arXiv subjects

E. H. Brandt

Publications and source records attributed to E. H. Brandt.

At least 19 recordsLinked to original sources

arXiv2011

Time Resolved Stroboscopic Neutron Scattering of Vortex Lattice Dynamics in Superconducting Niobium

Superconducting vortex lattices, glasses and liquids attract great interest as model systems of crystallization and as a source of microscopic information of the nature of superconductivity. We report for the first time direct microscopic measurements of the vortex lattice tilt modulus c44 in ultra-pure niobium using time-resolved small angle neutron scattering. Besides a general trend to faster vortex lattice dynamics for increasing temperatures we observe a dramatic changeover of the relaxation process associated with the non-trivial vortex lattice morphology in the intermediate mixed state. This changeover is attributed to a Landau-branching of the Shubnikov domains at the surface of the sample. Our study represents a showcase for how to access directly vortex lattice melting and the formation of vortex matter states for other systems.

cond-mat.str-el↗

arXiv2009

Nanomechanics of an individual vortex in an anisotropic type-II superconductor

As shown in recent experiments [Auslaender et al., Nature Physics 5, 35 (2009)] magnetic force microscopy permits one not only to image but also to manipulate an individual vortex in type-II superconductors, and this manipulation provides a new powerful tool to study vortex dynamics and pinning. We derive equations that describe the deformation of an individual vortex in an anisotropic biaxial type-II superconductor under the action of the microscope's magnetic tip. These equations take into account the driving force generated by the tip, the elastic force caused by the vortex deformation, and the pinning force exerted by point defects. Using these equations, we reproduce the main features of the experimental data obtained by Auslaender et al.

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arXiv2009

Transport Properties of Vortex Matter Governed by the Edge Inductance of Superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ Single Crystals

We study the distribution of transport current across superconducting Bi$_2$Sr$_2$CaCu$_2$O$_8$ crystals and the vortex flow through the sample edges. We show that the $T_x$ transition is of electrodynamic rather than thermodynamic nature, below which vortex dynamics is governed by the edge inductance instead of the resistance. This allows measurement of the resistance down to two orders of magnitude below the transport noise. By irradiating the current contacts the resistive step at vortex melting is shown to be due to loss of c-axis correlations rather than breakdown of quasi-long-range order within the a-b planes.

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arXiv2008

Surface energy and magneto-capacitance of superconductors under electric field bias

A superconducting layer exposed to a perpendicular electric field and a parallel magnetic field is considered within the Ginzburg-Landau (GL) approach. The GL equation is solved near the surface and the surface energy is calculated. The nucleation critical field of superconducting state at the surface depends on the magnetic and electric fields. Special consideration is paid to the induced magnetic-field effect cause d by diamagnetic surface currents. The latter effect is strongly dependent on the thickness of the sample. The effective inverse capacitance determines the effective penetration depth. It is found that the capacitance exhibits a jump at the surface critical field. An experiment is suggested for determining the change in the effective capacitance of the layer.

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arXiv2007

"Unusual" critical states in type-II superconductors

We give a theoretical description of the general critical states in which the critical currents in type-II superconductors are not perpendicular to the local magnetic induction. Such states frequently occur in real situations, e.g., when the sample shape is not sufficiently symmetric or the direction of the external magnetic field changes in some complex way. Our study is restricted to the states in which flux-line cutting does not occur. The properties of such general critical states can essentially differ from the well-known properties of the usual Bean critical states. To illustrate our approach, we analyze several examples. In particular, we consider the critical states in a slab placed in a uniform perpendicular magnetic field and to which two components of the in-plane magnetic field are then applied successively. We also analyze the critical states in a long thin strip placed in a perpendicular magnetic field which then is tilted towards the axis of the strip.

