- The paper introduces a combined 2DCS and Voigt profile analysis to effectively separate homogeneous and inhomogeneous linewidths in TMD excitons.
- It employs a joint fitting technique of diagonal and cross-diagonal spectral slices, significantly reducing parameter covariance compared to traditional PL methods.
- The findings establish 2DCS as a powerful tool for accurately quantifying microscopic dissipation and disorder in semiconductor materials.
Separation of Homogeneous and Inhomogeneous Broadening in Spectral Linewidths via Two-Dimensional Coherent Spectroscopy
Introduction
The disentanglement of homogeneous and inhomogeneous broadening mechanisms in optical spectroscopy is critical for elucidating microscopic dissipation and disorder in condensed matter systems, particularly for transition metal dichalcogenide (TMD) excitons. Traditional one-dimensional spectroscopic techniques, such as photoluminescence (PL), suffer from strong parameter covariance when fitting Voigt profiles for spectral lines exhibiting comparable homogeneous (Lorentzian) and inhomogeneous (Gaussian) widths. This covariance impedes reliable quantification of the underlying physical processes. The presented work provides a rigorous analysis demonstrating that two-dimensional coherent spectroscopy (2DCS) supplies orthogonal spectral constraints, reducing degeneracy and enabling robust extraction of homogeneous and inhomogeneous linewidths (2607.05564).
Experimental Methodology
The study examines hBN-encapsulated MoSe₂ at 8 K, a prototypical TMD system with excitonic features near the homogeneous linewidth limit. The experimental workflow involves parallel acquisition of PL and 2DCS data on the same flake, with spatial registration facilitated by hyperspectral PL imaging. PL spectra are acquired with a grating spectrometer using a focused HeNe excitation source, and subsequent lineshape analysis employs Voigt profile fitting. For 2DCS, the experimental setup integrates ultrafast pulse sequences, phase-stabilized delay lines, and heterodyne detection, providing a 2D spectral map with diagonal (excitation ≈ detection energy) and cross-diagonal projections.
Lineshape Analysis and Parameter Extraction
In the Voigt formalism, the total lineshape is a convolution of Lorentzian (homogeneous, width γ) and Gaussian (inhomogeneous, width σ) components. One-dimensional PL spectra inherently constrain only the total linewidth; empirical fits exhibit elongated and diagonally oriented (σ, γ) confidence regions (|ρ_σγ| ≈ 0.93), revealing strong parameter correlation. This degeneracy permits compensation between σ and γ, yielding poorly determined physical broadening mechanisms.
2DCS addresses this limitation by leveraging the contrasting dependencies of the diagonal and cross-diagonal lineshape slices. The diagonal slice is sensitive to both contributions, while the cross-diagonal slice is predominantly governed by homogeneous broadening. The authors implement a statistically rigorous joint fit to both slices, incorporating per-pixel uncertainties from repeated acquisitions. This approach minimizes the total χ² landscape across (σ, γ), with shared physical parameters but independent amplitude and offset fits for each slice.
Numerical Results
The quantitative comparison across multiple sample regions highlights key results:
- PL Voigt Fitting: Best-fit values σ = 0.56 ± 0.07 meV, γ = 1.00 ± 0.07 meV; strong covariance with axis ratio r = 5.1 ± 0.2.
- 2DCS Joint Fit: Best-fit values σ = 0.91 ± 0.08 meV, γ = 0.58 ± 0.08 meV; substantially reduced covariance (|ρ_σγ| = 0.73 ± 0.03) and axis ratio r = 2.6 ± 0.2.
The confidence regions in 2DCS are markedly more compact and less elongated, evidencing improved parameter separability. Notably, the extracted linewidths show systematic differences between PL and 2DCS, attributed to the former probing incoherently relaxed populations and the latter sampling directly the coherent nonlinear optical response. The methodology also confirms physical plausibility, as inhomogeneous broadening from static disorder is more prominent in coherent 2D readouts.
Theoretical Implications and Future Directions
The reduction in (σ, γ) degeneracy achieved through 2DCS establishes a new standard for spectroscopic precision in quantifying coherence and disorder. This multidimensional approach provides a general framework, extensible to other material systems, wherever Voigt-type lineshapes and comparable broadening sources coexist. Claims relying solely on linear-spectroscopy-extracted homogeneous linewidths, especially in state-of-the-art TMD samples, require careful reinterpretation considering these results.
Potential advancements include incorporating excitation-induced dephasing (EID) and excitation-induced shift (EIS) effects, which would further decouple the lineshape parameters due to their distinctive 2DCS spectral signatures. Such extensions could ultimately minimize the remaining parameter correlation and provide detailed insight into many-body and phonon-mediated effects in low-dimensional semiconductors.
Conclusion
This study provides clear, quantitative evidence that 2DCS significantly outperforms conventional PL-based Voigt analysis in separating homogeneous and inhomogeneous broadening mechanisms in excitonic systems. The joint fitting framework introduces rigorous statistical confidence to parameter extraction, improves the reliability of linewidth assignments, and sets a foundation for future high-precision nonlinear spectroscopic studies. The results recommend broad adoption of 2DCS for linewidth decomposition in systems with non-negligible both broadening channels, emphasizing the need to reevaluate prior studies predicated on one-dimensional approaches (2607.05564).