Evidence for Electron-hole Crystals in a Mott Insulator

<title>Abstract</title> Strongly correlated electrons enable the realization of a plethora of quantum states of matter, such as Wigner crystallization, fractional quantum Hall effect, and high-temperature superconductivity. When correlated electrons and holes are allowed to coexist, they become intertwined and fuel the pursuit of quantum excitonic states harbouring counterflow superfluidity^1,2 and topological orders with long-range quantum entanglement^3,4. While such collective quantum states have been reported in sophisticated multi-layered heterostructures^1,2,4–8, realizing and controlling such quantum states in a single natural strongly correlated material has remained challenging due to the fast particle recombination. Here, we report the creation of imbalanced electron-hole crystals in a doped multi-orbital honeycomb Mott insulator, α-RuCl₃, through gate-tunable non-invasive van der Waals (vdW) doping from graphene. The absence of layer separation allows the immediate visualization of electron-hole crystals <italic>via</italic> scanning tunneling microscopy (STM). Real-space imaging reveals two completely different charge orderings at the lower Hubbard band (LHB) and the upper Hubbard band (UHB) energies, whose origin can be attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational symmetry breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals can be directly visualized, further corroborating their nature as correlation-driven charge crystals⁹. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped multi-orbital honeycomb Mott insulator, combined with a gate-tunable electron reservoir, opens new doors in the search for exotic correlated bosonic states within strongly correlated materials^5,8,10–12.