Hall Effect in the Abrikosov Lattice of Type-II Superconductors

Abstract

We study vortex charging caused by the Lorentz force on supercurrent based on the augmented quasiclassical equa- tions of superconductivity. Our numerical study on an s-wave vortex lattice in the range $H_{\mathrm{c}1}<H<H_{\mathrm{c}2}$ reveals that each vortex core with a single flux quantum also accumulates charge due to the circulating supercurrent and has a Hall voltage across the core. The field dependence of the charge density at the core center is well described by $H(H_{\mathrm{c}2}-H)$ with a peak near $H_{\mathrm{c}2}/2$ originating from competition between the increasing magnetic field and the decreasing pair potential. The peak value of the accumulated charge in a core region of radius $0.5{\xi }_0$ is estimated to be about $\eta {\Delta }_0/(k_{\mathrm{F}}{\xi }_0)\times |e|$ C per $\Delta z=1$ nm along the flux line at low temperatures, where $\eta \equiv \pi {\epsilon }_0\Delta z/|e{|}^2=1.09\times 10^{18}$ ${\mathrm{J}}^{-1}$ with $e<0$ the charge of an electron, ${\Delta }_0$ the energy gap at $T=0$, $k_{\mathrm{F}}$ the Fermi wave number, and ${\xi }_0$ the coherence length at $T=0$.

arXiv comment5 pages, 4 figures

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Cited by in corpus (9)

• Large Hall angle of vortex motion in high-$T_c$ cuprate superconductors revealed by microwave flux-flow Hall effect
• Charging in a Superconducting Vortex Due to the Three Force Terms in Augmented Eilenberger Equations
• Hall Effect in the Vortex Lattice of d-Wave Superconductors with Anisotropic Fermi surfaces
• Charging due to Pair-Potential Gradient in Vortex of Type-II Superconductors
• Electronic States and Energy Dissipations of Vortex Core in Pure FeSe Single Crystals Investigated by Microwave Surface Impedance Measurements
• Vortex motion in tilted magnetic fields in highly layered electron-doped superconductor Nd2-xCexCuO4
• Approach to Solving Quasiclassical Equations with Gauge Invariance
• Charging in the vortex lattice of type-II superconductors
• Zero-Field Surface Charge Due to the Gap Suppression in $d$-Wave Superconductors