In the weak-coupling limit, we investigate two-leg ladders with a unit cell containing both Cu and O atoms as a function of doping. For purely repulsive interactions, using bosonization, we find significant differences with the single-orbital case: a completely massless quantum critical regime is obtained for a finite range of carrier concentration. In a broad region of the phase diagram, the ground state consists of a pattern of orbital currents plus a density wave. NMR properties of the Cu and O nuclei are presented for the various phases.
We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and the O
px and
py orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.
We study the influence of non-magnetic impurities on the phase diagram of doped two-leg Hubbard Cu–O ladders. In the absence of impurities, this system possesses d-wave superconducting states and orbital current states depending on the doping. A single, strong, scatterer modifies its environment locally and this effect is assessed using a renormalization group (RG) analysis. At high doping, disorder causes intraband instabilities and at low doping it promotes interband instabilities. In the former case, we extend the boundary conformal field theory method—developed in the context of single chains—to handle the ladder problem, and we find exact closed-form analytical expressions for the correlation functions. This allows us to compute experimentally measurable local quantities such as the nuclear magnetic resonance line broadenings and scanning tunneling microscope profiles. We also discuss the low-doping regime where the Kondo physics is at play, making qualitative predictions about its nature. Insight into collective effects is also given in the many weak impurities case, based on an RG approach. In this regime, one sees the interplay between interactions and disorder. We emphasize the influence of the O atoms on disorder effects both for the single- and for the many-defect situations.
We study the influence of non-magnetic impurities on the phase diagram of doped two-leg Hubbard Cu–O ladders. In the absence of impurities, this system possesses d-wave superconducting states and orbital current states depending on the doping. A single, strong, scatterer modifies its environment locally and this effect is assessed using a renormalization group (RG) analysis. At high doping, disorder causes intraband instabilities and at low doping it promotes interband instabilities. In the former case, we extend the boundary conformal field theory method—developed in the context of single chains—to handle the ladder problem, and we find exact closed-form analytical expressions for the correlation functions. This allows us to compute experimentally measurable local quantities such as the nuclear magnetic resonance line broadenings and scanning tunneling microscope profiles. We also discuss the low-doping regime where the Kondo physics is at play, making qualitative predictions about its nature. Insight into collective effects is also given in the many weak impurities case, based on an RG approach. In this regime, one sees the interplay between interactions and disorder. We emphasize the influence of the O atoms on disorder effects both for the single- and for the many-defect situations.
The two-leg $t\ensuremath{-}J$ ladder forms a spin liquid at half filling that evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e., rungs and legs equal) as a function of electron density n and the ratio
J/t. Two known limiting cases are
n<21, which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for
1>n>21. We find evidences for gapless behavior in both spin and charge channels for
J/t<0.3, consistent with Luttinger liquids in both bonding and antibonding bands (i.e.,
C2S2). This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger
J/t shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For
J/t<0.3 this is very weak, indicating a lack of pairing between these channels.
The relevance of the single-band two-dimensional Hubbard model to superconductivity in the doped cuprates has recently been questioned, based on density matrix renormalization group (DMRG) computations that found superconductivity over an unrealistically broad doping region upon electron-doping, yet a complete absence of superconductivity for hole-doping. We report very similar results from DMRG calculations on a
Cu2O3 two-leg ladder within the parent three-band correlated-electron Hamiltonian. The strong asymmetry found in our calculations are in contradiction to the deep and profound symmetry in the experimental phase diagrams of electron- and hole-doped cuprate superconductors, as seen from the occurrence of quantum critical points within the superconducting domes in both cases that are characterized by Fermi surface reconstruction, large jumps in carrier density, and strange metal behavior.