[Paper Review] The diverse magneto-optical selection rules in bilayer black phosphorus

Jhao-Ying Wu, Szu-Chao Chen+3 more|arXiv (Cornell University)|Dec 27, 2017

2D Materials and ApplicationsMaterials Science8 references3 citations

TL;DR

This study investigates the tunable magneto-optical selection rules in bilayer black phosphorus using a generalized tight-binding model and gradient approximation. It reveals that perpendicular electric and magnetic fields dramatically alter the selection rules, absorption peak characteristics, and Landau level structure, leading to anisotropic, non-monotonic, and field-dependent optical responses due to symmetry-breaking and sublattice-dependent envelope functions.

ABSTRACT

The magneto-optical properties of bilayer phosphorene is investigated by the generalized tight-binding model and the gradient approximation. The vertical inter-Landau-level transitions, being sensitive to the polarization directions, are mainly determined by the spatial symmetries of sub-envelope functions on the distinct sublattices. The anisotropic excitations strongly depend on the electric and magnetic fields. A perpendicular uniform electric field could greatly diversify the selection rule, frequency, intensity, number and form of symmetric absorption peaks. Specifically, the unusual magneto-optical properties appear beyond the critical field as a result of two subgroups of Landau levels with the main and side modes. The rich and unique magneto-absorption spectra arise from the very close relations among the geometric structures, multiple intralayer and interlayer hopping integrals, and composite external fields.

Motivation & Objective

• To understand the impact of perpendicular electric and magnetic fields on magneto-optical properties in bilayer black phosphorus.
• To investigate how geometric structure and interlayer interactions influence Landau level formation and optical transitions.
• To determine the role of sublattice symmetry and envelope function spatial distributions in shaping selection rules.
• To explore the emergence of new excitation channels and threshold frequency shifts near the critical electric field.
• To provide a theoretical framework for interpreting experimental magneto-optical spectroscopy in 2D anisotropic materials.

Proposed method

• Employing a generalized tight-binding model to describe electronic band structure under combined electric and magnetic fields.
• Using the gradient approximation to compute electric-dipole transition matrix elements between Landau levels.
• Calculating magneto-optical conductivity via the Kubo formula to predict absorption spectra.
• Analyzing sub-envelope function symmetries on distinct sublattices to determine selection rules.
• Systematically varying electric field strength to observe transitions in Landau level subgroups and spectral features.
• Comparing results across polarization directions (x- and y-polarized light) to quantify anisotropy.

Experimental results

Research questions

• RQ1 How do perpendicular electric and magnetic fields modify the magneto-optical selection rules in bilayer black phosphorus?
• RQ2 What is the role of sublattice symmetry and spatial distribution of sub-envelope functions in determining optical transition selection rules?
• RQ3 How does the critical electric field induce abrupt changes in threshold frequency and available excitation channels?
• RQ4 In what way do the Landau level subgroups (main and side modes) influence the number, frequency, and intensity of absorption peaks?
• RQ5 How do the optical responses in bilayer black phosphorus differ from those in isotropic 2D materials like graphene?

Key findings

• The selection rules are determined by the spatial symmetry of sub-envelope functions on distinct sublattices, leading to Δn = odd for x-polarization and Δn = even for y-polarization.
• A perpendicular electric field beyond the critical value (Ez,c) induces abrupt changes in threshold frequency and transitions from (0,0) to (0,1) excitation channels under x-polarization.
• The magneto-optical absorption spectra exhibit non-monotonous, oscillatory, and discontinuous dependences on the electric field, especially near Ez,c.
• Spectral intensity is significantly reduced from x- to y-polarization due to the velocity matrix element's dependence on the largest intralayer hopping integral.
• Absorption peak frequencies deviate from the linear or square-root Bz-dependence seen in graphene, indicating non-universal Landau level quantization.
• The emergence of two subgroups of Landau levels (main and side modes) under high Ez leads to rich, tunable, and complex magneto-absorption spectra.