Advances have been made both in the area of unconventional insulators and cuprate superconductors. One of the breakthrough discoveries of our research group was the discovery of a neutral Fermi surface in families of correlated insulators, constituting a new class of unconventional insulators. During this period, we have performed rigorous measurements of a slew of complementary properties in the first unconventional insulator SmB6, based on which we are able to definitely rule out an extrinsic origin of the measured quantum oscillations. By establishing the intrinsic bulk origin of quantum oscillations in the bulk insulator SmB6, we place at the forefront the inherent theoretical conundrum posed by a neutral Fermi surface that couples to a magnetic field but not an electric field. Another achievement was the magnetic field tuning of the unconventional insulator YbB12 from the regime in which an insulating Fermi surface is observed to the high magnetic field regime in which a metallic Fermi surface is observed. Our measurements reveal surprising similarities in the Fermi surface sections on the insulating side and the metallic side, while more of the Fermi surface is revealed on the metallic side, providing strong clues as to the nature of neutral low energy excitations responsible for the insulating Fermi surface that mirrors the high field metallic Fermi surface. This finding of a small Fermi surface in which the antinodal density of states is completely gapped points to an origin from Mott physics, requiring new models beyond Fermi surface models involving conventional electronic quasiparticles, and potentially suggesting resonances with Fermi surface models developed for correlated insulators. Recently we have further discovered an unusual superconducting phase of matter that is resilient beyond the highest accessible DC magnetic fields of 45T, using sensitive high magnetic field electrical transport measurements down to the lowest temperatures, shedding new light on the cuprate superconducting phase diagram.
