arXiv subjects

Ernst Helmut Brandt

Publications and source records attributed to Ernst Helmut Brandt.

At least 37 records · Page 2Linked to original sources

arXiv2004

Ginzburg-Landau Vortex Lattice in Superconductor Films of Finite Thickness

The Ginzburg-Landau equations are solved for ideally periodic vortex lattices in superconducting films of arbitrary thickness in a perpendicular magnetic field. The order parameter, current density, magnetic moment, and the 3-dimensional magnetic field inside and outside the film are obtained in the entire ranges of the applied magnetic field, Ginzburg Landau parameter kappa, and film thickness. The superconducting order parameter varies very little near the surface (by about 0.01) and the energy of the film surface is small. The shear modulus c66 of the triangular vortex lattice in thin films coincides with the bulk c66 taken at large kappa. In thin type-I superconductor films with kappa < 0.707, c66 can be positive at low fields and negative at high fields.

cond-mat.supr-con↗

arXiv2004

Bernoulli potential in type-I and weak type-II superconductors: III. Electrostatic potential above the vortex lattice

The electrostatic potential above the Abrikosov vortex lattice, discussed earlier by Blatter {\em et al.} {[}PRL {\bf 77}, 566 (1996){]}, is evaluated within the Ginzburg-Landau theory. Unlike previous studies we include the surface dipole. Close to the critical temperature, the surface dipole reduces the electrostatic potential to values below a sensitivity of recent sensors. At low temperatures the surface dipole is less effective and the electrostatic potential remains observable as predicted earlier.

cond-mat.supr-con↗

arXiv2003

Superconducting thin rings with finite penetration depth

Recently Babaei Brojeny and Clem [Phys. Rev. B 68, 174514 (2003)] considered superconducting thin-film rings in perpendicular magnetic fields in the ideal Meissner state with negligibly small magnetic penetration depth and presented useful analytical limiting expressions and numerical results for the magnetic-field and sheet-current profiles, trapped magnetic flux, self-inductance, magnetic moment, and focusing of magnetic flux into the hole when no net current flows in the ring. The present paper generalizes all these results to rings with arbitrary values of the two-dimensional effective penetration depth Λ= λ^2 /d (λis the London depth and d < λ/2 the film thickness) using a straightforward matrix inversion method. We also present results for the energy of a superconducting ring as a function of the applied magnetic induction B_a and the quantum number N defining the size of the fluxoid N ϕ_0 trapped in the hole.

cond-mat.supr-con↗

arXiv2003

Properties of the Ideal Ginzburg-Landau Vortex Lattice

The magnetization curves M(H) for ideal type-II superconductors and the maximum, minimum, and saddle point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1 <= H < Hc2 or inductions 0 <= B < Hc2 and Ginzburg-Landau parameters sqrt(1/2) <= kappa <= 1000. Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field B(x,y) and magnetization M(H, kappa) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting expressions and analytical interpolation formulas are presented.

cond-mat.supr-con↗

arXiv2003

Budd-Vannimenus theorem for superconductors

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

cond-mat.supr-con↗

arXiv2002

Shifts of the nuclear resonance in the vortex lattice in YBa$_2$Cu$_3$O$_7$

The NMR and NQR spectra of $^{63}$Cu in the CuO$_2$ plane of YBa$_2$Cu$_3$O$_7$ in the superconducting state are discussed in terms of the phenomenological theory of Ginzburg-Landau type extended to lower temperatures. We show that the observed spectra, Kumagai {\em et al.}, PRB {\bf 63}, 144502 (2001), can be explained by a standard theory of the Bernoulli potential with the charge transfer between CuO$_2$ planes and CuO chains assumed.

cond-mat.supr-con↗

arXiv2002

Why an ac magnetic field shifts the irreversibility line in type-II superconductors

We show that for a thin superconducting strip placed in a transverse dc magnetic field - the typical geometry of experiments with high-Tc superconductors - the application of a weak ac magnetic field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the "walking" motion of vortices in the two-dimensional critical state of the strip with in-plane ac field. Our theory explains the shaking effect that was used for detecting phase transitions of the vortex lattice in superconductors with pinning. Some recent experiments on this subject are discussed.

