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In correlated electronic systems, strong interactions and the interplaybetween different degrees of freedom may give rise to anomalous chargetransport properties, which can be tuned by external parameters liketemperature and magnetic field. Recently, magnetic quantum oscillations andmetallic low-temperature thermal conductivity have been observed in the Kondoinsulator YbB$_{12}$, whose resistivity is a few orders of magnitude higherthan those of conventional metals. As yet, these unusual observations are notfully understood. Here we present a detailed investigation of the behavior ofYbB$_{12}$ under intense magnetic fields using both transport and torquemagnetometry measurements. A low-field Hall anomaly, reminiscent of the Hallresponse associated with "strange-metal" physics, develops at $T < 1.5$ K. Attwo characteristic magnetic fields ($\mu_0H_1= 19.6$ T and $\mu_0H_2 \sim 31$T), signatures appear in the Hall coefficient, magnetic torque, andmagnetoresistance. We suggest that they are likely to be field-induced Lifshitztransitions. Moreover, above 35 T, the background resistivity displays anunusual, nonmetallic $T^{\alpha}$-behavior, with $\alpha$ being field-dependentand varying between -1.5 and -2. By normalizing the Shubnikov-de Haasoscillation amplitude to this $T^{\alpha}$-dependence, the calculated cyclotronmass becomes more consistent with that deduced from de Haas-van Alphenoscillations. Our results support a novel two-fluid scenario in YbB$_{12}$: aFermi-liquid-like fluid of charge-neutral quasiparticles coexists with chargecarriers that remain in a nonmetallic state. The former experience successiveLifshitz transitions and develop Landau quantization in applied magneticfields, whilst scattering between both fluids allows the Shubnikov-de Haaseffect to be observed in the electrical transport.

Hall anomaly, Quantum Oscillations and Possible Lifshitz Transitions in Kondo Insulator YbB$_{12}$: Evidence for Unconventional Charge Transport