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In type II superconductors under a magnetic field, the magnetic field penetrates as a quantized flux accompanied by the surrounding rotating currents (magnetic vortex). Because the motion of vortices dominates the electromagnetic behavior of superconductors, understanding their kinetics and dynamics is extremely important from scientific and application perspectives. In fact, the kinetics of vortices, flux flow, has been the subject of extensive long-term experimental and theoretical studies. However, our understanding of flux flow, even at the fundamental level, was far from satisfactory until recently. The key component of this problem is the electronic structure of the central part of the vortex (core), where quantized levels of non-superconducting carriers (quasiparticles) are formed. In most superconductors, the quantized nature is almost invisible because of the quantized level spread (dirty limit), which generates ordinary longitudinal flux-flow resistivity. On the other hand, for vortices with clean cores, where the aforementioned quantized nature is prominent, we expect a large Hall effect with a Hall angle of almost π/2. Thus, direct measurement of the Hall angle by the flux flow provides important fundamental information about the kinetics of the vortices. In particular, the study of materials with clean-core vortices is promising, as novel quantum effects are expected.

To experimentally discuss the flux flow, we need to work at high frequencies and low temperatures. However, the Hall effect measurement in microwaves, for instance, in cryogenic circumstances for highly conductive materials, is challenging. We recently developed a cross-shaped bimodal cavity technique to measure the microwave Hall effect in highly conductive materials and observed a large Hall angle of vortex motion in high-Tc cuprate superconductors, in which we expected the quantized nature of the core to be visible. Although our results are surprising and puzzling compared to those of previous flux-flow studies, which used a simpler longitudinal resistivity measurement (effective viscous drag coefficient measurement), it is extremely exciting to see if such a large flux-flow Hall angle is observed in other superconductors that are expected to have a clean vortex core.

In this study, we measured the flux-flow Hall effect in FeSe, which meets the above expectation. However, these results were unexpected. That is, we found that the tangent of the flux-flow Hall angle at low temperatures was approximately 0.5, which is equal to or smaller than that previously evaluated by effective viscous drag coefficient measurements. This contrasts with the results obtained for cuprate superconductors. We focus on the multiband nature of FeSe superconductivity and successfully explain the result in terms of the cancellation of the forces acting on the vortices by the hole and electron bands, which was already considered by Nicolai Kopin in microscopic theories. Thus, our observation of the flux-flow Hall effect in FeSe is a novel characteristic of multiband superconductors with electron and hole bands. This should become an important clue for controlling vortex motion through material design.

(Written by R. Ogawa on behalf of all the authors)