Crossed Luttinger liquid hidden in a quasi-two-dimensional material

Although the concept of Luttinger liquid (LL) that describes a one-dimensional (1D) interacting fermion system collapses in higher dimensions, it has been proposed to be closely related to many mysteries including the normal state of cuprate superconductor, unconventional metal, and quantum criticality. Therefore, the generalization of LL model to higher dimensions has attracted substantial research attention. Here we systematically investigate the electronic structure of a quasi-2D compound {\eta}-Mo4O11 using high-resolution angle-resolved photoemission spectroscopy and ab-initio calculation. Remarkably, we reveal a prototypical LL behavior originating from the crossing quasi-1D chain arrays hidden in the quasi-2D crystal structure. Our results suggest that {\eta}-Mo4O11 materializes the long sought-after crossed LL phase, where the orthogonal orbital components significantly reduce the coupling between intersecting quasi-1D chains and therefore maintain the essential properties of LL. Our finding not only presents a realization of 2D LL, but also provides a new angle to understand non-Fermi liquid behaviors in other 2D and 3D quantum materials.