Coulomb drag between helical Luttinger liquids

Abstract

We theoretically study Coulomb drag between two helical edges with broken spin-rotational symmetry, such as would occur in two capacitively coupled quantum spin Hall insulators. For the helical edges, Coulomb drag is particularly interesting because it specifically probes the inelastic interactions that break the conductance quantization for a single edge. Using the kinetic equation formalism, supplemented by bosonization, we find that the drag resistivity ${\rho }_D$ exhibits a nonmonotonic dependence on the temperature $T$. In the limit of low $T$, ${\rho }_D$ vanishes with decreasing $T$ as a power law if intraedge interactions are not too strong. This is in stark contrast to Coulomb drag in conventional quantum wires, where ${\rho }_D$ diverges at $T\to 0$ irrespective of the strength of repulsive interactions. Another unusual property of Coulomb drag between the helical edges concerns higher $T$ for which, unlike in the Luttinger liquid model, drag is mediated by plasmons. The special type of plasmon-mediated drag can be viewed as a distinguishing feature of the helical liquid---because it requires peculiar Umklapp scattering only available in the presence of a Dirac point in the electron spectrum.

22 pages, 7 figures

References in corpus (13)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Conductivity of a generic helical liquid
• Coulomb interaction in graphene: Relaxation rates and transport
• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
• Coulomb drag by small momentum transfer between quantum wires
• Coulomb drag between ballistic quantum wires
• Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
• Coulomb drag between helical edge states
• Quantum interference and spin-charge separation in a disordered Luttinger liquid
• Temperature dependence of Coulomb drag between finite-length quantum wires