Electron Scattering in 2D Semiconductors: Contrasting Dirac and Schr\"odinger Behavior

TL;DR

This paper compares electron scattering in 2D semiconductors modeled by Dirac and Schrödinger equations, highlighting their different regimes and validity for describing electronic transport at various energies.

Contribution

It provides a detailed analysis of scattering processes in 2D semiconductors using both Dirac and Schrödinger models, clarifying their applicability across energy regimes.

Findings

Low-energy scattering is nearly isotropic with low angular momentum dominance.

High-energy scattering shows signatures of linear dispersion with non-zero phase shifts.

Dissimilar behaviors between Dirac and Schrödinger carriers define their regimes of validity.

Abstract

Electronic transport through a material depends on the response to local perturbations induced by defects or impurities in the material. The scattering processes can be described in terms of phase shifts and corresponding cross sections. The multiorbital nature of the spinor states in transition metal dichalcogenides would naturally suggest the consideration of a massive Dirac equation to describe the problem, while the parabolic dispersion of its conduction and valence bands would invite a simpler Schr\"odinger equation description. Here, we contrast the scattering of massive Dirac particles and Schr\"odinger electrons, in order to assess different asymptotic regimes (low and high Fermi energy) for each one of the electronic models and describe their regime of validity or transition. At low energies, where the dispersion is approximately parabolic, the scattering processes are dominated by low angular momentum channels, which results in nearly isotropic scattering amplitudes. On the other hand, the differential cross section at high Fermi energies exhibits clear signatures of the linear band dispersion, as the partial phase shifts approach a non-zero value. We analyze the electronic dynamics by presenting differential cross sections for both attractive and repulsive scattering centers. The dissimilar behavior between Dirac and Schr\"odinger carriers points to the limits and conditions over which different descriptions are required for the reliable treatment of scattering processes in these materials.