[Paper Review] Optical probing of Wigner crystallization in monolayer WSe$_2$ via diffraction of longitudinal excitons

Artem N. Abramov, Emil Chiglintsev+7 more|arXiv (Cornell University)|Jan 22, 2026

2D Materials and Applications1 citations

TL;DR

The paper demonstrates an optical method to detect Wigner crystallization in monolayer WSe2 without magnetic fields by observing diffraction of longitudinal excitons, enabled by strong intervalley exchange.

ABSTRACT

Monolayer transition metal dichalcogenides (TMDs) are characterized by relatively large carrier effective masses and suppressed screening of the Coulomb interaction, which substantially enhances the correlation effects in these structures. The direct band gap allows to effectively optically probe these correlations. Here, we present an experimental observation of Wigner crystallization in monolayer $\mathrm{WSe}_2$ probed by the measurement of the exciton diffraction on the Wigner crystal (WC) periodic potential. We observe the formation of the WC phase in the absence of external magnetic fields at temperature range $T<26~\mathrm{K}$ and carrier concentrations $n$ $<2 imes10^{11}~\mathrm{cm}^{-2}$. The direct observation of the exciton diffraction is enabled by the strong exciton longitudinal-transverse splitting induced by the long-range intervalley exchange interaction, leading to the large detuning between main exciton peak and first diffraction peak. Our findings highlight that the valley degree of freedom of charge carriers in TMDs facilitates optical probing of correlated electron phases in these structures.

Motivation & Objective

• Motivate and detect Wigner crystallization in monolayer WSe2 without external magnetic fields.
• Use exciton–electron coupling to imprint a WC periodic potential that diffracts excitons.
• Differentiate two exciton branches (longitudinal and transverse) to enable optical observation.
• Map the WC phase diagram as a function of temperature and carrier density.
• Quantify the WC-induced oscillator strength transfer to first diffraction peaks.

Proposed method

• Fabricate a hBN-encapsulated WSe2 monolayer with graphene gates and dual gates to control carrier density and displacement field.
• Measure gate-dependent reflectance contrast at low temperature using a pulsed supercontinuum source and a high-NA objective.
• Analyze the data via second-derivative spectra to reveal weak WC diffraction features.
• Model WC diffraction using umklapp scattering and two exciton branches with explicit energies and dispersions.
• Fit the WC diffraction features with a Fano-based lineshape and a distributed-resonance approach to extract oscillator strength.
• Relate the main exciton blueshift to carrier density and predict diffraction peak energies from the linear and parabolic branches.

Experimental results

Research questions

• RQ1 Can Wigner crystallization be optically observed in monolayer WSe2 without an external magnetic field at T < 26 K and carrier density n < 2×10^11 cm^-2?
• RQ2 Do WC-induced periodic potentials cause detectable exciton diffraction, and how do the two exciton branches contribute to the diffraction signal?
• RQ3 How does intervalley exchange coupling influence the optical visibility of the Wigner crystal in monolayer TMDs?
• RQ4 What is the relationship between main exciton blueshift, WC periodic potential, and the energies of the first diffraction peaks?
• RQ5 What are the temperature and density ranges over which the WC phase is stable, and how does disorder affect these ranges?

Key findings

• Optical diffraction peak associated with the linearly dispersing exciton branch is observed at low temperature under electron doping, signaling WC formation without magnetic fields.
• The diffraction feature fades with increasing temperature and disappears around 26 K, indicating a WC melting transition.
• A phase diagram is presented with WC regions consistent with theory, showing WC observed up to a maximum density of ~2.5×10^11 cm^-2 at low temperature.
• The relative oscillator strength of the WC diffraction peak is extracted as f ≈ 3×10^-4 at 8 K and ≈ 9×10^-5 at 20 K, with an uncertainty of about an order of magnitude.
• Disorder is inferred to raise the observed critical density and to possibly explain the absence of WC under hole doping in this study.
• The approach leverages strong intervalley exchange to create a large longitudinal-transverse exciton splitting, enabling spectral separation of the WC-induced diffraction peak from the main exciton.