We report magnetic quantum oscillations measured using torque magnetisation in the Kondo insulator YbB$_{12}$ and discuss the potential origin of the underlying Fermi surface. Observed quantum oscillations as well as complementary quantities such as a finite linear specific heat capacity in YbB$_{12}$ exhibit similarities with the Kondo insulator SmB$_6$, yet also crucial differences. Small heavy Fermi sections are observed in YbB$_{12}$ with similarities to the neighbouring heavy fermion semimetallic Fermi surface, in contrast to large light Fermi surface sections in SmB$_6$ which are more similar to the conduction electron Fermi surface. A rich spectrum of theoretical models is suggested to explain the origin across different Kondo insulating families of a bulk Fermi surface potentially from novel itinerant quasiparticles that couple to magnetic fields, yet do not couple to weak DC electric fields.
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