Magnetic-Field-Induced Wigner Crystallization of Charged Interlayer Excitons in Transition Metal Dichalcogenide Bilayers

We develop the theory of the magnetic-field-induced Wigner crystallization effect for charged interlayer excitons (CIE) discovered recently in transition-metaldichalcogenide (TMD) heterobilayers [1]. The Wigner crystal phase has been one of the longest anticipated exotic correlated phases, a phase that is very closely related to excitonic insulator, and originally was thought of as a periodic array of electrons held in place when their Coulomb repulsion energy exceeds the Fermi and thermal fluctuation energies. Here, we derive the ratio of the average potential interaction energy to the average kinetic energy for the many-particle CIE system subjected to the perpendicular magnetic field of an arbitrary strength, analyze the weak and strong field regimes, and discuss the ’cold’ crystallization phase transition for the CIE system in the strong field regime [2]. We also generalize the effective g-factor concept previously formulated for interlayer excitons [3], to include the formation of CIEs in electrostatically doped TMD heterobilayers. We show that magnetic-field-induced Wigner crystallization and melting of CIEs, the two correlated phases that block or allow the CIE transport in the system, can be observed in strong-field magneto-photoluminescence experiments with TMD heterobilayes of systematically varied electron-hole doping concentrations. Our results advance the capabilities of the TMD bilayers as a new family of transdimensional quantum materials. – [1] L.A.Jauregui, et al., Science 366, 870 (2019); [2] I.V.Bondarev and Yu.E.Lozovik, Communications Physics (Nature) 5, 315 (2022); [3] P.Nagler, et al., Nature Communications 8, 1551 (2017).