  Black phosphorus (BP) offers considerable promise for infrared and visible
photonics. Efficient tuning of the bandgap and higher subbands in BP by
modulation of the Fermi level or application of vertical electric fields has
been previously demonstrated, allowing electrical control of its above bandgap
optical properties. Here, we report modulation of the optical conductivity
below the band-gap (5-15 um) by tuning the charge density in a two-dimensional
electron gas (2DEG) induced in BP, thereby modifying its free carrier dominated
intraband response. With a moderate doping density of 7x10^12/cm2 we were able
to observe a polarization dependent epsilon-near-zero behavior in the
dielectric permittivity of BP. The intraband polarization sensitivity is
intimately linked to the difference in effective fermionic masses along the two
crystallographic directions, as confirmed by our measurements. Our results
suggest the potential of multilayer BP to allow new optical functions for
emerging photonics applications.