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arXiv2006

Self field of ac current reveals voltage-current law in type-II superconductors

The distribution of ac magnetic fields in a thin superconducting strip is calculated when an ac current is applied to the sample. The edge barrier of the strip to flux penetration and exit is taken into account. The obtained formulas provide a basis to extract voltage-current characteristics in the bulk and at the edges of superconductors from the measured ac magnetic fields. Based on these results, we explain the spatial and temperature dependences of the profiles of the ac magnetic field measured in a Bi2Sr2CaCu2O8 strip [D.T. Fuchs et al., Nature 91, 373 (1998)].

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arXiv2005

Equilibrium First-Order Melting and Second-Order Glass Transitions of the Vortex Matter in Bi$_2$Sr$_2$CaCu$_2$O$_8$

The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local \emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking'. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.

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arXiv2005

Sheet-current distribution in a dc SQUID washer probed by vortices

We present a novel method, based on vortex imaging by low-temperature scanning electron microscopy (LTSEM), to directly image the sheet-current distribution in YBa2Cu3O7 dc SQUID washers. We show that the LTSEM vortex signals are simply related to the scalar stream function describing the vortex-free circulating sheet-current distribution J. Unlike previous inversion methods that infer the current distribution from the measured magnetic field, our method uses pinned vortices as local detectors for J. Our experimental results are in very good agreement with numerical calculations of J.

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arXiv2005

Anisotropic superconducting strip in an oblique magnetic field

The critical state of a thin superconducting strip in an oblique applied magnetic field H_a is analyzed without any restrictions on the dependence of the critical current density j_c on the local magnetic induction {\bf B}. In such a strip, j_c is not constant across the thickness of the sample and differs from J_c/d, where J_c is the critical sheet current. It is shown that in contrast to the case of {\bf B}-independent j_c, the profiles H_z(x) of the magnetic-field component perpendicular to the strip plane generally depend on the in-plane component H_{ax} of the applied magnetic field H_a, and on how H_a is switched on. On the basis of this analysis, we explain how and under what conditions one can extract j_c({\bf B}) from the magnetic-field profiles H_z(x) measured by magneto-optical imaging or by Hall-sensor arrays at the upper surface of the strip.

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arXiv2005

Asymmetry of magnetic-field profiles in superconducting strips

We analyze the magnetic-field profiles H_z(x) at the upper (lower) surface of a superconducting strip in an external magnetic field, with z perpendicular to the plane of the strip and x along its width. The external magnetic field H_a is perpendicular or inclined to the plane of the strip. We show that an asymmetry of the profiles H_z(x) appears in an oblique magnetic field H_a and also in the case when the angular dependence of the critical current density j_c in the superconductor is not symmetric relative to the z axis. The asymmetry of the profiles is related to the difference ΔH_z(x) of the magnetic fields at the upper and lower surfaces of the strip, which we calculate. Measurement of this difference or, equivalently, of the asymmetry of the profiles can be used as a new tool for investigation of flux-line pinning in superconductors.

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arXiv2004

Superconducting strip in an oblique magnetic field

As an example for a seemingly simple but actually intricate problem, the Bean critical state is studied in a superconducting strip of finite thickness d and width 2w >> d placed in an oblique magnetic field. The analytical solution is obtained to leading order in the small parameter d/w. The critical state depends on how the applied magnetic field is switched on, e.g., at constant tilt angle, or first the perpendicular and then the parallel field component. For these two basic scenarios the distributions of current density and magnetic field are obtained in the critical states. In particular, we find the shapes of the flux-free core and of the lines separating regions with opposite direction of the critical currents, the detailed magnetic field lines (along the vortex lines), and both components of the magnetic moment. The component of the magnetic moment parallel to the strip plane is a nonmonotonic function of the applied magnetic field.

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arXiv2004

Bernoulli potential in type-I and weak type-II superconductors: I. Surface charge

The electrostatic potential close to the surface of superconductors in the Meissner state is discussed. We show that beside the Bernoulli potential, the quasiparticle screening, and the thermodynamic contribution due to Rickayzen, there is a non-local contribution which is large for both type-I and weak type-II superconductors.

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arXiv2004

Bernoulli potential in type-I and weak type-II supercoductors: II. Surface dipole

The Budd-Vannimenus theorem is modified to apply to superconductors in the Meissner state. The obtained identity links the surface value of the electrostatic potential to the density of free energy at the surface which allows one to evaluate the electrostatic potential observed via the capacitive pickup without the explicit solution of the charge profile.

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arXiv2003

Effect of pinning on the vortex-lattice melting line in type-II superconductors

The vortex-lattice melting line in three-dimensional type-II superconductors with pinning is derived by equating the free energies of the vortex system in the solid and liquid phases. We account for the elastic and pinning energies and the entropy change that originates from the disappearance of the phonon shear modes in the liquid. The pinning is assumed to be caused by point defects and to be not too strong so that the melting line lies inside the so-called bundle-pinning region. We show that the derived equation for the melting line is equivalent to some Lindemann criterion, which however differs from that used previously. Estimating the effect of pinning on the entropy jump at melting, we find the upper critical point of the melting line from the condition that this jump vanishes. We also consider the H-T phase diagrams of type-II superconductors for different strengths and types of pinning and analyze the two recently discussed scenarios how the melting line and the order--disorder line merge.

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arXiv2002

"Vortex-melting front" in thin superconductors with pinning

Magneto-optical observations of a second flux front, which occurs at the second peak in the magnetization of Bi_2 Sr_2 CaCu_2 O_x single crystals related to the known first order ``vortex-lattice melting'', are reconsidered. We show that, in thin samples, electrodynamics necessarily leads to an extended region in which the magnetic induction adopts a nearly constant value close to that at which the phase transition occurs at thermal equilibrium. In this region a dynamical phase mixture of vortex ``solid'' and ``liquid'' should exist. Interestingly, the observed second flux front does not mark the ``melting'' front, as it was naively interpreted earlier, but indicates the disappearance of the last ``solid droplets''.

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arXiv2002

The Average Kinetic Energy of the Superconducting State

Isothermal magnetization curves are plotted as the magnetization times the magnetic induction, $4 πM \cdot B$, versus the applied field, H. We show here that this new curve is the average kinetic energy of the superconducting state versus the applied field, for type-II superconductors with a high Ginzburg-Landau parameter $κ$. The maximum of $4 πM \cdot B$ occurs at a field, $H^{*}$, directly related to the upper critical field, $H_{c2}$, suggesting that $H_{c2}(T)$ may be extracted from such plots even in cases when it is too high for direct measurement. We obtain these plots both theoretically, from the Ginzburg-Landau theory, and experimentally, using a Niobium sample with $T_c = 8.5 K$, and compare them.

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arXiv2001

Calculation of levitation forces in permanent-superconductor systems

The magnetic levitation forces of a superconducting disk (SC) levitated by a cylindrical permanent magnet (PM) have been calculated from first principles for superconductors with finite thickness. The current $j(ρ,z)$ and field $B(ρ,z)$ profiles in the SC in the non-uniform magnetic field generated by the PM have been derived. The levitation force is observed to depend non-linearly on the critical current density $j_c$ and on the thickness of the SC. The flux creep is described by a current-voltage law $E(j)=E_c(j/j_c)^n$, from which we show that the levitation force depends on the speed at which the PM approaches or recedes from the SC, which accounts for the experimentally observed force creep phenomenon. The stiffness of the system has been derived by calculating the minor force loops. The numerical results reproduce many of the features exhibited by experiments.

cond-mat.supr-con↗

arXiv2001

Charge profile in vortices

The electric charge density in the vortex lattice of superconductors is studied within the Ginzburg-Landau theory. We show that the electrostatic potential $ϕ$ is proportional to the GL function, $ϕ\propto|ψ|^2-|ψ_\infty|^2$. Numerical results for the triangular vortex lattice are presented.

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