Theory of exciton polarons in 2D Wigner crystals

TL;DR

The paper develops a microscopic theory of exciton polarons in a 2D Wigner crystal realized in monolayer TMDs, treating the electrons as localized harmonic oscillators and coupling the exciton to these sites via spin-dependent contact interactions. A Chevy-like variational subspace and a site-by-site solution yield an exciton self-energy that captures standard repulsive and attractive polarons, an exciton Umklapp resonance, and a novel Wigner polaron arising from vibrational excitations of the crystal. In a spin-disordered WC, the two attractive-polaron branches remain parallel and do not hybridize, explained by spatial spin separation and strong electronic correlations, aligning with experiments in WSe$_2$ and WS$_2$; the theory also explains the appearance and scaling of the WP, and the density- and disorder-driven evolution of the spectra. The framework provides a quantitative tool to interpret exciton-polaron spectra in TMDs, highlighting the essential role of electronic interactions and disorder- and phonon-related effects in these strongly correlated 2D systems.

Abstract

Monolayer transition-metal dichalcogenides (TMDs) provide a platform for realizing Wigner crystals and enable their detection via exciton spectroscopy. We develop a microscopic theoretical model for excitons interacting with the localized electrons of the Wigner crystal, including their vibrational motion. In addition to the previously observed exciton-Umklapp feature, the theory reproduces and explains the higher-band attractive-polaron resonances recently reported experimentally. Our model further uncovers that the appearance of two equal-strength and parallel attractive polarons, as commonly observed in WSe$_2$ and WS$_2$, is a signature of strong correlations in the electronic system. Altogether, our results demonstrate that accounting for electronic interactions is essential to reproduce and interpret the exciton-polaron spectra of TMDs.

Figures (8)

• Figure 1: Illustration of excitons ($X$) interacting with a spin-disordered Wigner crystal of electrons in WSe$_2$ and the resulting exciton reflection spectrum as a function of electron density $n$zhang_2:2025wang:2025. The electrons are modeled as distinguishable particles subject to effective harmonic potentials originating from the restoring Coulomb forces of the Wigner crystal lattice. The exciton can form singlet (S) or triplet (T) trions through interactions with spin-down or spin-up electrons, giving rise to attractive polarons AP$_\text{S}$ and AP$_\text{T}$. Above the attractive polarons, Wigner polarons (WPs) emerge: APs dressed with vibrational excitations of the Wigner crystal with frequency $\omega_T$.
• Figure 2: Polaron spectrum as a function of electron density $n$, corresponding to an exciton interacting with a spin-polarized Wigner crystal of electrons in WSe$_2$. Aside from the attractive polaron (AP) and repulsive polaron (RP) peaks, the Umklapp resonance (UP) and the Wigner polaron (WP) are also observed. The black dotted line indicates the energy $E_{\text{AP}}+2\omega_T$ (see main text) and the black dashed line indicates the expected Umklapp energy $E_{\mathrm{UP}}= E_{\mathrm{RP}} +\frac{4 \pi^2 n}{\sqrt{3}m_X}$.
• Figure 3: a-b) Polaron spectrum in WSe$_2$ as a function of electron density $n$, corresponding to an exciton interacting with a) a spin-disordered Wigner crystal, b) a mixture of two non-interacting Fermi seas. c) The singlet (ground state) attractive polaron (AP) wave function as a colormap in the Wigner crystal (WC) case at $n= 6 \times 10^{11}$cm$^{-2}$, showing it is localized only on the spin-down sites. The plotted wave function is only the excitonic portion of the full AP wave function in the zero excitation subspace (see $\alpha$ component of the wave function discussed in the Eq. (S2) of the SM supmat).
• Figure S1: Polaron spectrum in the Wigner crystal model plotted as a function of $l_e/a$ at density $n= 6 \times 10^{11}$cm$^{-2}$. The harmonic oscillator length is changed by varying $\kappa$, smoothly interpolating between the Wigner crystal case (left) and a homogeneous spin mixture of distinguishable electrons (right).
• Figure S2: Relaxed disordered Wigner crystal and its phonon spectrum. (a) Phonon eigenfrequencies as a function of mode index for a $25\times25$ triangular lattice with Yukawa interactions at $n = 10^{11}$ cm${}^2$. (b) The spatial distribution of the lowest energy eigenmode, illustrating the emergence of localized phonon modes away from the pinned regions. (c) Real-space configuration of the same system, showing fixed electrons (gray), mobile electrons (black), a single trion (blue) with larger mass, and pinned disorder sites (red) confined by harmonic traps.