Flux-flow Hall Effect Research Articles

Microwave Flux-flow Hall Effect in a Multi-band Superconductor FeSe

We have measured the flux-flow Hall effect in a multi-band superconductor FeSe pure single crystal to investigate the nature of the vortex core state by means of the cross-shaped bimodal cavity technique. We found that the flux-flow Hall angle of FeSe at low temperatures is about 0.5, which is equal to or smaller than that evaluated by the effective viscous drag coefficient measurements. This feature is in contrast to the cuprate superconductors. The conductivity tensor of multi-band superconductors that are contributed from holes and electrons shows partial cancellation of the flux-flow Hall voltage by the electrons and holes, which can explain the observed feature. Therefore, our study suggests the appearance of the multi-band nature in the vortex dynamics.

Exploring Vortex Dynamics in a Multi-band Superconductor

We measured the microwave flux-flow Hall effect in FeSe, where the cancellation of holes and electrons was observed. This is a novel effect of multi-band superconductors.

Size dependence in flux-flow Hall effect using time-dependent Ginzburg-Landau equations

We study the Hall effect in square, planar type-II superconductors using numerical simulations of time dependent Ginzburg-Landau (TDGL) equations. The Hall field in some type-II superconductors displays sign-change behavior at some magnetic fields due to the induced field of vortex flow, when its contribution is strong enough to reverse the field direction. In this work, we use modified TDGL equations which couple an externally applied current, and also incorporate normal-state and flux-flow Hall effects. We obtain the profile of Hall angle as a function of applied magnetic field for four different sizes (l\times l) of the superconductor: l/ \xi belongs to {3, 5, 15, 20}. We obtain vastly different profiles for each size, proving that size is an important parameter that determines Hall behavior. We find that electric field dynamics provides an insight into several anomalous features including signchange of Hall angle, and leads us to the precise transient behavior of order parameter responsible for them.

Large Hall angle of vortex motion in high- Tc cuprate superconductors revealed by microwave flux-flow Hall effect

We investigated the nature of the quasi-particle state in the vortex core by means of the flux-flow Hall effect measurements at 15.8 GHz. We measured the flux-flow Hall effect in cuprate superconductors, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{y}$ and YBa$_{2}$Cu$_{3}$O$_{y}$ single crystals, whose equilibrium $B$-$T$ phase diagrams were different. As a result, we found that the Hall angle is independent of the magnetic field, and reaches an order of unity at low temperatures in BSCCO. However, in YBCO, the angle increases with increasing magnetic field even at low temperatures. We understood that this difference in the magnetic field dependence of the Hall angle is due to the difference in the influence of the pinning, which originated from the difference in the vortex state (liquid vs. solid) between the two materials. However, as a common feature, both materials showed a large tangent of the Hall angle at low temperatures, which was larger by an order of magnitude than those obtained in the effective viscous drag coefficient measurements. We discussed the origin of the discrepancy both in terms of the possible nonlinearity of the viscous drag force and possible hidden dissipation mechanisms. The unexpectedly large Hall angle of the vortex motion in cuprates revealed in our flux-flow Hall effect study poses a serious question on the fundamental understanding of the motion of the quantized vortex in superconductors, and it deserves further investigation.

Microwave Hall effect measurement for materials in the skin depth region

We developed a new microwave Hall effect measurement method for materials in the skin depth region at low temperatures using a cross-shaped bimodal cavity. We analytically calculated electromagnetic fields in the cross-shaped cavity and the response of the cavity including the sample, whose property is represented by the surface impedance tensor; furthermore, we constructed the method to obtain the Hall component of the surface impedance tensor in terms of the change in resonance characteristics. To confirm the validity of the new method, we applied our method to measure the Hall effect in metallic Bi single crystals at low temperatures, and we confirmed that the microwave Hall angles coincide with the DC Hall angle. Thus, it becomes clear that the Hall angle measurement under cryogenic conditions becomes possible without any complicated tuning mechanisms, and our bimodal cavity method can be used to measure the microwave Hall effect on materials in the skin depth region. The result opens a new approach to discuss the Hall effect in condensed matter physics such as the microwave flux-flow Hall effect in superconductors.

