classical and quantum degrees of freedom may drag itself out of the metastable state by a sequential process. The sequence starts with the tunneling of the quantum component which then triggers a distortion of the trapping potential holding the classical part. Provided this distortion is large enough to turn the metastable state into an unstable one, the classical component can escape. This process reminds of the famous baron Muenchhausen who told the story of rescuing himself from sinking in a swamp by pulling himself up by his own hair--we thus term this decay the `Muenchhausen effect'. We show that such a composite system can be conveniently studied and implemented in a dc-SQUID featuring asymmetric dynamical parameters. We determine the dynamical phase diagram of this system for various choices of junction parameters and system preparations.

cond-mat.supr-con↗

arXiv2008

The dynamically asymmetric SQUID: Münchhausen effect

We report on a complex zero-temperature decay channel of a classical object in a metastable state coupled to a quantum degree of freedom. This setting can be realized in a dc-SQUID where both Josephson-junctions have identical critical currents I_c but feature strongly asymmetric dynamical parameters; more precisely, selecting both parameters C and 1/R adequately large for one and small for the other junction makes the first junction behave essentially classical but lets quantum effects be present for the second one. The decay process is initiated by the tunneling of the quantum junction, which distorts the trapping potential of the classical junction; the metastable state of the latter then becomes unstable if the distortion is large enough. We present the dynamical phase diagram of this system providing the dependence of this decay channel on the external bias current I and on the coupling strength between the two junctions, determined by the loop inductance L.

cond-mat.supr-con↗

arXiv2008

Joint free energy distribution in the random directed polymer problem

We consider two configurations of a random directed polymer of length L confined to a plane and ending in two points separated by 2u. Defining the mean free energy $\bar F$ and the free energy difference F' of the two configurations, we determine the joint distribution function P_{L,u}(\bar F,F') using the replica approach. We find that for large L and large negative free energies $\bar F$, the joint distribution function factorizes into longitudinal (P_{L,u} (\bar F)) and transverse (P_{u}(F')) components, which furthermore coincide with results obtained prevously via different independent routes.

cond-mat.dis-nn↗

arXiv2006

Surface Melting of the Vortex Lattice in Layered Superconductors: Density Functional Theory

We study the effects of an $ab$-surface on the vortex-solid to vortex-liquid transition in layered superconductors in the limit of vanishing inter-layer Josephson coupling. We derive the interaction between pancake vortices in a semi-infinite sample and adapt the density functional theory of freezing to this system. We obtain an effective one-component order-parameter theory which can be used to describe the effects of the surface on vortex-lattice melting. Due to the absence of protecting layers in the neighbourhood of the surface, the vortex lattice formed near the surface is more susceptible to thermal fluctuations. Depending on the value of the magnetic field, we predict either a continuous or a discontinuous surface melting transition. For intermediate values of the magnetic field, the surface melts continuously, assisting the formation of the liquid phase and suppressing hysteresis above the melting transition, a prediction consistent with experimental results. For very low and very high magnetic fields, the surface melts discontinuously. The two different surface melting scenarios are separated by two surface multicritical points, which we locate on the melting line.

cond-mat.supr-con↗

arXiv2005

Surface melting of the vortex lattice

We discuss the effect of an (ab)-surface on the melting transition of the pancake-vortex lattice in a layered superconductor within a density functional theory approach. Both discontinuous and continuous surface melting are predicted for this system, although the latter scenario occupies the major part of the low-field phase diagram. The formation of a quasi-liquid layer below the bulk melting temperature inhibits the appearance of a superheated solid phase, yielding an asymmetric hysteretic behavior which has been seen in experiments.

cond-mat.supr-con↗

arXiv2005

Dissociation of vortex stacks into fractional-flux vortices

We discuss the zero field superconducting phase transition in a finite system of magnetically coupled superconducting layers. Transverse screening is modified by the presence of other layers resulting in topological excitations with fractional flux. Vortex stacks trapping a full flux and present at any finite temperature undergo an evaporation transition which corresponds to the depairing of fractional-flux vortices in individual layers. We propose an experiment with a bi-layer system allowing us to identify the dissociation of bound vortex molecules.

