  The quest to understand the nature of the electronic state in SmB6 has been
challenging, perplexing and surprising researchers for over half a century. In
the theoretically predicted topological Kondo insulator SmB6, the nature of the
bulk electronic structure is not characterised unambiguously by quantum
oscillations due to contrary interpretations. One simple definition of an
electrical insulator is a material that lacks a Fermi surface and here we
report the results of our investigation into its existence in SmB6 by Compton
scattering. Compton scattering measures occupied electron momentum states, is
bulk sensitive due to the high energy of the incoming photons and is also an
ultra-fast probe of the correlated many-body electron wavefunction. Remarkably,
direct evidence for a three-dimensional remnant Fermi surface is observed.
However, a further dichotomy is raised in that the full occupancy expected of a
conventional metal is not reproduced. Our observation of a remnant Fermi
surface using a momentum-resolved probe provides significant new evidence that
the paradigm of a bulk insulator is not robust for SmB6.
