Non-Born effects in the scattering of electrons in a conducting strip with a low concentration of impurities

Abstract

We extend the theory of non-Born effects in resistivity $\rho$ of clean conducting tubes (developed in our previous work arXiv:1810.00426) to ``strips'' -- quasi-one-dimensional structures in 2D conductors. Here also an original Van Hove singularity in dependence of $\rho$ on the position of chemical potential $\varepsilon$ is asymmetrically split in two peaks for attracting impurities. However, since amplitudes of scattering at impurities depend on their positions, these peaks are inhomogeneously broadened. Strongest broadening occurs in the left peak, arising, for attracting impurities, due to scattering at quasistationary levels. In contrast with the case of tube these levels form not a unique sharp line, but a relatively broad impurity band with a weak quasi-Van Hove feature on its lower edge. Different parts of $\rho(\varepsilon)$ are dominated by different groups of impurities: close to the minimum the most effective scatterers, paradoxically are the ``weakest'' impurities -- those, located close to nodes of the electronic wave-function, so that the bare scattering matrix elements are suppressed. The quasi-Van Hove feature at left maximum is dominated by strongest impurites, located close to antinodes.