[Paper Review] Electric-field-tunable intervalley excitons and phonon replicas in bilayer WSe$_2$

Mashael M. Altaiary, Erfu Liu+8 more|arXiv (Cornell University)|Jan 27, 2021

2D Materials and Applications45 references4 citations

TL;DR

This study reports the direct observation of electric-field-tunable intervalley excitons between the Q conduction and Γ valence valleys in bilayer WSe₂ via photoluminescence. By applying a gate-tunable electric field, the energy ordering and dominant luminescence between the QΓ and QK excitons can be switched, while pronounced phonon replicas—especially two-phonon ones—arise from resonant exciton-phonon coupling, with theory confirming the assignments through excellent agreement with experimental Stark shifts and replica spectra.

ABSTRACT

We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon replicas, in which two-phonon replicas outshine the one-phonon replicas due to the existence of (nearly) resonant exciton-phonon scatterings and numerous two-phonon scattering paths. We can simulate the replica spectra by comprehensive theoretical modeling and calculations. The good agreement between theory and experiment for the Stark shifts and phonon replicas strongly supports our assignment of Q$Γ$ and QK excitons.

Motivation & Objective

• To identify and characterize intervalley excitons in bilayer WSe₂, specifically the QΓ exciton between the Q conduction and Γ valence valleys.
• To investigate the tunability of excitonic states via an external electric field in a 2D transition metal dichalcogenide heterostructure.
• To understand the origin and spectral characteristics of phonon replicas in the excitonic luminescence, particularly the dominance of two-phonon over one-phonon processes.
• To validate the assignment of QΓ and QK excitons through comparison of experimental Stark shifts and phonon replica spectra with comprehensive theoretical modeling.

Proposed method

• Photoluminescence spectroscopy was performed on gated bilayer WSe₂ devices to probe excitonic transitions under varying electric fields.
• Gate-tunable electric fields were applied to modulate the interlayer potential and control the energy levels of intervalley excitons.
• Theoretical modeling was used to simulate the Stark shifts and phonon replica spectra, incorporating exciton-phonon coupling and multiple scattering pathways.
• Theoretical calculations included the effects of (nearly) resonant exciton-phonon scattering to explain the enhanced two-phonon replica intensity.
• Spectral analysis focused on identifying energy positions, relative intensities, and field-dependent shifts of the QΓ and QK excitons and their phonon replicas.
• Comparison between experimental data and theoretical simulations was used to confirm the assignment of the QΓ and QK excitons and their distinct dipole moments.

Experimental results

Research questions

• RQ1 What is the nature and energy position of the intervalley exciton formed between the Q conduction valley and Γ valence valley in bilayer WSe₂?
• RQ2 How does an applied electric field tune the energy levels and relative intensity of the QΓ and QK excitons?
• RQ3 Why are two-phonon replicas more intense than one-phonon replicas in the luminescence spectrum of bilayer WSe₂?
• RQ4 What is the role of resonant exciton-phonon scattering in shaping the phonon replica spectra?
• RQ5 To what extent do theoretical models accurately reproduce the observed Stark shifts and phonon replica intensities?

Key findings

• The QΓ intervalley exciton lies ~18 meV below the QK exciton and dominates the photoluminescence in bilayer WSe₂.
• An external electric field can reverse the energy ordering between the QΓ and QK excitons, switching their relative dominance in luminescence.
• The QΓ and QK excitons exhibit distinct interlayer electric dipole moments, as evidenced by their different Stark shift behaviors under gate tuning.
• Two-phonon replicas are significantly more intense than one-phonon replicas due to resonant exciton-phonon scattering and multiple scattering pathways.
• Theoretical simulations of Stark shifts and phonon replicas show excellent agreement with experimental data, confirming the assignment of QΓ and QK excitons.
• The observed phonon replica spectra are well explained by a comprehensive model including exciton-phonon coupling and interference effects in the scattering amplitudes.