Fig. 2: Evolution of the local holon and spinon occupations with increasing displacement field.

The upper and lower panels show the occupations for the holons (upper panel) and spinons (lower panel) obtained from the parton mean-field computation for the Hamiltonian in Eq. 1a and b. The empty (○, ▽, △) and filled (●, ▼, ▲) symbols represent holon and spinon occupations, respectively, on the MM, XM, and MX sites. The size of the markers is set so that the area of the bounding box surrounding them is proportional to the corresponding occupations determined from the parton mean-field computations. LH MI stands for layer-hybridized Mott insulator. a For small E_z, both the holons and spinons are LH; the spinons pair leading to an electronic superconductor when the holons are condensed (see text). b With increasing E_z, the holons are localized at MM and MX sites, forming an “excitonic" Mott insulator, and thus retain their LH character (see text). The spinons are also LH and remain paired, resulting in an electronic MI with charge and spin gaps, respectively. The plots in a, b are generated for values of the electric field corresponding to the red and green  × -markers in Figs. 3 and 4, respectively. With large E_z, the spinons and holons localize on the MX sites in a layer-polarized Mott insulator; see supplementary material Sec. II.