Charged Bosons Made of Fermions in Bilayer Semiconductors: Crystallization and Melting

Laser excited quasi-2D heterostructures of transition metal dichalcogenides (TMDCs) have been shown to allow for quite a few higher-order excitonic bound states such as trions (charged excitons), biexcitons (neutral excitonic molecules), charged biexcitons, and more [1-5]. Such a large variety of coupled electron-hole quasiparticle excitations opens the door to a variety of new laser-driven phenomena in these systems, including metal-insulator transitions, Bose-Einstein condensation (BEC), and even unconventional superconductivity [6-10]. Recently [5,10], a doubly charged excitonic complex was reported experimentally in laser excited bilayer TMDCs in accord with theory predictions—the quaternion, a tightly bound complex of a free charge carrier in the top layer coupled to a like-charge trion in the bottom layer—provided that the entire heterostructure is placed close to a metallic surface to screen the excessive repulsive interaction in the system. Because such quaternions carry two net charges and are also bosonic, their BEC would be a superfluid and so also a Schafroth superconductor [11]. We develop a theoretical framework to explain the latest experimental observations of the Zeeman effect for quaternions in perpendicular magnetostatic field [10]. Our theory is based on group theoretical analysis and spin-Hamiltonian formalism. We show that the quaternion ground state is the spin-triplet to exhibit a quadratic magnetic field shift like that known for hydrogen-like atoms. In addition to prospective laser-driven BEC and superconductivity of bosonic quaternion excitations, another fascinating possibility we discuss for quaternions is that, as they are charged bosons, they could form bosonic Wigner crystal. Such a light-induced quasiparticle crystal would be an ‘atom-like’ supersolid inside of the crystalline material. Wigner crystallization is controlled by the ratio of the Coulomb repulsion energy to the average single-particle kinetic energy of an ensemble of charge carriers [12,13]. Due to the double charge and quadruple mass as compared to electrons, this ratio is at least 10 times greater for quaternions, suggesting higher crystallization temperature ($T_c$) than $T_c\sim10$ K reported for electrons in monolayer TMDCs [14,15]. Higher $T_c$ implies higher $T$ of Wigner solid-liquid phase transition (melting), in which case one could expect high-$T$ BEC and light-induced superconductivity of quaternions as well. We show theoretically that for initial density at melting $\sim10^{11}$ cm$^{-2}$ the quaternion quasiparticle dispersion equation does indeed fulfill the Landau superfluidity criterion [16].

Acknowledgements: This research is supported by the U.S. ARO grant No. W911NF-24-1-0237.