Wigner Crystal Within Monolayer Transition Metal Dichalcogenides

Experiments show that in doped monolayer transition metal dichalcogenides (TMDs), spin-selective photo-pumping induces a much larger spin imbalance than expected. We hypothesize that this arises from ferromagnetic domains formed by doped electrons, which interact with the spins of photo-pumped electrons, aligning them with the injected spins. To test this, we study the magnetic properties of doped electrons without photo-pumping and propose that a Wigner crystal forms at low doping levels when the K and K' valleys are lightly populated. This crystal comprises two species of electron gas with opposite spins and opposite valley index, given that at high spin-orbit coupling, there is spin-momentum locking. Using a tight-binding model, we show that the Wigner crystal is described by the XYZ spin model, whose mean-field phase diagram reveals spontaneous magnetization, confirming ferromagnetic behavior.