Incoherent Scatterer in a Luttinger Liquid: A New Paradigmatic Limit

We address the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. The asymptotic behavior at zero temperature is governed by a new stable fixed point: A Goldstone mode dominates the low energy dynamics, leading to universal behavior. This limit is marked by equal probabilities for forward and backward scattering. Notwithstanding this nontrivial scattering pattern, we find that the shot noise as well as cross-current correlations vanish. We thus present a paradigmatic picture of an impurity in the Luttinger model, alternative to the Kane-Fisher picture.

Figure 1

Quantum wire comprising two incoming ($l=1,2$) and two outgoing ($l=3,4$) chiral modes connecting to an extended scattering region. Wiggly lines denote coherent scattering channels; dark shading represents a region of capacitive charging (the quantum dot). (a) Cartoon of possible real space structure in fractional quantum Hall effect geometry subject to gating. (b) Alternative view adjusted to our modeling with its tunneling hot spots $x_i$ and lead observation points ${\tilde{x}}_l$.