Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium
arXiv:2002.04907 · doi:10.1103/PhysRevB.101.195404
Abstract
The renormalization of conductances in a Y junction of spinless Luttinger-liquid wires additionally coupled to acoustic longitudinal phonons is investigated in fermionic representation. This system corresponds to geometry of a tunneling experiment and exhibits the interplay between the Coulomb repulsion and the attractive retarded interaction mediated by phonons. The retardation effects related to the propagation of phonons through the junction with arbitrary transmission and reflection amplitudes are taken into account. The appearing logarithmic corrections to conductances of the junction are treated in a renormalization group approach, and scaling exponents are calculated up to infinite order in the interaction after RPA-type summation. The fixed points and corresponding scaling exponents are considered in various non-equilibrium regimes. We show that the boundary exponent and the bulk anomalous dimension of fermion operator are characterized by two different Luttinger parameters, referring to the main wire, thanks to non-local character of phonon-mediated interaction. In the limiting case of the junction of only two wires, the scaling exponents found by our method are in exact correspondence with previous bosonization analysis.
arXiv comment20 pages, 10 figures
References in corpus (25)
- Landauer Conductance of Luttinger Liquids with Leads
- Junctions of three quantum wires
- Phonon induced backscattering in helical edge states
- Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator
- Junction of several weakly interacting quantum wires: a renormalization group study
- Resonant tunneling of interacting electrons in a one-dimensional wire
- Transport of interacting electrons through a double barrier in quantum wires
- Wentzel-Bardeen singularity and phase diagram for interacting electrons coupled to acoustic phonons in one dimension
- Spin polarised scanning tunneling probe for helical Luttinger liquids
- Conductance through a potential barrier embedded in a Luttinger liquid: nonuniversal scaling at strong coupling
- Tunneling into a Luttinger liquid revisited
- Y-junction connecting Luttinger liquids: fixed point structure and conductances
- Phonon-assisted tunneling in interacting suspended single wall carbon nanotubes
- Duality of Weak and Strong Scatterer in Luttinger liquid Coupled to Massless Bosons
- Fundamental limits to helical edge conductivity due to spin-phonon scattering
- Electron backscattering from dynamical impurities in a Luttinger liquid
- A fermionic approach to tunneling through junctions of multiple quantum wires
- Transport properties of a two-lead Luttinger liquid junction out of equilibrium: fermionic representation
- Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling
- Rectification in Y-junctions of Luttinger liquid wires
- Y-junction of Luttinger-liquid wires out of equilibrium
- Phase diagram and phonon-induced backscattering in topological insulator nanowires
- Spin-polarized tunneling into helical edge states: asymmetry and conductances
- Finite frequency noise in chiral Luttinger liquid coupled to phonons
- Impurity entropy of junctions of multiple quantum wires