Hall anomaly by vacancies in a pinned lattice of vortices: A quantitative analysis based on the thin-film data from Bi2.1Sr1.9CaCu2.0

The Hall anomaly, as appears in the mixed-state Hall resistivity of type-II superconductors, has been the subject of numerous theories, but there is not yet a consensus on its origin. In this paper, we conduct a quantitative analysis of the magnetotransport measurements on ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}{\mathrm{CaCu}}_{2.0}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (BSCCO) thin films by Zhao et al. [Phys. Rev. Lett. 122, 247001 (2019)] and validate a previously proposed vacancy mechanism [cf. Ao, J. Phys. Condens. Matter. 10, L677 (1998)] with many-body vortex correlations for the phenomenon. The model attributes the Hall anomaly to the motion of vacancies in pinned fragments of the vortex lattice. Its validity is first examined by an exploration of the vortex states near the Kosterlitz-Thouless transition on the vortex crystal. Comparisons are then carried out between the measured activation energies with the calculated creation energy of the vortex-antivortex pair and the vacancy energy on the flux-line lattice, with no adjustable parameter. Our analysis elucidates the theoretical basis and prerequisites of the vacancy model. In particular, the vacancy activation energies are an order of magnitude smaller than that of a sole vortex line. The proposed mechanism may provide a macro-theoretical framework for other studies.