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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.
We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically-doped Bi$_2$Se$_3$-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is
We investigate energy transfer between counter-propagating quantum Hall edge channels (ECs) in a two-dimensional electron system at filling factor u=1. The ECs are separated by a thin impenetrable potential barrier and Coulomb coupled, thereby const
A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the wrong chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp co
In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coh
The spin-polarized surface states in topological insulators offer unique transport characteristics which make them distinguishable from trivial conductors. Due to the topological protection, these states are gapless over the whole surface of the mate