Quantum transport regimes in quartic dispersion materials with Anderson disorder

TL;DR

This study investigates how quartic dispersion in certain 2D materials affects electronic transport in nanoribbons under Anderson disorder, revealing unique conductance and localization behaviors near the band edge.

Contribution

It provides a systematic numerical analysis of transport regimes in 1D and Q1D quartic dispersion nanoribbons, highlighting the effects of disorder and the emergence of singularities.

Findings

Conductance drops sharply at the quartic band edge in 1D systems.

Singularities near the band edge suppress conductance in Q1D nanoribbons.

Wider nanoribbons can have shorter mean-free-paths due to denser singularities.

Abstract

Mexican-hat-shaped quartic dispersion manifests itself in certain families of single-layer twodimensional hexagonal crystals such as compounds of groups III-VI and groups IV-V as well as elemental crystals of group V. Quartic band forms the valence band edge in various of these structures, and some of the experimentally confirmed structures are GaS, GaSe, InSe, SnSb and blue phosphorene. Here, we numerically investigate strictly-one-dimensional (1D) and quasi-one dimensional (Q1D) nanoribbons with quartic dispersion and systematically study the effects of Anderson disorder on their transport properties with the help of a minimal tight-binding model and Landauer formalism. We compare the analytical expression for the scaling function with simulation data to deduce about the domains of diffusion and localization regimes. In 1D, it is shown that conductance drops dramatically at the quartic band edge compared to a quadratic band. As for the Q1D nanoribbons, a set of singularities emerge close to the band edge, which suppress conductance and lead to short mean-free-paths and localization lengths. Interestingly, wider nanoribbons can have shorter mean-free-paths because of denser singularities. However, the localization lengths do not necessarily follow the same trend. The results display the peculiar effects of quartic dispersion on transport in disordered systems.