Transmissions Through Barriers and Resonant Tunneling in a Luttinger Liquid

Abstract

We present a review of the theory of the single channel Luttinger liquid applied to transport in nanostructure devices. Our main focus will be on the effects of barriers, or constrictions in a single channel wire. In particular, we show that repulsively interacting electrons incident upon a single barrier are completely reflected at zero temperature (T). At finite T, the conductance vanishes as a power of T, and at T = 0, power law current-voltage characteristics are predicted. We next discuss resonant tunneling through a double barrier structure and show that the resonance peaks have a width which vanishes as a power of T as T → 0. Moreover, the T dependence of the resonance lineshapes are described by a universal scaling function, which has non Lorentzian tails. Possible experimental realizations of this are discussed, including a connection to edge transport in the fractional quantum Hall regime.