Landau levels and magneto-transport property of monolayer phosphorene

TL;DR

This paper theoretically studies Landau levels and magneto-transport in monolayer phosphorene, revealing anisotropic properties, analytical expressions at low fields, and a Hofstadter butterfly spectrum at high fields.

Contribution

It provides a comprehensive analysis combining effective extbf{ extit{k$ullet$p}} and tight-binding models to describe Landau levels and magneto-transport in phosphorene, including analytical solutions and high-field spectra.

Findings

Landau levels depend linearly on magnetic field and index at low fields.

Wavefunctions are strongly anisotropic due to effective mass differences.

Hofstadter butterfly spectrum observed at high magnetic fields.

Abstract

We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective \textbf{\emph{k$\cdot$p}} Hamiltonian and tight-binding (TB) model. At low field regime, we find that the LLs linearly depend both on the LL index $n$ and magnetic field $B$, which is similar with that of conventional semiconductor two-dimensional electron gas. The Landau splittings of conduction and valence band are different and the wavefunctions corresponding to the LLs are strongly anisotropic due to the different anisotropic effective masses. An analytical expression for the LLs in low energy regime is obtained via solving the decoupled Hamiltonian, which agrees well with the numerical calculations. At high magnetic regime, a self-similar Hofstadter butterfly (HB) spectrum is obtained by using the TB model. The HB spectrum is consistent with the Landau level fan calculated from the effective \textbf{\emph{k$\cdot$p}} theory in a wide regime of magnetic fields. We find the LLs of phosphorene nanoribbon depend strongly on the ribbon orientation due to the anisotropic hopping parameters. The Hall and the longitudinal conductances (resistances) clearly reveal the structure of LLs.