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/τF ) -as opposed to the power-law behavior occurring at short times -and the emerging electron lifetime obeys τ −1 F ∝ T for spinful as well as spinless electrons. For strong interactions, (T τF ) ≪ 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.

Finite-temperature spectroscopy of dirty helical Luttinger liquids

“…The full Beta function encodes the crossover between ω 2γ for high frequency ω ≫ ω * (low T ) and T 2γ at low frequency ω ≪ ω * (high T ). The former is precisely the ZBA discussed above; the latter is consistent with the result previously reported by Le Hur [67].…”

“…For the former, the quasiparticle peak remains asymmetric, while for the latter, the smeared peak approaches a Lorentzian at high temperature. The broadening of the peak is nicely captured by a 2πγT inelastic rate as discussed by Le Hur [66,67]. We note that the linear in T and γ broadening is very robust starting from low temperature until T becomes comparable to the ultraviolet cutoff, as illustrated in Fig.…”

Dephasing by electron–electron interactions in a ballistic Mach–Zehnder interferometer

“…it is non-analytic in U 0 ∝ α. Such dephasing rates proportional to T have also been found in non-chiral Luttinger liquids [31]- [32]. At large repulsive coupling, U 0 → +∞, we have the universal result ϕ → π T .…”

High-temperature Aharonov-Bohm effect in transport through a single-channel quantum ring

“…Being peculiar to closed geometry, ZMD is qualitatively different from dephasing in open geometry, where two quantum wires with a magnetic flux between them are weakly tunnel coupled at two points. In the latter case, the dephasing rate is given by the single particle decay rate in a homogeneous Lut tinger liquid (~α 2 T for spinless electrons) [42][43][44][45][46]. A remarkable feature of γ ϕ in Eq.…”