Transport properties of Lix(NH3)yFe2(TezSe1−z)2 single crystals in the mixed state

We study the electric transport properties of Lix(NH3)yFe2(TezSe)2 single crystals with and 0.6 in the mixed state. Thermally-activated flux-flow, vortex glass and flux-flow Hall effect (FFHE) behaviors are observed. Experimental results show that there are rich vortex phases existing in these systems and the vortex liquid states occupy broad regions of phase diagrams. Further analysis suggests that thermal fluctuation plays an important role in the vortex phase diagrams of Lix(NH3)yFe2(TezSe)2. Moreover, for Lix(NH3)yFe2Se2, there is no sign reversal of FFHE in the mixed state and a scaling behavior with is observed.

Γ-Stability and Vortex Motion in Type II Superconductors

We consider a time-dependent Ginzburg–Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative Γ-stability result relating the Ginzburg–Landau energy to the renormalized energy.

Thermally activated energy and flux-flow Hall effect ofFe1+y(Te1+xSx)z

Thermally activated flux flow (TAFF) and flux flow Hall effect (FFHE) of Fe(Te,S) single crystal in the mixed state are studied in magnetic fields up to 35 T. Thermally activated energy (TAE) is analyzed using conventional Arrhenius relation and modified TAFF theory which is closer to experimental results. The results indicate that there is a crossover from single-vortex pinning region to collective creep pinning region with increasing magnetic field. The temperature dependence of TAE is different for H//ab and H//c. On the other hand, the analysis of FFHE in the mixed state indicates that there is no Hall sign reversal. We also observe scaling behavior |Rhoxy(H)| = A*Rhoxx(H)^beta.

Flux-flow Hall effect in clean type-II superconductors.

We calculate the Ohmic and Hall components of the flux-flow conductivity for clean superconductors in a magnetic field H\ensuremath{\ll}${\mathit{H}}_{\mathit{c}2}$ and investigate the sign of the Hall effect. Each component of the conductivity consists of two contributions: from electrons localized in the vortex cores, and from electrons above the gap. These contributions are determined by the parameters ${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\tau} and ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\tau}, respectively, where ${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\sim}${\mathrm{\ensuremath{\Delta}}}^{2}$/${\mathit{E}}_{\mathit{F}}$ is the distance between the energy levels in the vortex core, ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is the cyclotron frequency (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\ll}${\mathrm{\ensuremath{\omega}}}_{0}$), and \ensuremath{\tau} is the relaxation time. In the superclean limit, \ensuremath{\tau}\ensuremath{\gg}${\mathit{E}}_{\mathit{F}}$/${\mathrm{\ensuremath{\Delta}}}^{2}$, the Ohmic component is small and the Hall conductivity resembles that for the high-field regime in a normal metal. In a moderately clean case, ${\mathrm{\ensuremath{\Delta}}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\ll}\ensuremath{\tau}\ensuremath{\ll}${\mathit{E}}_{\mathit{F}}$/${\mathrm{\ensuremath{\Delta}}}^{2}$, the Hall component is small. Its sign in the mixed state may differ from the sign in the normal state depending on the detailed structure of the Fermi surface. We conclude that the sign reversal can be intrinsic. We discuss implications of our results for mutual friction in superfluid $^{3}\mathit{B}$.

Sign change of the flux flow Hall effect in HTSC

A novel mechanism for the sign change of the Hall effect in flux flow region is proposed. The difference δ n between the electron density at the center of the vortex core and that far outside the vortex causes the additional contribution to the Hall conductivity δσ xy = - δnec/ B. This contribution can be bigger that the conventional one in the dirty case Δ( T)τ < 1. If the electron density inside the core exceeds the electron density outside the core the double sign change may occur as a function of temperature and magnetic field.

Sign reversal of the flux flow Hall effect in oxygen deficient YBa 2Cu 3O x films

The Hall effect of high temperature superconductors has been reported to slow in some cases a striking sign reversal near T c, the origin of which is not yet fully understood. We report on measurements of the Hall effect in the mixed state of oxygen deficient YBa 2Cu 3O x thin films, for 7≥×≥6.7. Although no sign reversal of the Hall resistivity ϱ xy is present for the as-prepared film, it is clearly observed once the oxygen content of the film is reduced to x=6.9 and 6.85. However, by further reducing the oxygen content to x=6.7, the sign reversal vanishes again. The latter might be a consequence of the increase of the resistivity with decreasing oxygen content, since it has been suggested that the amplitude of the reversed Hall resistivity may be related to the mean free path.

