Transport statistics and thermoelectric performance of Hofstadters butterfly

We investigate electrons subject to a magnetic field that may tunnel along a square lattice and additionally to two electronic leads. Using non-equilibrium Greens functions we evaluate the transmission and from that particle and energy currents and zero-frequency noise of the setup. We identify sweet spots for which the transmission reaches unity over broad frequency windows – carried by topologically protected boundary modes that are quite robust against local fluctuations of on-site energies. These transmission plateaus can be exploited for the implementation robust current standards, clocks and thermoelectric devices.