  Topological insulators are a recently discovered class of materials with
fascinating properties: While the inside of the solid is insulating,
fundamental symmetry considerations require the surfaces to be metallic. The
metallic surface states show an unconventional spin texture, electron dynamics
and stability. Recently, surfaces with only a single Dirac cone dispersion have
received particular attention. These are predicted to play host to a number of
novel physical phenomena such as Majorana fermions, magnetic monopoles and
unconventional superconductivity. Such effects will mostly occur when the
topological surface state lies in close proximity to a magnetic or electric
field, a (superconducting) metal, or if the material is in a confined geometry.
Here we show that a band bending near to the surface of the topological
insulator Bi$_2$Se$_3$ gives rise to the formation of a two-dimensional
electron gas (2DEG). The 2DEG, renowned from semiconductor surfaces and
interfaces where it forms the basis of the integer and fractional quantum Hall
effects, two-dimensional superconductivity, and a plethora of practical
applications, coexists with the topological surface state in Bi$_2$Se$_3$. This
leads to the unique situation where a topological and a non-topological, easily
tunable and potentially superconducting, metallic state are confined to the
same region of space.
