arXiv subjects

Vadim B. Geshkenbein

Publications and source records attributed to Vadim B. Geshkenbein.

16 recordsLinked to original sources

arXiv2024

Creep-enhanced vortex pinning revealed through nonmonotonic relaxation of the Campbell length

We study the effects of flux creep on the linear AC response of the vortex lattice in single crystals Ca$_3$Ir$_4$Sn$_{13}$ by measuring the Campbell penetration depth, $λ_{\rm \scriptscriptstyle C}(T,H,t)$. Thermal fluctuations release vortices from shallow pinning sites, only for them to become re-trapped by deeper potential wells, causing an initial increase of the effective Labusch parameter, which is proportional to the pinning well curvature. This effect cannot be detected in conventional magnetic relaxation measurements but is revealed by our observation of a nonmonotonic time evolution of $λ_{\rm \scriptscriptstyle C}(T,H,t)$, which directly probes the average curvature of the occupied pinning centers. The time evolution of $λ_{\rm \scriptscriptstyle C}(T,H,t)$ was measured at different temperatures in samples with different densities of pinning centers produced by electron irradiation. The curves can be collapsed together when plotted on a logarithmic time scale $t \to T\ln{(t/t_0)}$ confirming that the time evolution is driven by flux creep. The $λ_{\rm \scriptscriptstyle C}(T,H,t)$ is hysteretic with a noticeable nonmonotonic relaxation in the presence of a vortex density gradient (after zero-field cooling), but is monotonic after field cooling, where the vortex density is uniform. This result quantitatively corroborates the novel picture of vortex creep based on the strong pinning theory.

cond-mat.supr-con↗

arXiv2024

Superconductivity in atomically thin films: 2D critical state model

The comprehensive understanding of superconductivity is a multi-scale task that involves several levels, starting from the electronic scale determining the microscopic mechanism, going to the phenomenological scale describing vortices and the continuum-elastic scale describing vortex matter, to the macroscopic scale relevant in technological applications. The prime example for such a macro-phenomenological description is the Bean model that is hugely successful in describing the magnetic and transport properties of bulk superconducting devices. Motivated by the development of novel devices based on superconductivity in atomically thin films, such as twisted-layer graphene, here, we present a simple macro-phenomenological description of the critical state in such two-dimensional (2D) thin films. While transverse screening and demagnetization can be neglected in these systems, thereby simplifying the task in comparison with usual film- and platelet shaped samples, surface and bulk pinning are important elements to be included. We use our 2D critical state model to describe the transport and magnetic properties of 2D thin-film devices, including the phenomenon of non-reciprocal transport in devices with asymmetric boundaries and the superconducting diode effect.

cond-mat.supr-con↗

arXiv2023

Strong pinning transition with arbitrary defect potentials

Dissipation-free current transport in type II superconductors requires vortices to be pinned by defects in the underlying material. The pinning capacity of a defect is quantified by the Labusch parameter $κ\sim f_p/ξ\bar{C}$, measuring the pinning force $f_p$ relative to the elasticity $\bar{C}$ of the vortex lattice, with $ξ$ denoting the coherence length (or vortex core size) of the superconductor. The critical value $κ= 1$ separates weak from strong pinning, with a strong defect at $κ> 1$ able to pin a vortex on its own. So far, this weak-to-strong pinning transition has been studied for isotropic defect potentials, resulting in a critical exponent $μ= 2$ for the onset of the strong pinning force density $F_\mathrm{pin} \sim n_p f_p (ξ/a_0)^2(κ-1)^μ$, with $n_ p$ denoting the density of defects and $a_0$ the intervortex distance. The behavior changes dramatically when studying anisotropic defects with no special symmetries: the strong pinning then originates out of isolated points with length scales growing as $ξ(κ- 1)^{1/2}$, resulting in a different force exponent $μ= 5/2$. Our analysis of the strong pinning onset for arbitrary defect potentials $e_p(\mathbf{R})$, with $\mathbf{R}$ a planar coordinate, makes heavy use of the Hessian matrix describing its curvature and leads us to interesting geometrical structures. Both, onset and merger points are defined by local differential properties of the Hessian's determinant $D(\mathbf{R})$, specifically, its minima and saddle points. Extending our analysis to the case of a random two-dimensional pinning landscape, we discuss the topological properties of unstable and bistable regions as expressed through the Euler characteristic, with the latter related to the local differential properties of $D(\mathbf{R})$ through Morse theory.