cond-mat.supr-con↗

arXiv2004

Superconducting tetrahedral quantum bits

We propose a new design for a quantum bit with four superconducting islands in the topology of a symmetric tetrahedron, uniformly frustrated with one-half flux-quantum per loop and one-half Cooper-pair per island. This structure emulates a noise-resistant spin-1/2 system in a vanishing magnetic field. The tetrahedral quantum bit combines a number of advances such as a doubly degeneracy ground state minimizing decoherence via phonon radiation, a weak quadratic sensitivity to electric and magnetic noise, relieved constraints on the junction fabrication, a large freedom in manipulation, and attractive measurement schemes. The simultaneous appearance of a degenerate ground state and a weak noise sensitivity are consequences of the tetrahedral symmetry, while enhanced quantum fluctuations derive from the special magnetic frustration. We determine the spectral properties of the tetrahedral structure within a semiclassical analysis and confirm the results numerically. We show how proper tuning of the charge-frustration selects a doubly degenerate ground state and discuss the qubit's manipulation through capacitive and inductive coupling to external bias sources. The complete readout of all the spin-components is achieved through coupling of the internal qubit currents to external junctions driven close to criticality during the measurement.

cond-mat.supr-con↗

arXiv2004

Peak effect at the weak- to strong pinning crossover

In type-II superconductors, the magnetic field enters in the form of vortices; their flow under application of a current introduces dissipation and thus destroys the defining property of a superconductor. Vortices get immobilized by pinning through material defects, thus resurrecting the supercurrent. In weak collective pinning, defects compete and only fluctuations in the defect density produce pinning. On the contrary, strong pins deform the lattice and induce metastabilities. Here, we focus on the crossover from weak- to strong bulk pinning, which is triggered either by increasing the strength $f_\mathrm{p}$ of the defect potential or by decreasing the effective elasticity of the lattice (which is parametrized by the Labusch force $f_\mathrm{Lab}$). With an appropriate Landau expansion of the free energy we obtain a peak effect with a sharp rise in the critical current density $j_\mathrm{c} \sim j_0 (a_0ξ^2 n_p) (ξ^2/a_0^2) (f_\mathrm{p}/f_\mathrm{Lab} -1)^2$.

cond-mat.supr-con↗

arXiv2003

Weak- to strong pinning crossover

Material defects in hard type II superconductors pin the flux lines and thus establish the dissipation-free current transport in the presence of a finite magnetic field. Depending on the density and pinning force of the defects and the vortex density, pinning is either weak-collective or strong. We analyze the weak- to strong pinning crossover of vortex matter in disordered superconductors and discuss the peak effect appearing naturally in this context.

cond-mat.supr-con↗

arXiv2003

Quantum fluctuations in thin superconducting wires of finite length

In one dimensional wires, fluctuations destroy superconducting long-range order and stiffness at finite temperatures; in an infinite wire, quasi-long range order and stiffness survive at zero temperature if the wire's dimensionless admittance $μ$ is large, $μ> 2$. We analyze the disappearance of this superconductor-insulator quantum phase transition in a finite wire and its resurrection due to the wire's coupling to its environment characterized through the dimensionless conductance $K$. Integrating over phase slips, we determine the flow of couplings and establish the $μ$--$K$ phase diagram.

cond-mat.supr-con↗

arXiv2003

Impact of long-range interactions on the disordered vortex lattice

The interaction between the vortex lines in a type-II superconductor is mediated by currents. In the absence of transverse screening this interaction is long-ranged, stiffening up the vortex lattice as expressed by the dispersive elastic moduli. The effect of disorder is strongly reduced, resulting in a mean-squared displacement correlator = <[u(R,L)-u(0,0)]^2> characterized by a mere logarithmic growth with distance. Finite screening cuts the interaction on the scale of the London penetration depth λand limits the above behavior to distances R<λ. Using a functional renormalization group (RG) approach, we derive the flow equation for the disorder correlation function and calculate the disorder-averaged mean-squared relative displacement \propto ln^{2σ} (R/a_0). The logarithmic growth (2σ=1) in the perturbative regime at small distances [A.I. Larkin and Yu.N. Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979)] crosses over to a sub-logarithmic growth with 2σ=0.348 at large distances.

cond-mat.supr-con↗