  The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$.
By employing top- and back-gate electric fields at high magnetic field, the
Landau levels of the Dirac cones in the top and bottom topological surface
states can be tuned independently. When one surface is tuned to the
electron-doped side of the Dirac cone and the other surface to the hole-doped
side, the quantum Hall edge channels are counter-propagating. The opposite edge
mode direction, combined with the opposite helicities of top and bottom
surfaces, allows for scattering between these counter-propagating edge modes.
The total Hall conductance is integer valued only when the scattering is
strong. For weaker interaction, a non-integer quantum Hall effect is expected
and measured.

Mesoscale and Nanoscale Physics