Kinetic equations for clean superconductors: Application to the flux flow hall effect

The kinetic equations for clean superconductors (l≫ξ) are derived. Expanding the equations for the time dependent Green functions in the quasiclassical parameter, the new contributions are found which contain the derivatives of the distribution functions with respect to the quasiparticle momentum. The transition from the ultra-clean case (no relaxation) to a relaxation-dominated behavior, for which the kinetic equations coincide with the usual quasiclassical approximation, occurs for the relaxation time of the order of ℏEF/Δ2. The kinetic equations can be used for various dynamic processes in superconductors including the flux-flow Hall effect. The derived equations, after necessary modifications for the p-wave pairing, are especially suitable for nonstationary problems in the theory of superfluidity of3He.

Anomalies in free flux-flow Hall effect.

The low-${T}_{c}$ layered superconductor $2H\ensuremath{-}\mathrm{Nb}{\mathrm{Se}}_{2}$ shows remarkable results for free flux-flow Hall effect. At low magnetic fields, the Nozi\`eres-Vinen result of a field-independent Hall angle appears to hold. At larger fields, a marked departure occurs leading to an extremely sharp and pronounced minimum slightly below ${H}_{c2}$, unaccounted for in the standard theoretical models. The results suggest the existence of collective dynamics and phase transitions (such as melting) in a clean flux line lattice.

Magnetoelastic theory of type-II superconductors in the mixed state.

This paper presents a macroscopic theory for analyzing the magnetoelastic response of elastic type-II superconductors in the mixed state. The theory includes not only the vortex-dynamic effect, the normal-current effect, and the flux-flow Hall effect, but also the effect of the London moment induced by the local motion of the deformable superconductor in the mixed state. The theory is considered to be valid within the framework of the generalized Galilean relativity at the magnetoquasistatic approximation. By this theory, a set of linearized coupled wave equations is derived to study some problems concerning magnetoelastic wave propagation in type-II superconductors in the mixed state. Attenuation and dispersion behaviors of the magnetoelastic wave are then analyzed. It is shown that the nonlocal effect on the length scale of the London penetration depth may be of importance in analyzing the propagation behavior of the magnetoelastic wave at frequencies higher than the depinning frequency. It is also shown that the effect of the London moment induced by dynamic deformation can be of significance as compared with the effect of the normal Lorentz current on the magnetoelastic coupling behavior of elastic type-II superconductors in the mixed state. Furthermore, it is found that there is a phase change between the transverse elastic wave and the magnetic wave induced in the type-II superconductor in the mixed state. This effect is found to be closely related to the vortex-dynamic properties of the superconductor.

Modelling of thermomagnetoelectric effects in type-II superconductors in the mixed state

This article presents a phenomenological theory for studying thermomagnetoelectric effects in type-II superconductors in the mixed state. In the theoretical model, the anisotropic effect, the vortex dynamic effect, the flux-flow Hall effect and the thermomagnetic effects in the type-II superconductor in the mixed state are all taken into account self-consistently. It is shown that, at the London approximation, the classical first and second London equations for superconductors in the Meissner state are modified for the superconductors in the mixed state due to vortex dynamic effects, which are, in general, nonlinear. At the linear approximation, effective constitutive equations and field equations are derived to describe the thermomagnetoelectric behavior of anisotropic type-II superconductors in the mixed state. It is shown that the derived field equations are, in general, coupled due to the vortex dynamic effects. A possible solution of a plane thermomagnetic wave in the type-II superconductor in the mixed state is also studied illustratively.

Sign reversal of the flux-flow Hall effect in sputtered a-axis- and c-axis-oriented films of 1:2:3 superconducting cuprates.