cond-mat.supr-con↗

arXiv2021

Creep effects on the Campbell response in type II superconductors

Applying the strong pinning formalism to the mixed state of a type II superconductor, we study the effect of thermal fluctuations (or creep) on the penetration of an ac magnetic field as quantified by the so-called Campbell length $λ_\textrm{C}$. Within strong pinning theory, vortices get pinned by individual defects, with the jumps in the pinning energy ($Δe_\mathrm{pin}$) and force ($Δf_\mathrm{pin}$) between bistable pinned and free states quantifying the pinning process. We find that the evolution of the Campbell length $λ_{\rm C}(t)$ as a function of time $t$ is the result of two competing effects, the change in the force jumps $Δf_\mathrm{pin}(t)$ and a change in the trapping area $S_\mathrm{trap}(t)$ of vortices; the latter describes the area around the defect where a nearby vortex gets and remains trapped. Contrary to naive expectation, we find that during the decay of the critical state in a zero-field cooled (ZFC) experiment, the Campbell length $λ_{\rm C}(t)$ is usually nonmonotonic, first decreasing with time $t$ and then increasing for long waiting times. Field cooled (FC) experiments exhibit hysteretic effects in $λ_\textrm{C}$; relaxation then turns out to be predominantly monotonic, but its magnitude and direction depends on the specific phase of the cooling--heating cycle. Furthermore, when approaching equilibrium, the Campbell length relaxes to a finite value, different from the persistent current which vanishes at long waiting times $t$, e.g., above the irreversibility line. Finally, measuring the Campbell length $λ_\textrm{C}(t)$ for different states, zero-field cooled, field cooled, and relaxed, as a function of different waiting times $t$ and temperatures $T,$ allows to "spectroscopyse" the pinning potential of the defects.

cond-mat.supr-con↗

arXiv2021

Hessian characterization of a vortex in a maze

Recent advances in vortex imaging allow for tracing the position of individual vortices with high resolution. Pushing an isolated vortex through the sample with the help of a controlled $dc$ transport current and measuring its local $ac$ response, the pinning energy landscape could be reconstructed along the vortex trajectory [$\text{L. Embon } et\ al.$, $\text{Scientific Reports}$ $\mathbf{5}$, $7598$ $(2015)$]. This setup with linear tilts of the potential landscape reminds about the dexterity game where a ball is balanced through a maze. The controlled motion of objects through such tilted energy landscapes is fundamentally limited to those areas of the landscape developing local minima under appropriate tilt. We introduce the Hessian stability map and the Hessian character of a pinning landscape as new quantities to characterize a pinning landscape. We determine the Hessian character, the area fraction admitting stable vortex positions, for various types of pinning potentials: assemblies of cut parabolas, Lorentzian- and Gaussian-shaped traps, as well as a Gaussian random disordered energy landscape, with the latter providing a universal result of $(3-\sqrt{3})/6 \approx 21\%$ of stable area. Furthermore, we discuss various aspects of the vortex-in-a-maze experiment.

cond-mat.supr-con↗

arXiv2020

The role of rare events in the pinning problem

Type II superconductors exhibit a fascinating phenomenology that is determined by the dynamical properties of the vortex matter hosted by the material. A crucial element in this phenomenology is vortex pinning by material defects, e.g., immobilizing vortices at small drives and thereby guaranteeing dissipation-free current flow. Pinning models for vortices and other topological defects, such as domain walls in magnets or dislocations in crystals, come in two standard variants: i) weak collective pinning, where individual weak defects are unable to pin, while the random accumulation of many force centers within a collective pinning volume combines into an effective pin, and ii) strong pinning, where strong defects produce large vortex displacements and bistabilities that lead to pinning on the level of individual defects. The transition between strong and weak pinning is quantified by the Labusch criterion $κ\approx f_p/\bar{C}ξ= 1$, where $f_p$ and $\bar{C}$ are the force of one defect and the effective elasticity of the vortex lattice, respectively ($ξ$ is the coherence length). Here, we show that a third generic type of pinning becomes dominant when the pinning force $f_p$ enters the weak regime, the pinning by rare events. We find that within an intermediate regime $1/2 < κ< 1$, compact pairs of weak defects define strong pinning clusters that extend the mechanism of strong pinning into the weak regime. We present a detailed analysis of this cluster-pinning mechanism and show that its pinning-force density parametrically dominates over the weak pinning result. The present work is a first attempt to include correlations between defects into the discussion of strong pinning.

