On the theory of impurity resistance in quantum systems

Stefan Kirchner, Johann Kroha

Hyun Jung Lee, R. Bulla

Marko Žnidarič

We study the breaking of integrability by a finite density of dilute impurities, specifically the emerging diffusive transport. Provided the distance between impurities (localized perturbations) is large, one would expect the scattering rates to be additive, and therefore, the resistivity to be proportional to the number of impurities (the so-called Matthiessen's rule). We show that this is, in general, not the case. If transport is anomalous in the original integrable system without impurities, the diffusion constant in the nonintegrable system at low impurity density has a nontrivial power-law dependence on the impurity density, with the power being determined by the dynamical scaling exponent of anomalous transport. We also find a regime at high impurity density in which, counterintuitively, adding more impurities to an already diffusive system increases transport rather than decreases it.

Luca Dell’Anna, Walter Metzner

We analyze the dc charge transport in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. The transport decay rate is linear in temperature everywhere on the Fermi surface except at cold spots on the Brillouin zone diagonal. For pure systems, this leads to a dc resistivity proportional to T(3/2) in the low-temperature limit. In the presence of impurities the residual impurity resistance at T=0 is approached linearly at low temperatures.

Sergey Bravyi, David Gosset