The reverse quantum limit and its implications for unconventional quantum oscillations in YbB12

The quantum limit in a Fermi liquid, realized when a single Landau level is occupied in strong magnetic fields, gives rise to unconventional states, including the fractional quantum Hall effect and excitonic insulators. Stronger interactions in metals with nearly localized f -electron degrees of freedom increase the likelihood of these unconventional states. However, access to the quantum limit is typically impeded by the tendency of f -electrons to polarize in a strong magnetic field, consequently weakening the interactions. In this study, we propose that the quantum limit in such systems must be approached in reverse, starting from an insulating state at zero magnetic field. In this scenario, Landau levels fill in the reverse order compared to regular metals and are closely linked to a field-induced insulator-to-metal transition. We identify YbB 12 as a prime candidate for observing this effect and propose the presence of an excitonic insulator state near this transition. Metallic systems in magnetic fields enter the quantum limit when the cyclotron energy exceeds the Fermi energy. Here the authors introduce the analogue of the quantum limit for insulators, where the Zeeman energy exceeds the cyclotron energy, and show that it explains key features of the Kondo insulator YbB 12 .