Rashba-controlled thermal valve in helical liquids

In the context of one-dimensional fermionic systems, helical Luttiger liquids are not only characterized by intriguing spin properties, but also by the possibility to be manipulated by means of electrostatic gates, exploiting finite Rashba coupling. We use this property to show that a heterostructure composed of a helical Luttinger liquid, contacted to two metallic leads and supplemented by top gates, can be used as a tunable thermal valve. By relying on bosonization techniques and scattering of plasmonic modes, we investigate the performance of this valve with respect to electron-electron interactions, temperature, and properties of the gates. The maximal modulation of the thermal conductance that the proposed device can achieve is, for experimentally relevant parameters, around $7 \%$. Such variation can be both positive or negative. Moreover, a modification in the geometry of the gate can lead to particular temperature dependencies related to interference effects. We also argue that the effects we predict can be used to establish the helical nature of the edge states in two-dimensional topological insulators.