cond-mat.supr-con↗

arXiv2001

Surface charge of a flat superconducting slab in the Meissner state

The electrostatic potential in the flat superconducting slab is evaluated in the framework of the Ginzburg-Landau theory extended by Bardeen to low temperatures. For magnetic fields below B_c1, we discuss the formation of a surface charge induced by the Bernoulli potential of the suppercurrents.

cond-mat.supr-con↗

arXiv2001

Electrostatic potential in a superconductor

The electrostatic potential in a superconductor is studied. To this end Bardeen's extension of the Ginzburg-Landau theory to low temperatures is used to derive three Ginzburg-Landau equations - the Maxwell equation for the vector potential, the Schroedinger equation for the wave function and the Poisson equation for the electrostatic potential. The electrostatic and the thermodynamic potential compensate each other to a great extent resulting into an effective potential acting on the superconducting condensate. For the Abrikosov vortex lattice in Niobium, numerical solutions are presented and the different contributions to the electrostatic potential and the related charge distribution are discussed.

cond-mat.supr-con↗

arXiv2001

Peak effect, vortex-lattice melting-line and order - disorder transition in conventional and high-T superconductors

We investigate the order - disorder transition line from a Bragg glass to an amorphous vortex glass in the H-T phase diagram of three-dimensional type-II superconductors with account of both pinning-caused and thermal fluctuations of the vortex lattice. Our approach is based on the Lindemann criterion and on results of the collective pinning theory and generalizes previous work of other authors. It is shown that the shapes of the order - disorder transition line and the vortex lattice melting curve are determined only by the Ginzburg number, which characterizes thermal fluctuations, and by a parameter which describes the strength of the quenched disorder in the flux-line lattice. In the framework of this unified approach we obtain the H-T phase diagrams for both conventional and high-Tc superconductors. Several well-known experimental results concerning the fishtail effect and the phase diagram of high-Tc superconductors are naturally explained by assuming that a peak effect in the critical current density versus H signalizes the order - disorder transition line in superconductors with point defects.

cond-mat.supr-con↗

arXiv2001

Theory of Type-II Superconductors with Finite London Penetration Depth

Previous continuum theory of type-II superconductors of various shapes with and without vortex pinning in an applied magnetic field and with transport current, is generalized to account for a finite London penetration depth lambda. This extension is particularly important at low inductions B, where the transition to the Meissner state is now described correctly, and for films with thickness comparable to or smaller than lambda. The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow naturally from an equation of motion for the current density in which the integral kernel now accounts for finite lambda. New geometries considered here are thick and thin strips with applied current, and `washers', i.e. thin film squares with a slot and central hole as used for SQUIDs.

cond-mat.supr-con↗

arXiv2000

Meissner-London currents in superconductors with rectangular cross section

Exact analytic solutions are presented for the magnetic moment and screening currents in the Meissner state of superconductor strips with rectangular cross section in a perpendicular magnetic field and/or with transport current. The extension to finite London penetration is achieved by an elegant numerical method which works also for disks. The surface current in the specimen corners diverges as l^(-1/3) where l is the distance from the corner. This enhancement reduces the barrier for vortex penetration and should increase the nonlinear Meissner effect in d-wave superconductors.

cond-mat.supr-con↗

arXiv2000

Superconductors in realistic geometries: Geometric edge barrier versus pinning

The magnetic response of type-II superconductors can be irreversible due to two different reasons: vortex pinning and barriers for flux penetration. Even without bulk pinning and in absence of a microscopic Bean-Lingston surface barrier for vortex penetration, superconductors of nonellipsoidal shape can exhibit a large geometric barrier for flux penetration. This edge barrier and the resulting irreversible magnetization loops and flux-density profiles are computed from continuum electrodynamics for superconductor strips and disks with constant thickness, both without and with bulk pinning. Expressions for the field of first flux entry H_en and for the reversibility field H_rev above which the pin-free magnetization becomes reversible are given. Both fields are proportional to the lower critical field H_c1 and else depend only on the specimen shape. These realistic results are compared with the reversible magnetic behavior of ideal superconductor ellipsoids.

