Effective<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math>factor in black phosphorus thin films

Abstract

We theoretically investigate the effective $g$ factor in the black phosphorus (BP) thin films (TFs) based on a multiband $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ theory. We demonstrate that the effective single particle $g$ factor in pristine BP TF is anisotropic arising from its anisotropic band structure with ${g}_{xx}^{*}\ensuremath{\approx}{g}_{yy}^{*}\ensuremath{\approx}2.0$ and ${g}_{zz}^{*}$ sensitively depending on the interband coupling and the band gap. The ${g}_{zz}^{*}$ approaches 2.0 with increasing hole doping density and gate electric field since both of them minish the interband coupling by reducing the overlap integral between the electron and hole wave functions. We also estimate the exchange interaction enhancement on the effective single particle $g$ factor by using the screened Hartree-Fock approximation. The exchange interaction enhanced $g$ factor (${g}_{\text{ex}}$) shows maxima (minima) at odd (even) filling factors. The effective $g$ factor (${g}^{*}$) oscillates with the increase of magnetic field and sensitively depends on the Landau level broadening as well as the gate electric field since both of them affect the interband coupling and the electron-electron interactions.