Quantum Hall studies of a Semi-Dirac Nanoribbon

TL;DR

This paper investigates the unique electronic and transport properties of semi-Dirac nanoribbons under magnetic fields, revealing non-equidistant Landau levels, dispersive bulk bands, and anisotropic magneto-transport, with implications for 2D materials like phosphorene.

Contribution

It provides a comprehensive analysis of semi-Dirac nanoribbons' Landau levels, Hofstadter butterfly, and conductivities, highlighting differences from Dirac systems and introducing a real-space Kubo approach.

Findings

Landau levels are non-equidistant in semi-Dirac systems.

Hall conductivity shows quantization proportional to 2n, distinct from graphene.

Anisotropic magneto-transport behavior observed in semi-Dirac ribbons.

Abstract

Here we comprehensively investigate Landau levels, Hofstadter butterfly and transport properties of a semi-Dirac nanoribbon in a perpendicular magnetic field using a recently developed real-space implementation of the Kubo formula based on Kernel Polynomial Method. A Dirac ribbon is considered to compare and contrast our results for a semi-Dirac system. We find that the Landau levels being non-equidistant from each other for the semi-Dirac case (true for a Dirac as well), the flatness of the energy bands vanishes in the bulk and becomes dispersive for a semi-Dirac ribbon in contrast to a Dirac system. This feature is most discernible for intermediate values of the external field. We further compute the longitudinal ($\sigma_{xx}$ and $\sigma_{yy}$) and the transverse or Hall ($\sigma_{xy}$) conductivities where the Hall conductivity shows a familiar quantization, namely, $\sigma_{xy} \propto 2n$ (the factor `2' includes the spin degeneracy) which is highly distinct from a Dirac system, such as graphene. We also observe anisotropic behavior in magneto-transport in a semi-Dirac ribbon owing to the dispersion anomalies in two different longitudinal directions. Our studies may have important ramifications for monolayer phosphorene.