Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator

Abstract

Topological quantum matter is characterized by non-trivial global invariants of the bulk which induce gapless electronic states at its boundaries. A case in point are two-dimensional topological insulators (2D-TI) which host one-dimensional (1D) conducting helical edge states protected by time-reversal symmetry (TRS) against single-particle backscattering (SPB). However, as two-particle scattering is not forbidden by TRS [1], the existence of electronic interactions at the edge and their notoriously strong impact on 1D states may lead to an intriguing interplay between topology and electronic correlations. In particular, it is directly relevant to the question in which parameter regime the quantum spin Hall effect (QSHE) expected for 2D-TIs becomes obscured by these correlation effects that prevail at low temperatures [2]. Here we study the problem on bismuthene on SiC(0001) which has recently been synthesized and proposed to be a candidate material for a room-temperature QSHE [3]. By utilizing the accessibility of this monolayer-substrate system on atomic length scales by scanning tunneling microscopy/spectroscopy (STM/STS) we observe metallic edge channels which display 1D electronic correlation effects. Specifically, we prove the correspondence with a Tomonaga-Luttinger liquid (TLL), and, based on the observed universal scaling of the differential tunneling conductivity (dI/dV), we derive a TLL parameter K reflecting intermediate electronic interaction strength in the edge states of bismuthene. This establishes the first spectroscopic identification of 1D electronic correlation effects in the topological edge states of a 2D-TI.

References in corpus (25)

• 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
• Luttinger Liquid Behavior in Carbon Nanotubes
• Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• 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
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Probing spin-charge separation in a Tomonaga-Luttinger liquid
• One-dimensional transport in polymer nanofibers
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Sub-nm wide electron channels protected by topology
• Critical Behavior of a Point Contact in a Quantum Spin Hall Insulator
• A one-channel conductor in an ohmic environment: mapping to a TLL and full counting statistics
• A new paradigm for the quantum spin Hall effect at high temperatures
• Scanning Tunneling Microscopy of a Luttinger Liquid
• Dynamical Coulomb Blockade Observed in Nano-Sized Electrical Contacts
• Magnetic moments in a helical edge can make weak correlations seem strong
• Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids
• Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges
• Time-resolved pure spin fractionalization and spin-charge separation in helical Luttinger liquid based devices
• Zero bias anomaly in the density of states of low-dimensional metals
• Zero-bias anomaly in nano-scale hole-doped Mott insulators on a triangular silicon surface

Cited by in corpus (55)

• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Atomically Thin Quantum Spin Hall Insulators
• Imaging gate-tunable Tomonaga-Luttinger liquids in 1H-MoSe${}_2$ mirror twin boundaries
• Signature of large-gap quantum spin Hall state in the layered mineral jacutingaite
• 2024 roadmap on 2D topological insulators
• Microwave Applications of Photonic Topological Insulators
• Epitaxial Growth of Ultraflat Bismuthene with Large Topological Band Inversion Enabled by Substrate-Orbital-Filtering Effect
• Helical Liquids in Semiconductors
• Disorder effects of vacancies on the electronic transport properties of realistic topological insulators nanoribbons: the case of bismuthene
• Tuning the Many-body Interactions in a Helical Luttinger Liquid
• Local manifestations of thickness dependent topology and axion edge state in topological magnet MnBi${}_2$Te${}_4$
• Observation of quantum spin Hall states in Ta${}_2$Pd${}_3$Te${}_5$
• A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta${}_2$Pd${}_3$Te${}_5$
• Multi-Band Superconductivity in Strongly Hybridized 1T'-WTe${}_2$/NbSe${}_2$ Heterostructures
• Observation of magnetism induced topological edge state in antiferromagnetic topological insulator MnBi4Te7
• A gate-tunable quantum phase transition in a topological excitonic insulator
• Coherent spin transport through helical edge states of topological insulator
• Manipulating Hubbard-type Coulomb blockade effect of metallic wires embedded in an insulator
• Charge transport of a spin-orbit-coupled Luttinger liquid
• General scatterings and electronic states in the quantum-wire network of moiré systems
• Ultrafast Momentum-resolved Hot Electron Dynamics in the Two-dimensional Topological Insulator Bismuthene
• Theory of Glide Symmetry Protected Helical Edge States in WTe${}_2$ Monolayer
• Electronic structure and signature of Tomonaga-Luttinger liquid state in epitaxial CoSb${}_{1-x}$ nanoribbons
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Discovery of a Topological Charge Density Wave
• Electrically tunable correlated domain wall network in twisted bilayer graphene
• Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples
• Tomonaga Luttinger liquid in the topological edge channel of multilayer FeSe
• Explicit derivation of the chiral and (generic) helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation
• Quasi-One-Dimensional Higher-Order Topological Insulators
• Spin and charge transport through helical Aharonov-Bohm interferometer with strong magnetic impurity
• Robustness of Helical Edge States Under Edge Reconstruction
• Helical Luttinger liquid on the edge of a 2-dimensional topological antiferromagnet
• Characterization of helical Luttinger liquids in microwave stepped-impedance edge resonators
• Localization of the Helical Edge States in the Absense of External Magnetic Field
• Nearly perfect spin-filtering in curved two-dimensional topological insulators
• Band manipulation and spin texture in interacting moiré helical edges
• Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid
• Two-channel Kondo problem in coupled interacting helical liquids
• Tunable helical crystals
• Fractionalized Spin Excitations in the Edge Ferromagnetic State of Graphene: Signature of the Ferromagnetic Luttinger Liquid
• Backscattering off a driven Rashba impurity at the helical edge
• Parameters of Tomonaga-Luttinger liquid in a quasi-1D material with Coulomb interactions
• Evidence of a two-dimensional nitrogen crystalline structure on silver surfaces
• Quantum Coherent Transport of 1D ballistic states in second order topological insulator Bi${}_4$Br${}_4$
• Robust Luttinger liquid state of 1D Dirac fermions in a van der Waals system Nb${}_9$Si${}_4$Te${}_{18}$
• Strong Spin Filtering by Silicon Nanoparticles with Adsorbed Bismuth Atom Clusters: Role of Symmetry and Electrostatic Control of the Direction of the Spin Polarization
• Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Ta2Pd3Te5 topological thermometer
• Topologically protected one-dimensional electronic states in group IV two-dimensional Dirac materials
• Tunneling maps of interacting electrons in real time: anomalous tunneling in quantum point-contacts beyond the steady state regime
• Edge Reconstruction in a Quantum Spin Hall Insulator
• Lifting topological protection in a quantum spin Hall insulator by edge coupling