Films of R${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ (R=Y, Ho, and Eu) have been obtained with c-axis orientation perpendicular to the film plane, by two dc sputtering methods, on different kinds of substrates. Also, pure a-axis-oriented films of ${\mathrm{EuBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ have been grown by dc magnetron sputtering. The films have been characterized by x-ray diffraction, resistivity, and critical current. The Hall effect has been measured in the normal and in the mixed state using a magnetic field up to 9 T. The films show a strong anisotropy in the normal state, with n-type and p-type behaviors in a-axis and c-axis films, respectively. All the films show sign reversal of the Hall resistivity in the mixed state. The maximum positive value (a-axis films) and the minimum negative value (c-axis films) of the Hall-effect resistivity are sample dependent. The analysis of this result shows that the enhancement of the effect occurs when the samples are in the transition region between the dirty and clean regimes. Films with very different values of the mean free path l and coherence length ${\ensuremath{\xi}}_{0}$ show a vanishing small effect in comparison with films that present l\ensuremath{\simeq}${\ensuremath{\xi}}_{0}$.

Transport properties and fluctuations in type-II superconductors near Hc2.

We study the flux-flow Hall effect and thermomagnetic transport near the upper critical field \hctwo\ in extreme type-II superconductors starting from a suitable generalization of the time dependent Ginzburg-Landau equations. We explicitly incorporate the effects of backflow into the calculations of the local electric field and current, leading to a current which is properly divergenceless. The Hall conductivity calculated from this current agrees with other mean-field calculations which assume a uniform applied electric field (the Schmid-Caroli-Maki solution), thereby vindicating these simplified treatments. We then use these results to calculate the transverse thermomagnetic effects (the Ettingshausen and Nernst effects). The effects of thermal fluctuations and nonlocal elasticity of the flux lattice are incorporated using a method recently developed by Vecris and Pelcovits [G. Vecris and R. A. Pelcovits, Phys. Rev. B {\bf 44}, 2767 (1991)]. Our results, taken together with those of Vecris and Pelcovits, provide a rather complete description of the transport properties of the flux lattice state near \hctwo, at least within the framework of time dependent Ginzburg-Landau theory.

The flux-flow hall effect in type II superconductors. An explanation of the sign reversal

We consider a time-dependent Ginzburg-Landau (TDGL) model modified to take into account two mechanisms responsible for the Hall voltage in superconductors: the usual effect of the magnetic field on the normal current, and the vortex traction by the superflow. For the BCS model of superconductivity, the contribution of the vortex traction is proportional to the energy derivative of the quasiparticle density of states. Our theory gives the correct order of magnitude for the Hall angle in the mixed state. It predicts that the vortex-traction mechanism results in a negative Hall angle for the quasiparticle spectrum with a positive energy derivative of the density of states averaged over the Fermi surface, and vice versa. For the Fermi surface with a complicated shape, the sign of the Hall effect in the mixed state can be different from that in the normal state. If the signs are opposite, the Hall angle changes its sign as a function of the magnetic field belowH c2 .

Sign change of the flux-flow Hall resistance in high-Tc superconductors.

We consider a contributon to the flux-flow Hall effect that arises from the existence of large thermomagnetic effects in the mixed state of the high-${\mathit{T}}_{\mathit{c}}$ superconductors. From the measured values of the Seebeck and Nernst-Ettingshausen effects we find that this contribution is as large as the direct flux-flow contribution to the Hall effect, but has the opposite sign for a positive Seebeck coefficient. Therefore it leads to a sign change of the Hall resistance. A calculation of the temperature and field dependence of the Hall resistivity yields good agreement with the data.

Flux-flow Hall effect in superconducting Tl2Ba2CaCu2O8 films.

In both high-${\mathit{T}}_{\mathit{c}}$ and low-${\mathit{T}}_{\mathit{c}}$ superconductors, the Hall effect in the mixed state often shows a sign reversal below ${\mathit{T}}_{\mathit{c}}$ that contradicts standard theories for flux-vortex motion. We have measured the mixed-state Hall effect in high-quality superconducting films of ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, and find that the Hall angle \ensuremath{\alpha} below ${\mathit{T}}_{\mathit{c}}$ consists of two components: A field-independent component exhibits a complicated temperature dependence, including a sign change near ${\mathit{T}}_{\mathit{c}}$, while a second component with very weak temperature dependence is linear in field and resembles the normal-state Hall angle. The field independence of the sign-reversing component is evidence for vortex motion, and can be understood in terms of simple drag forces acting on vortices.