cond-mat.supr-con↗

arXiv2019

Experimental test of strong pinning and creep in current-voltage characteristics of type II superconductors

Pinning and creep determine the current--voltage characteristic of a type II superconductor and thereby its potential for technological applications. The recent development of strong pinning theory provides us with a tool to assess a superconductor's electric properties in a quantitative way. Motivated by the observation of typical excess-current characteristics and field-scaling of critical currents, here, we analyze current--voltage characteristics measured on 2H-NbSe$_2$ and $a$-MoGe type II superconductors within the setting provided by strong pinning theory. The experimentally observed shift and rounding of the voltage-onset is consistent with the predictions of strong pinning in the presence of thermal fluctuations. We find the underlying parameters determining pinning and creep and discuss their consistency.

cond-mat.supr-con↗

arXiv2019

Strong pinning theory of thermal vortex creep in type II superconductors

We study thermal effects on pinning and creep in type-II superconductors where vortices interact with a low density $n_p$ of strong point-like defects with pinning energy $e_p$ and extension $ξ$, the vortex core size. Defects are classified as strong if the interaction between a single pin and an individual vortex leads to the appearance of bistable solutions describing pinned and free vortex configurations. Extending the strong pinning theory to account for thermal fluctuations, we provide a quantitative analysis of vortex depinning and creep. We determine the thermally activated transitions between bistable states using Kramer's rate theory and find the non-equilibrium steady-state occupation of vortex states. The latter depends on the temperature $T$ and vortex velocity $v$ and determines the current--voltage (or force--velocity) characteristic of the superconductor at finite temperatures. We find that the $T=0$ linear excess-current characteristic $v \propto (j-j_c) \, Θ(j-j_c)$ with its sharp transition at the critical current density $j_c$, keeps its overall shape but is modified in three ways due to thermal creep: a downward renormalization of $j_c$ to the thermal depinning current density $j_\mathrm{dp}(T) < j_c$, a smooth rounding of the characteristic around $j_\mathrm{dp}(T)$, and the appearance of thermally assisted flux flow (TAFF) ${v \propto j \exp(-U_0/k_{\rm \scriptscriptstyle B} T)}$ at small drive $j \ll j_c$, with the activation barrier $U_0$ defined through the energy landscape at the intersection of free and pinned branches. This characteristic emphasizes the persistence of pinning of creep at current densities beyond critical.

cond-mat.supr-con↗

arXiv2018

Thermal depinning and creep in strong pinning theory

Pinning and thermal creep determine the response of numerous systems containing superstructures, e.g., vortices in type II superconductors, domain walls in ferroics, or dislocations in metals. The combination of drive and thermal fluctuations lead to the superstructure's depinning and its velocity $v$ determines the electric, magnetic, or mechanical response. It is commonly believed that pinning and creep collapse above the critical drive $F_c$, entailing a sharp rise in the velocity $v$. We challenge this perception by studying the effects of thermal fluctuations within the framework of strong vortex pinning in type-II superconductors. In fact, we show that pinning and thermal creep persist far beyond the critical force. The resulting force-velocity characteristic largely maintains its zero-temperature shape and thermal creep manifests itself by a downward renormalisation of the critical drive. Such characteristics is in agreement with Coulomb's law of dry friction and has been often observed in experiments.

cond-mat.supr-con↗

arXiv2016

Competing structures in two dimensions: square-to-hexagonal transition

We study a system of particles in two dimensions interacting via a dipolar long-range potential $D/r^3$ and subject to a square-lattice substrate potential $V({\bf r})$ with amplitude $V$ and lattice constant $b$. The isotropic interaction favors a hexagonal arrangement of the particles with lattice constant $a$, which competes against the square symmetry of the substrate lattice. We determine the minimal-energy states at fixed external pressure $p$ generating the commensurate density $n = 1/b^2 = (4/3)^{1/2}/a^2$ in the absence of thermal and quantum fluctuations, using both analytical and numerical techniques. At large substrate amplitude $V > 0.2\, e_D$, with $e_D = D/b^3$ the dipolar energy scale, the particles reside in the substrate minima and hence arrange in a square lattice. Upon decreasing $V$, the square lattice turns unstable with respect to a zone-boundary shear-mode and deforms into a period-doubled zig-zag lattice. Analytic and numerical results show that this period-doubled phase in turn becomes unstable at $V \approx 0.074\, e_D$ towards a non-uniform phase developing an array of domain walls or solitons; as the density of solitons increases, the particle arrangement approaches that of a rhombic (or isosceles triangular) lattice. At a yet smaller substrate value estimated as $V \approx 0.046\, e_D$, a further solitonic transition establishes a second non-uniform phase which smoothly approaches the hexagonal (or equilateral triangular) lattice phase with vanishing amplitude $V$. At small but finite amplitude $V$, the hexagonal phase is distorted and hexatically locked at an angle of $φ\approx 3.8^\circ$ with respect to the substrate lattice. The square-to-hexagonal transformation in this two-dimensional commensurate-incommensurate system thus involves a complex pathway with various non-trivial lattice- and modulated phases.

