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arXiv:cond-mat/0610374 · Physical Review B

Backscattering off a dynamical impurity in one-dimensional Fermi systems: A perturbative computation

Carlos Naón, Mariano J. Salvay

Published Mar 8, 2007• 2 citations
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Abstract

We investigate the problem of backscattering off a time-dependent and spatially extended barrier in a one-dimensional noninteracting electron gas. By performing a perturbative expansion in the backscattering amplitude, we compute the total energy density of the system. We show how the free fermion spectrum and the conductance of the system are affected by the interplay between dynamical and geometrical properties of the impurity.

DOI
10.1103/physrevb.75.113102

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We investigate the problem of backscattering off a time-dependent and spatially extended barrier in a one-dimensional noninteracting electron gas. By performing a perturbative expansion in the backscattering amplitude, we compute the total energy density of the system. We show how the free fermion spectrum and the conductance of the system are affected by the interplay between dynamical and geometrical properties of the impurity.
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Electron backscattering in a Luttinger liquid with an impurity is investigated in the presence of zero point motion of the phonon lattice. The impurity can mean either a mass defect, an elastic defect, or a pinning defect. The phonon spectrum is then affected by the presence of the defect, which enters in the renormalization group (RG) equations for backscattering. The RG equation becomes dependent on the energy cutoff for finite Debye frequency ${\ensuremath{\omega}}_{D}$ giving rise to finite energy effects. We compute the local density of states and show how the renormalization group flow is affected by a finite ${\ensuremath{\omega}}_{D}$.
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We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1∕21∕21∕2 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density-matrix renormalization-group data. We present results for the density of states, the density profile, and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.