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

Clean quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states $\ensuremath{\nu}$ and resistivity $\ensuremath{\rho}$, occurring when the Fermi level crosses the bottom of some transversal quantization subband. However, taking the scattering on impurities into the account should smear the singularities. As we have shown in our previous work [Phys. Rev. B 99, 035414 (2019)], for the case of clean conducting tubes, the character of smearing strongly depends on the impurity concentration $n$. For $n\ensuremath{\gg}{n}_c$, the singularities are simply rounded, while for $n\ensuremath{\ll}{n}_c$, the initial peak is asymmetrically split into two for the case of attracting impurities, ${n}_c$ being a crossover concentration. In this work, we extend our consideration to ``strips''---quasi-one-dimensional structures in 2D conductors. Here also for $n\ensuremath{\ll}{n}<sub>c</sub>$, an original Van Hove singularity is asymmetrically split into two peaks. However, in contrast to the tube case, the amplitudes of scattering at impurities depend on their positions and these peaks are inhomogeneously broadened. The strongest broadening occurs in the left peak, arising, for attracting impurities, due to the scattering at the quasistationary levels that form a relatively broad impurity band with a weak quasi-Van Hove feature on its lower edge. Different parts of $\ensuremath{\rho}(\ensuremath{\varepsilon})$ are dominated by different groups of impurities: close to the minimum the most effective scatterers, paradoxically, are the ``weakest'' impurities located close to nodes of the electronic wave function. The quasi-Van Hove feature at the left maximum is dominated by the strongest impurities located close to antinodes.