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

Although the concept of the Luttinger liquid (LL) describing a one-dimensional (1D) interacting fermion system 1 , 2 collapses at higher dimensions, it has been proposed to be relevant to enigmatic problems in condensed matter physics including the normal state of cuprate superconductors 3 – 5 , unconventional metals 6 , 7 and quantum criticality 8 , 9 . Here we investigate the electronic structure of quasi-2D η-Mo 4 O 11 , a charge-density wave material, using high-resolution angle-resolved photoemission spectroscopy and ab initio calculations. We show a prototypical LL behaviour originating from the crossed quasi-1D chain arrays hidden in the quasi-2D crystal structure. Our results suggest that η-Mo 4 O 11 materializes the crossed LL phase 10 – 12 in its normal state, where the orthogonal orbital components substantially reduce the coupling between intersecting quasi-1D chains and therefore maintain the essential properties of the LL. Our finding not only presents a realization of a 2D LL, but also provides a new angle to understand non-Fermi liquid behaviour in other 2D and 3D quantum materials. The Luttinger liquid is a theoretical concept used to describe interacting fermions in a 1D system. Now it is shown that the model also describes electron physics in η-Mo 4 O 11 , a quasi-2D material in which 1D chains cross each other.