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.

arXiv comment22 pages, 7 figures

References in corpus (42)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantum Spin Hall Effect
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Observation of Quantum Spin Hall States in InAs/GaSb Bilayers under Broken Time-Reversal Symmetry
• Coulomb drag
• Inelastic electron backscattering in a generic helical edge channel
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Interaction-induced criticality in Z_2 topological insulators
• Phonon induced backscattering in helical edge states
• 1D-1D Coulomb Drag Signature of a Luttinger Liquid
• Conductivity of a generic helical liquid
• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
• Coulomb interaction in graphene: Relaxation rates and transport
• Coulomb drag by small momentum transfer between quantum wires
• Coulomb drag in graphene: perturbation theory
• Current drag in capacitevly coupled Luttinger constrictions
• Coulomb drag between two spin incoherent Luttinger liquids
• Coulomb Drag between Quantum Wires
• Positive and negative Coulomb drag in vertically integrated one-dimensional quantum wires
• Random Rashba spin-orbit coupling at the quantum spin Hall edge
• Coulomb drag between ballistic one-dimensional electron systems
• Coulomb drag of Luttinger liquids and quantum-Hall edges
• Luttinger liquids with curvature: Density correlations and Coulomb drag effect
• Coulomb drag shot noise in coupled Luttinger liquids
• Coulomb drag between one-dimensional conductors
• Helical Quantum Edge Gears in 2D Topological Insulators
• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• 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
• Transport and Coulomb drag for two interacting carbon nanotubes
• Coulomb drag between quantum wires with different electron densities
• Quantum interference and spin-charge separation in a disordered Luttinger liquid
• Temperature dependence of Coulomb drag between finite-length quantum wires
• Ultranarrow resonance in Coulomb drag between quantum wires at coinciding densities

Cited by in corpus (9)

• Helical Liquids in Semiconductors
• Does delta-$T$ noise probe quantum statistics?
• Localization-Driven Correlated States of Two Isolated Interacting Helical Edges
• Composite helical edges from Abelian fractional topological insulators
• Tunneling Aharonov-Bohm interferometer on helical edge states
• Spin-orbit coupling and resonances in the conductance of quantum wires
• Correlated insulator in two Coulomb-coupled quantum wires
• Selective damping of plasmons in coupled two-dimensional systems by Coulomb drag
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges