  The search for a Fermi surface in the absence of a conventional Fermi liquid
has thus far yielded very few potential candidates. Among promising materials
are spin-frustrated Mott insulators near the insulator-metal transition, where
theory predicts a Fermi surface associated with neutral low energy excitations.
Here we reveal another route to experimentally realise a Fermi surface in the
absence of a Fermi liquid by the experimental study of a Kondo insulator
SmB$_6$ positioned close to the insulator-metal transition. We present
experimental signatures down to low temperatures ($\ll 1$ K) associated with a
Fermi surface in the bulk, including a sizeable linear specific heat
coefficient, and on the application of a finite magnetic field, bulk magnetic
quantum oscillations, finite quantum oscillatory entropy, and substantial
enhancement in thermal conductivity well below the charge gap energy scale.
Thus, the weight of evidence indicates that despite an extreme instance of
Fermi liquid breakdown in Kondo insulating SmB$_6$, a Fermi surface arises from
novel itinerant low energy excitations that couple to magnetic fields, but not
weak DC electric fields.
