Two-channel Kondo problem in coupled interacting helical liquids

Abstract

We study the two-channel Kondo problem in the context of two interacting helical liquids coupled to a spin-$\frac{1}{2}$ magnetic impurity. We show that the interactions between the two helical liquids significantly affect the phase diagram and other observable properties. Using a multichannel Luttinger liquid formalism, we analyze both the Toulouse limit, where an exact solution is available, and the weak coupling limit, which can be studied via a perturbative renormalization group (RG) approach. We recover the results for the `decoupled' limit (interactions between the helical liquids switched off) and point out deviations from the known results due to this coupling. The model under study is mapped to a model of two effectively decoupled helical liquids coupled to an impurity. The perturbative RG study shows that each of these channels can flow to either a Ferromagnetic (FM) or an Anti-Ferromagnetic (AFM) fixed point. We obtain the phase diagram of the coupled system as a function of the system parameters. The observable consequences of the interaction between the two channels are captured using linear response theory. We compute the negative correction to the conductance due to the Kondo scattering processes and show how it scales with the temperature as a function of inter-channel interaction.

arXiv comment15 pages. Comments welcome

References in corpus (51)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Effect
• Bosonization and Strongly Correlated Systems
• Reflection symmetric second-order topological insulators and superconductors
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Kondo physics in carbon nanotubes
• Edge conduction in monolayer WTe2
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• A four-qubit germanium quantum processor
• Realization of a minimal Kitaev chain in coupled quantum dots
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• NRG study of the Kondo effect in the presence of itinerant-electron ferromagnetism
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Critical Behavior of a Point Contact in a Quantum Spin Hall Insulator
• Corner Junction as a Probe of Helical Edge States
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• Localization at the Edge of 2D Topological Insulator by Kondo Impurities with Random Anisotropies
• Probing the Kondo density of states in a three-terminal quantum ring
• Jumps in current-voltage characteristics in disordered films
• On the Emery-Kivelson Solution of the two channel Kondo problem
• Simple Bosonization Solution of the 2-channel Kondo Model: I. Analytical Calculation of Finite-Size Crossover Spectrum
• Anderson-Yuval approach to the multichannel Kondo problem
• Kondo lattice on the edge of a two-dimensional topological insulator
• Helical Liquids in Semiconductors
• Quantum Dot in 2D Topological Insulator: The Two-channel Kondo Fixed Point
• Interacting two helical edge modes in quantum spin Hall systems
• Exact results for the Kondo screening cloud of two helical liquids
• Electrical control of the Kondo effect in a helical edge liquid
• Simple description of the anisotropic two-channel Kondo problem
• Mesoscopic transport in two-dimensional topological insulators
• Transport in helical Luttinger Liquid with Kondo impurities
• Kondo Impurities Coupled to Helical Luttinger Liquid: RKKY-Kondo Physics Revisited
• Tuning the Many-body Interactions in a Helical Luttinger Liquid
• Nontrivial interplay of strong disorder and interactions in quantum spin-Hall insulators doped with dilute magnetic impurities
• Spin-orbit interactions in a helical Luttinger liquid with a Kondo impurity
• Kondo Problems in Tomonaga-Luttinger liquids
• Duality in multi-channel Luttinger Liquid with local scatterer
• Measuring the Kondo Cloud by Current Cross Correlations in Helical Liquids
• Local impurity in multichannel Luttinger liquid
• Analytical and Numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity
• Berezinskii-Kosteriltz-Thouless transition in disordered multi-channel Luttinger liquids
• Electrically tunable two-channel Kondo fixed points in helical liquids
• Quantum criticality in Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators

Cited by in corpus (4)

• Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
• A simple electronic ladder model harboring ${\mathbb{Z}}_4$ parafermions
• Bosonization solution of the Kondo lattice in a Luttinger liquid