  We study transport properties of the helical edge states of two-dimensional
integer and fractional topological insulators via double constrictions. Such
constrictions couple the upper and lower edges of the sample, and can be made
and tuned by adding side gates to the system. Using renormalization group and
duality mapping, we analyze phase diagrams and transport properties in each of
these cases. Most interesting is the case of two constrictions tuned to
resonance, where we obtain Kondo behavior, with a tunable Kondo temperature.
Moving away from resonance gives the possibility of a metal-insulator
transition at some finite detuning. For integer topological insulators, this
physics is predicted to occur for realistic interaction strengths and gives a
conductance $G$ with two temperature $T$ scales where the sign of $dG/dT$
changes; one being related to the Kondo temperature while the other is related
to the detuning.
