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

Bernd Braunecker*, Cristina Bena, Pascal Simon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)

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.

Original languageEnglish
Article number035136
Number of pages16
JournalPhysical Review. B, Condensed matter and materials physics
Volume85
Issue number3
DOIs
Publication statusPublished - 31 Jan 2012

Keywords

  • HEISENBERG ANTIFERROMAGNETIC CHAINS
  • SPIN-CHARGE SEPARATION
  • CORE-SHELL NANOWIRES
  • CARBON NANOTUBES
  • QUANTUM WIRES
  • ONE-DIMENSION
  • HOLE GAS
  • TRANSPORT
  • STATE
  • HETEROSTRUCTURES

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