Quantum Hall studies of a Semi-Dirac Nanoribbon

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.

References in corpus (18)

• The electronic properties of graphene
• Room-Temperature Quantum Hall Effect in Graphene
• Unconventional Integer Quantum Hall effect in graphene
• The Kernel Polynomial Method
• Phase coexistence and metal-insulator transition in few-layer phosphorene: A computational study
• Landau level spectroscopy of ultrathin graphite layers
• Structural and electronic properties of germanene on MoS${}_2$
• Merging of Dirac points in a two-dimensional crystal
• Modeling electronic structure and transport properties of graphene with resonant scattering centers
• A new magnetic field dependence of Landau levels on a graphene like structure
• Zero modes of tight binding electrons on the honeycomb lattice
• Landau levels and magneto-transport property of monolayer phosphorene
• High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy
• Real-space calculation of the conductivity tensor for disordered topological matter
• Stable single-layer honeycomb like structure of silica
• Floquet band structure of a semi-Dirac system
• Enhanced Screening in Chemically Functionalized Graphene
• Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity

Cited by in corpus (1)

• Power law decay of local density of states oscillations near a line defect in a system with semi-Dirac points