From nodal liquid to nodal charge gap in a frustrated Hubbard model

We investigate the physics of frustrated three-leg Hubbard ladders in the band limit when hopping across the ladder’s rungs (t_⊥) is of the same order as hopping along them (t) and much greater than the onsite Coulomb repulsion (U). We show that this model exhibits a striking electron-hole asymmetry close to half filling: the hole-doped system at low temperatures develops a resonating valence bond (RVB)-like d-wave gap [pseudogap close to (π,0)] coinciding with gapless nodal excitations (nodal liquid); in contrast, the electron-doped system is seen to develop a Mott gap at the nodes, whilst retaining a metallic character of its majority Fermi surface. At lower temperatures in the electron-doped case, d-wave superconducting correlations—here, coexisting with gapped nodal excitations—are already seen to arise. Upon further doping the hole-doped case, the RVB-like state yields to d-wave superconductivity. Such physics is reminiscent of that exhibited by the high- temperature cuprate superconductors, notably electron-hole asymmetry as noted by angle-resolved photoemission spectroscopy and the resistivity exponents observed. This toy model also reinforces the importance of a more thorough experimental investigation of the known three-leg ladder cuprate systems, and may have some bearing on low-dimensional organic superconductors.