Impact of an electron Wigner crystal on exciton propagation

Abstract

The strong Coulomb interaction in 2D materials facilitates the formation of tightly bound excitons and charge-ordered phases of matter. A prominent example is the formation of a crystalline phase from free charges due to mutual Coulomb repulsion, known as the Wigner crystal. While exciton-electron interactions have been used as a sensor for Wigner crystallization, its impact on exciton properties has been poorly understood so far. Here, we show that the weak potential induced by periodically ordered Wigner crystal electrons has a major impact on exciton propagation, albeit having only a minor influence on exciton energy. The effect is tunable with carrier density determining the Wigner crystal confinement and temperature via thermal occupation of higher subbands. Our work provides microscopic insights into the interplay between excitons and charge-ordered states identifying key signatures in exciton transport, and establishes a theoretical framework for understanding exciton propagation in the presence of strong electronic correlations.

Figures (4)

• Figure 1: Schematic illustration of exciton transport in the presence of an electron Wigner crystal. The periodic arrangement of electrons in a Wigner crystal lattice gives rise to a potential that excitons can be trapped in, slowing down their propagation. The colored Gaussian curves illustrate the real-space charge density of electrons confined in a Wigner lattice with the periodicity set by the Wigner lattice constant $a_W$ that is generally comparable to the spatial extent of the exciton $a_X$.
• Figure 2: Exciton band structures and group velocities along a horizontal cut of the Wigner crystal Brillouin zone in hBN-encapsulated MoSe$_2$ monolayers for (a) low carrier density $n_e=10^{11}$$\mathrm{cm}^{-2}$ (corresponding to a Wigner lattice period $a_W\approx{34}$ nm) and (b) high carrier density $n_e=10^{12}$$\mathrm{cm}^{-2}$ ($a_W\approx{11}$ nm). The bare bands without a Wigner crystal potential are shown with dashed lines. The flattening of the bands at the edges of the Brillouin zone (yellow areas in [(a)-(b)]), results in quenched group velocities at larger momenta [(c)-(d)]. The group velocities are superimposed by the corresponding exciton occupations for the two lowest-lying bands.
• Figure 3: Density-dependent exciton diffusion coefficient in the presence of an electron Wigner crystal in hBN-encapsulated MoSe$_2$ monolayers at cryogenic temperatures ($T$=4 K). At low carrier densities, the Wigner crystal electrons are strongly localized (inset), i.e., their spatial extent $\xi$ is much smaller than the Wigner lattice period $a_W$. This gives rise to the emergence of flattened exciton bands and suppressed exciton diffusion. As the carrier density is increased, Wigner electrons become less confined, exciton bands become increasingly parabolic, and exciton diffusion approaches the limit of free excitons (blue line). In strong contrast, free electron-exciton scattering gives rise to a decrease in the exciton diffusion as a functon of carrier density (dashed gray line).
• Figure 4: Temperature-dependent exciton diffusion in the presence of a Wigner crystal. Exciton band structure with the bands overlaid by the exciton occupation at $T=12$ K, revealing (a) a large occupation of higher-lying exciton bands at low densities and (b) their negligible occupation at high densities. (c) Exciton diffusion coefficient at three different temperatures. For $T=8$ and 12 K, exciton diffusion becomes non-monotonous as a function of carrier density, reflecting the behaviour of the effective thermal group velocity (inset).