Transport of single and double point contacts in 2D fractional topological insulators

We study transport properties of the helical edge states of 2D integer and fractional

topological insulators (TIs/ FTIs), via one and two constrictions (quantum point

contacts). Such constrictions can be made by adding a gate to the systems where the

coupling between edge states on either side of 2D sample is electronically tuned by this

gate. We study the stability of both the conducting (weak backscattering limit) and

insulating fixed points (weak tunneling limit). Moreover, we explore interesting physics

when double impurity is on resonance, leading to perfect transmission (weak

backscattering limit) and Kondo physics (weak tunneling limit). Using renormalization

group and duality mapping, we analyze phase diagrams for the following cases: (i) single

constriction in FTI, which is a generalization of the single constriction in TIs studied by

J. Teo and C. Kane. (ii) two constrictions in TIs, and (iii) two constrictions in FTIs. We

find different behaviors depending on interaction strength and particularly a regime

where conductance is non-monotonic as a function of temperature in the experimentally

accessible parameter regime.