Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids

Abstract

We provide analytic expressions for the Green's functions in position-frequency space as well as for the tunneling density of states of various Luttinger liquids at zero temperature: the standard spinless and spinful Luttinger liquids, the helical Luttinger liquid at the edge of a topological insulator, and the Luttinger liquid that appears either together with an ordering transition of nuclear spins in a one-dimensional conductor, or in spin-orbit split quantum wires in an external magnetic field. The latter system is often used to mimic a helical Luttinger liquid, yet we show here that it exhibits significantly different response functions and, to discriminate, we call it the spiral Luttinger liquid. We give fully analytic results for the tunneling density of state of all the Luttinger liquids as well as for most of the Green's functions. The remaining Green's functions are expressed by simple convolution integrals between analytic results.

17 pages, 4 figures; corresponding to published version

References in corpus (35)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Nonlocal edge state transport in the quantum spin Hall state
• The Quantum Spin Hall Effect: Theory and Experiment
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• One-Dimensional Hole Gas in Germanium/Silicon Nanowire Heterostructures
• Spin-charge separation and localization in one-dimension
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Majorana edge states in interacting one-dimensional systems
• Probing spin-charge separation in a Tomonaga-Luttinger liquid
• Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
• Anyonic interferometry without anyons: How a flux qubit can read out a topological qubit
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• One-dimensional conduction in Charge-Density Wave nanowires
• Electron Transport in a Multi-Channel One-Dimensional Conductor: Molybdenum Selenide Nanowires
• Corner Junction as a Probe of Helical Edge States
• Strong and Tunable Spin-Orbit Coupling of One-Dimensional Holes in Ge/Si Core/Shell Nanowires
• Tunneling between edge states in a quantum spin Hall system
• Nuclear Magnetism and Electronic Order in 13C Nanotubes
• Spin-orbital effects in magnetized quantum wires and spin chains
• Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas
• Topologically non-trivial superconductivity in spin-orbit coupled systems: Bulk phases and quantum phase transitions
• Competing effects of interactions and spin-orbit coupling in a quantum wire
• Strongly modulated transmission of a spin-split quantum wire with local Rashba interaction
• Metal-insulator transition in a quantum wire driven by a modulated Rashba spin-orbit coupling
• Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling
• Spin polarised scanning tunneling probe for helical Luttinger liquids
• Spin-orbit induced spin-density wave in a quantum wire
• Spin-polarized currents through interacting quantum wires with nonmagnetic leads
• Local Spectral Weight of a Luttinger Liquid: Effects from Edges and Impurities
• Local density of states of 1D Mott insulators and CDW states with a boundary
• Spin-orbit coupling and spectral function of interacting electrons in carbon nanotubes

Cited by in corpus (37)

• Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase
• Correlation effects in two-dimensional topological insulators
• Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Atomically Thin Quantum Spin Hall Insulators
• Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
• Helical Liquids in Semiconductors
• Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges
• Tuning the Many-body Interactions in a Helical Luttinger Liquid
• Helical nuclear spin order in two-subband quantum wires
• Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields
• Strongly anisotropic spin response as a signature of the helical regime in Rashba nanowires
• Low-energy properties of fractional helical Luttinger liquids
• Spin-orbit interactions in a helical Luttinger liquid with a Kondo impurity
• Physics in one dimension: theoretical concepts for quantum many-body systems
• Finite-temperature conductance of weakly interacting quantum wires with Rashba spin-orbit coupling
• Kane-Mele Hubbard model on a zigzag ribbon: stability of the topological edge states and quantum phase transitions
• Enhancement of tunneling density of states at a Y junction of spin-1/2 Tomonaga Luttinger liquid wires
• The Two-Band Luttinger Liquid with Spin-Orbit Coupling: Applications to Monatomic Chains on Surfaces
• Interaction effects in a microscopic quantum wire model with strong spin-orbit interaction
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Electronic structure and signature of Tomonaga-Luttinger liquid state in epitaxial CoSb${}_{1-x}$ nanoribbons
• Spectral properties of one-dimensional spiral spin density wave states
• Magnetic-field switchable metal-insulator transitions in a quasi-helical conductor
• Structure factor of interacting one-dimensional helical systems
• Nonequilibrium transport of helical Luttinger liquids through a quantum dot
• Nonlocal Damping of Helimagnets in One-Dimensional Interacting Electron Systems
• Tunneling Spectroscopy of a Spiral Luttinger Liquid in Contact with Superconductors
• Spin-polarized tunneling into helical edge states: asymmetry and conductances
• Electrical and thermal transport in the quasi-atomic limit of coupled Luttinger liquids
• Kinetic processes in Fermi-Luttinger liquids
• Tunneling spectroscopy between one-dimensional helical conductors
• Tunneling between helical Majorana modes and helical Luttinger liquids
• Charge and spin density in the helical Luttinger liquid
• Density of states of interacting quantum wires with impurities: a Dyson equation approach
• Exact results, transient generalized Gibbs ensembles, and analytic approximations for spacetime propagators of massive, real scalar fields in one spatial dimension
• Elastic precession of electronic spin states in interacting integer quantum Hall edge channels