Topological transition and its connection with the conductivity and thermopower anomalies in two-dimensional systems

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Abstract
The conductivity and thermopower of a two-dimensional electron gas in the case when the Fermi level is placed near the origin of one of the size-quantization subbands are considered. The intersection of the Fermi level with the size-quantization level causes the topological change of the Fermi surface, which results in anomalies in the conductivity and thermopower. It is shown that a consistent quantitative description of the anomaly requires that the distortion of the electronic states in the populating subband by the random potential be taken into account. A general expression for the electron relaxation time in the vicinity of the transition is derived with the use of diagrammatic techniques. Detailed calculations are performed for two models of the random potential: Gaussian white noise and the screened Coulomb potential.