Anomalous 3D bulk AC conduction within the Kondo gap of SmB$_6$ single crystals

The Kondo insulator SmB$_6$ displays anomalous transport behavior at low temperatures which has recently been proposed to originate from in-gap topological surface states. Here, we investigate the low energy optical conductivity within the hybridization gap of single crystals of SmB$_6$ via time domain terahertz spectroscopy. Samples grown by both optical floating zone and aluminum flux methods are investigated and are found to display significant 3D bulk conduction originating within the Kondo gap that is many orders of magnitude larger than any known impurity band conduction. The nature of these in-gap states and their coupling with the low energy spin excitons of SmB$_6$ is discussed. Additionally, we show that any surface states, which lie below our detection threshold if present, must have a sheet resistance of R $\ge$ 1 k$\Omega$.