Exciton insulator in a moiré lattice

Interlayer electron and hole can be paired up through coulomb interaction to form an exciton insulator when their kinetic energy is substantially smaller than the interaction energy. The traditional platform to realize such an interlayer interaction is the double quantum well with dielectric material between electron and hole, for which an external magnetic field is required to generate Landau level flat bands that can reduce the kinetic energy of charged carriers. When both quantum wells are at the half filling of the lowest landau level, the electron-electron repulsive interaction, by the particle-hole transformation in one well, will be equivalent to electron-hole attractive interaction, from which interlayer exciton and its condensation can emerge. In a two-dimensional twisted homostructure or an angle aligned heterostructure, there exists a moiré superlattice, in which bands are folded into the mini-Brillouin zone by the large moiré period. Gap opening at the boundary of mini-Brillouin zone can form the well-known moiré flat band. This review will discuss how to use the moiré flat bands to generate exciton insulator in the absence of external magnetic field in transitional metal dichalcogenide (TMD) moiré heterostructure. Unlike the double quantum well where symmetric well geometry is used, the moiré related sample can have multiple different geometries, including monolayer TMD-hexagonal boron nitride-moiré structure, moiré-moiré structure, and monolayer TMD-bilayer TMD structure. The carriers in those structures can be well tuned to locate equally in different layers, and particle-hole transformation in the moiré first Hubbard band can transform the interlayer repulsive coulomb interaction into attractive interaction, which is the same as that in quantum well under magnetic field. We will show that by using differential contrast reflection spectrum, interlayer photoluminescence, 2s exciton sensing, quantum capacitance and microwave impedance microscopy, the signature of exciton fluid can be identified. The excitonic coherence features in those structures will promise by using the coulomb drag technique and counter flow technique in future. In general, exciton in moiré lattice is a promising candidate for studying the Bose-Hubbard model in solids and can well realize exciton superfluidity, excitonic mott insulator as well as the crossover between them.