cond-mat.stat-mech↗

arXiv2015

Competing structures in 2D-trapped dipolar gases

We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which competes against the square symmetry of the underlying optical lattice with lattice constant $b$ and amplitude $V$. We find the minimal-energy states at the commensurate density $n = 1/b^2$ and establish the complete square-to-triangular transformation pathway of the lattice with decreasing $V$ involving period-doubled, solitonic, and distorted-triangular configurations.

cond-mat.quant-gas↗

arXiv2014

Flux Dependent Crossover Between Quantum and Classical Behavior in a dc-SQUID

In a coupled system of one classical and one quantum mechanical degree of freedom, the quantum degree of freedom can facilitate the escape of the whole system. Such unusual escape characteristics have been theoretically predicted as "Münchhausen effect". We implement such a system by shunting one of the two junctions of a dc-SQUID with an additional capacitance. In our experiments, we detect a crossover between quantum and classical escape processes related to the direction of escape. We find that, under varying external magnetic flux, macroscopic quantum tunneling periodically alternates with thermally activated escape, a hallmark of the "Münchhausen effect".

cond-mat.supr-con↗

arXiv1999

Andreev Spectroscopy for Superconducting Phase Qubits

We propose a new method to measure the coherence time of superconducting phase qubits based on the analysis of the magnetic-field dependent dc nonlinear Andreev current across a high-resistance tunnel contact between the qubit and a dirty metal wire and derive a quantitative relation between the subgap I-V characteristic and the internal correlation function of the qubit.

cond-mat↗

arXiv1999

Defect-Unbinding Transition in Layered Superconductors

We establish a new interstitial-vacancy unbinding transition of the Berezinskii-Kosterlitz-Thouless type, transforming the three dimensional pancake vortex lattice of a decoupled layered superconductor into a defected solid. This transition is the natural finite-field extension of the vortex-anti-vortex unbinding transition establishing the zero-field superfluid stiffness. At finite Josephson coupling, the defect unbinding transition turns into a topological decoupling transition.

cond-mat.supr-con↗

arXiv1998

Thermal Suppression of Strong Pinning

We study vortex pinning in layered type-II superconductors in the presence of uncorrelated disorder for decoupled layers. Introducing the new concept of variable-range thermal smoothing, we describe the interplay between strong pinning and thermal fluctuations. We discuss the appearance and analyze the evolution in temperature of two distinct non-linear features in the current-voltage characteristics. We show how the combination of layering and electromagnetic interactions leads to a sharp jump in the critical current for the onset of glassy response as a function of temperature.

cond-mat.supr-con↗

arXiv1997

Thermodynamics of the first-order vortex lattice melting transition in YBa$_2$Cu$_3$O$_{7-δ}$

Using the London approximation within the high field scaling regime, we calculate the jump in the specific heat $Δc$ at the first-order melting transition of the vortex lattice in YBa$_2$Cu$_3$O$_{7-δ}$. This has recently been measured [A. Schilling et al., Phys. Rev. Lett. (78), 4833 (1997)] and reported to be at least 100 times higher than expected from the fluctuations of field induced vortices alone. We demonstrate how the correct treatment of the temperature dependence of the model parameters, which are singular at the mean-field $B_{c2}$ line, leads to good agreement between the predictions of the London model and the size of the experimental jump. In addition, we consider the changes in the slopes of the magnetization $Δ(\partial M/\partial T)$ and $Δ(\partial M/\partial H)$ at the transition. Using continuum anisotropic scaling theory we demonstrate the consistency of measurements at different angles of the magnetic field with respect to the crystal c-axis.

cond-mat.supr-con↗