[Paper Review] Optical manipulation of valley coherence via Landau level transitions in black phosphorus and WTe2 monolayers

Xinyu Mu, Shihao Li+2 more|arXiv (Cornell University)|Mar 9, 2026

2D Materials and Applications0 citations

TL;DR

A theoretical study showing that valley quantum interference can be substantially enhanced by inter-Landau level transitions in black phosphorus and WTe2 monolayers due to anisotropic transition probabilities, with material- dependent differences.

ABSTRACT

Valley coherence is of great significance for exploring fundamental quantum phenomena and developing next-generation valleytronic devices. Herein, we theoretically investigate the valley quantum interference engineered by inter-Landau level (LL) transitions in black phosphorus (BP) and WTe2 monolayers. In contrast to the non-Landau-quantized regime, valley quantum interference is enhanced by over 20-fold, or even significantly stronger, in virtue of striking anisotropic environment. Such anisotropy originates from the distinct electron transition probabilities along the armchair and zigzag directions of BP and WTe2 monolayers. Especially, BP is capable of more effectively strengthening the valley quantum interference response due to its greater directional disparity in electron transition probabilities. The interference fringes also present distinct spectral profiles (e.g., different dip and peak numbers in one interference period) owing to different transition selection rules in BP and WTe2 monolayers. In spite of these discrepancies, normalized interference intensities follow two exponential functions of magnetic field and Landau level index for all the transitions δn = n'- n = -4, -2, 0, +2, +4 (where n and n' indicate the LL indexes of valence and conduction bands, respectively), and the interference spectra exhibit C2 rotational symmetry about the crystallographic azimuthal angle of 90°.

Motivation & Objective

• Investigate valley quantum interference engineered by inter-Landau level transitions in BP and WTe2 monolayers.
• Understand how anisotropy along armchair and zigzag directions affects valley coherence.
• Compare BP and WTe2 in terms of their ability to strengthen valley interference.
• Characterize spectral profiles and symmetry of interference patterns under Landau quantization.

Proposed method

• Theoretical analysis of inter-Landau level transitions in BP and WTe2 monolayers.
• Evaluation of valley quantum interference through transition probabilities along different crystallographic directions.
• Extraction of normalized interference intensities as functions of magnetic field and Landau level index.
• Identification of selection rules for Landau level transitions and their impact on interference patterns.
• Analysis of symmetry properties, including C2 rotational symmetry around the azimuthal angle.

Experimental results

Research questions

• RQ1 Does inter-Landau level transition engineering enhance valley quantum interference in BP and WTe2 monolayers?
• RQ2 How does anisotropy between armchair and zigzag directions influence valley coherence?
• RQ3 Which material—BP or WTe2—exhibits stronger valley interference due to directional disparities?
• RQ4 What are the spectral characteristics (dip/peak structure) of interference fringes under LL transitions?
• RQ5 What symmetry properties govern the interference patterns in these monolayers?

Key findings

• Valley quantum interference is enhanced by over 20-fold due to inter-Landau level transitions in these materials.
• BP shows stronger interference responses owing to greater directional disparity in transition probabilities.
• Interference fringes exhibit distinct spectral profiles with varying dip and peak numbers per period depending on the material.
• Normalized interference intensities follow two exponential functions of magnetic field and Landau level index for δn = -4, -2, 0, +2, +4.
• Interference spectra display C2 rotational symmetry about the crystallographic azimuthal angle of 90 degrees.