Helical Quantum Edge Gears in 2D Topological Insulators

We show that two-terminal transport can measure the Luttinger liquid (LL) parameter $K$, in helical LLs at the edges of two dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip inter-edge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature ($T\to 0$) perfect drag regime, the conductance is $(e^2\mathrm{/}h)(2K+1)\mathrm{/}(K+1)$. At higher $T$ we predict a conductivity $\sim T^{-4K+3}$. The conductivity for a single edge is also computed.