cond-mat.supr-con↗

arXiv2000

Critical State in Thin Anisotropic Superconductors of Arbitrary Shape

A thin flat superconductor of arbitrary shape and with arbitrary in-plane and out-of-plane anisotropy of flux-line pinning is considered, in an external magnetic field normal to its plane. It is shown that the general three-dimensional critical state problem for this superconductor reduces to the two-dimensional problem of an infinitely thin sample of the same shape but with a modified induction dependence of the critical sheet current. The methods of solving the latter problem are well known. This finding thus enables one to study the critical states in realistic samples of high-Tc superconductors with various types of anisotropic flux-line pinning. As examples, we investigate the critical states of long strips and rectangular platelets of high-Tc superconductors with pinning either by the ab-planes or by extended defects aligned with the c-axis.

cond-mat.supr-con↗

arXiv2000

Exact Solution for the Critical State in Thin Superconductor Strips with Field Dependent or Anisotropic Pinning

An exact analytical solution is given for the critical state problem in long thin superconductor strips in a perpendicular magnetic field, when the critical current density j_c(B) depends on the local induction B according to a simple three-parameter model. This model describes both isotropic superconductors with this j_c(B) dependence, but also superconductors with anisotropic pinning described by a dependence j_c(theta) where theta is the tilt angle of the flux lines away from the normal to the specimen plane.

cond-mat.supr-con↗

arXiv1999

Irreversible Magnetization of Pin-Free Type II Superconductors

The magnetization curve of a type II superconductor in general is hysteretic even when the vortices exhibit no volume or surface pinning. This geometric irreversibility, caused by an edge barrier for flux penetration, is absent only when the superconductor has precisely ellipsoidal shape or is a wedge with a sharp edge where the flux lines can penetrate. A quantitative theory of this irreversibility is presented for pin-free disks and strips with constant thickness. The resulting magnetization loops are compared with the reversible magnetization curves of ideal ellipsoids.

cond-mat↗

arXiv1999

AC Response of Thin Film Superconductors at Various Temperatures and Magnetic Fields

The basic theory of the linear and nonlinear ac susceptibilities of type-II superconductors is outlined for various geometries, e.g. circular and elliptic disks, rings, and strips of thin films or of thicker platelets in a perpendicular magnetic field. It is shown how the linear susceptibility depends on the linear complex resistivity or on the complex penetration depth, and the nonlinear susceptibility on the nonlinear dependence of the electric field on the current density and magnetic induction. The dependence of these constitutive laws on the temperature and on various material properties like pinning forces, pinning energies, structural defects, and granularity, leads to an implicit dependence of the ac susceptibility on these parameters.

cond-mat↗

arXiv1999

Analytic Solution for the Critical State in Superconducting Elliptic Films

A thin superconductor platelet with elliptic shape in a perpendicular magnetic field is considered. Using a method originally applied to circular disks, we obtain an approximate analytic solution for the two-dimensional critical state of this ellipse. In the limits of the circular disk and the long strip this solution is exact, i.e. the current density is constant in the region penetrated by flux. For ellipses with arbitrary axis ratio the obtained current density is constant to typically 0.001, and the magnetic moment deviates by less than 0.001 from the exact value. This analytic solution is thus very accurate. In increasing applied magnetic field, the penetrating flux fronts are approximately concentric ellipses whose axis ratio b/a < 1 decreases and shrinks to zero when the flux front reaches the center, the long axis staying finite in the fully penetrated state. Analytic expressions for these axes, the sheet current, the magnetic moment, and the perpendicular magnetic field are presented and discussed. This solution applies also to superconductors with anisotropic critical current if the anisotropy has a particular, rather realistic form.

cond-mat↗