  Black phosphorus (bP) is the second known elemental allotrope with a layered
crystal structure that can be mechanically exfoliated down to atomic layer
thickness. We have fabricated bP naked quantum wells in a back-gated field
effect transistor geometry with bP thicknesses ranging from $6\pm1$ nm to
$47\pm1$ nm. Using an encapsulating polymer superstrate, we have suppressed bP
oxidation and have observed field effect mobilities up to 600 cm$^2$/Vs and
on/off current ratios exceeding $10^5$. Importantly, Shubnikov-de Haas (SdH)
oscillations observed in magnetotransport measurements up to 35 T reveal the
presence of a 2-D hole gas with Schr\"odinger fermion character in an
accumulation layer at the bP/oxide interface. Our work demonstrates that 2-D
electronic structure and 2-D atomic structure are independent. 2-D carrier
confinement can be achieved in layered semiconducting materials without
necessarily approaching atomic layer thickness, advantageous for materials that
become increasingly reactive in the few-layer limit such as bP.
