The electron lifetime in Luttinger liquids

Abstract

We investigate the decoherence of the electron wavepacket in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature $T$ and long times $t$, we show that the electron Green's function for a fixed wavevector close to one Fermi point decays as $\exp (-t/{\tau }_F)$, as opposed to the power-law behavior occurring at short times, and the emerging electron lifetime obeys ${\tau }_F^{-1}\propto T$ for spinful as well as spinless electrons. For strong interactions, $(T{\tau }_F)\ll 1$, reflecting that the electron is not a good Landau quasiparticle in LLs. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi Golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LLs.

arXiv comment20 pages, 1 column, 6 figures, 1 Table; expands cond-mat/0110307 and cond-mat/0503652; final version to appear in PRB

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Cited by in corpus (33)

• The spin-incoherent Luttinger liquid
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Bosonization of one dimensional fermions out of equilibrium
• Electron transport in disordered Luttinger liquid
• Non-equilibrium Luttinger liquid: Zero-bias anomaly and dephasing
• Precursor of Laughlin state of hard core bosons on a two leg ladder
• Voltage and dephasing probes: a full counting statistics discussion
• Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
• Full counting statistics of Luttinger liquid conductor
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• Universal dephasing in a chiral 1D interacting fermion system
• Analytically solvable model of an electronic Mach-Zehnder interferometer
• Double-gap superconducting proximity effect in nanotubes
• Quantum interference and spin-charge separation in a disordered Luttinger liquid
• Non-equilibrium quantum transport through a dissipative resonant level
• Spin-charge separation in an Aharonov-Bohm interferometer
• Effective field theory for ersatz Fermi liquids
• Detection of entanglement by helical Luttinger liquids
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• Charge Fractionalization in a Mesoscopic Ring
• Non-equilibrium charge noise and dephasing from a spin-incoherent Luttinger liquid
• Finite-temperature spectroscopy of dirty helical Luttinger liquids
• Exceptional Luttinger Liquids from sublattice dependent interaction
• Twisted bilayer graphene as a terahertz plasmonic crystal