Abstract
Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states and the resistivity , occurring when the Fermi level crosses a bottom of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration being the dimensionless amplitude of scattering. For , the singularities are simply rounded at —the Born scattering rate. For , the single-impurity non-Born effects in scattering become essential despite . The peak of the resistivity is asymmetrically split in a Fano-resonance manner (however, with a more complex structure). Namely, for , there is a broad maximum at , while for , there is a deep minimum at . The behavior of below the minimum depends on the sign of . In case of repulsion, monotonically grows with and saturates for . In case of attraction, has a sharp maximum at . The latter feature is due to resonant scattering at quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.
- Received 24 October 2018
DOI:https://doi.org/10.1103/PhysRevB.99.035414
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