Optical probing of Wigner crystallization in monolayer WSe$_2$ via diffraction of longitudinal excitons

TL;DR

This work demonstrates optical access to Wigner crystallization in a monolayer WSe$_2$ without magnetic field, observing a diffraction feature from the linearly dispersing exciton branch caused by a WC-induced periodic potential. By leveraging strong intervalley exchange, which yields a sizable longitudinal–transverse exciton splitting, the authors spectrally resolve umklapp-scattered diffraction peaks and extract their energies and oscillator strengths as a function of carrier density and temperature. A combined experimental-theoretical framework is developed: second-derivative spectroscopy isolates the weak WC diffraction signal, and a weak-potential, six-beam diffraction model connects the observed peaks to the WC reciprocal lattice and disorder effects, enabling estimation of phase boundaries. The results underscore the utility of valley physics in TMDs for optical probing of correlated electron phases and highlight disorder as a key factor shaping the WC phase in realistic samples.

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 $n$ $<2\times10^{11}~\mathrm{cm}^{-2}$. 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.

Figures (6)

• Figure 1: Optical detection of Wigner crystallization. (a) Schematic of the studied device, consisting of WSe$_2$ monolayer, layers of hBN, graphene contact and gates with connected voltage sources. (b) Dependence of the reflectance contrast spectrum on the gate voltage, with X$^0$ corresponding to main exciton, X$^+$ and X$^-$ corresponding to positive and negative trions, the arrow indicates electron (n) and hole (p) doping. (c) The left panel shows the excitonic branches in monolayer WSe$_2$ with parabolic (red) and linear (blue) dispersion. The right panel shows the change of main exciton energy due to doping and the folding of the energy bands due to the Wigner crystal potential and the resulting diffraction peaks for both exciton branches. (d) Second derivative of reflection spectra with respect to energy. The contrast is increased by 100 times in the selected area. The map shows the blueshift of main exciton extracted from fit (dash-dotted line) and energy shift of Wigner resonances (the excitonic branch with parabolic dispersion is denoted by black dotted line, branch with linear dispersion is denoted by grey dashed line).
• Figure 2: Observation of Wigner crystal at different temperatures. (a) Dependence of the reflectance contrast spectrum on the gate voltage for different temperatures (8 K - left, 20 K - center, 30 K - right). (b) Dependence of main exciton energy on applied voltage at a temperature of 8 K (red), 20 K (blue), 30 K (green). Pink area indicates the displacement of the main exciton corresponding to the range of carrier densities where Wigner crystal resonance is discernible. (c) Second derivatives of reflection spectra at 8 K and 20 K (blue squares) and fit functions (red solid lines). (d) Phase diagram. The blue region corresponds to the theoretically calculated state of the Wigner crystal. The red lines show the range of carrier densities at temperatures of 8 K and 20 K, where the Wigner crystal is observed experimentally.
• Figure 3: Oscillator strength of the longitudinal exciton diffraction peak. (a) Second derivative of main exciton resonance fit function (red dash-dotted line) and experimental second derivative of the Wigner resonance spectra (blue squares) and its fit function (red solid line). Values are increased by 100 times for the diffraction peak. (b) Theoretically calculated dependence of the relative oscillator strength on charge carrier density (solid lines) and experimental values (circles) for 8 K (red data) and 20 K (blue data).
• Figure 4: Exciton resonance parameters. (a) The reflection spectrum of the main exciton at 8 K and at 0 V (blue squares) and its fit (red line). (b) Energy shift of the main exciton at applied voltage. (c) Change of $\Gamma_0$ at applied voltage. (d) Change of $\Gamma_m$ at applied voltage.
• Figure 5: Typical dependence of concentration on applied voltage.