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

We investigate the physics of frustrated 3-leg Hubbard ladders in the band limit, when hopping across the ladder's rungs (t$_{\perp}$) is of the same order as hopping along them (t) 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 ($\pi$,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 (ARPES) and the resistivity exponents observed. This toy model also reinforces the importance of a more thorough experimental investigation of the known 3-leg ladder cuprate systems, and may have some bearing on low dimensional organic superconductors.