arXiv:0804.2779 · Physical Review B

Orbital current patterns in doped two-leg Cu-O Hubbard ladders

Piotr Chudziński, M. Gabay, Thierry Giamarchi

Published Aug 28, 2008• 32 citations

Abstract

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.

DOI: 10.1103/physrevb.78.075124

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arXiv:0804.2779 · Physical Review B

Orbital current patterns in doped two-leg Cu-O Hubbard ladders

Piotr Chudziński, M. Gabay, Thierry Giamarchi

Published Aug 28, 2008• 32 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.78.075124

Related papers

Phase diagram of hole doped two-leg Cu−O ladders

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In the weak coupling limit, we establish the phase diagram of a two-leg ladder with a unit cell containing both Cu and O atoms, as a function of doping. We use bosonization and design a specific renormalization group procedure to handle the additional degrees of freedom. Significant differences are found with the single orbital case; for purely repulsive interactions, a completely massless quantum critical region is obtained at intermediate carrier concentrations (well inside the bands) where the ground state consists of an incommensurate pattern of orbital currents plus a spin density wave structure.In the weak coupling limit, we establish the phase diagram of a two-leg ladder with a unit cell containing both Cu and O atoms, as a function of doping. We use bosonization and design a specific renormalization group procedure to handle the additional degrees of freedom. Significant differences are found with the single orbital case; for purely repulsive interactions, a completely massless quantum critical region is obtained at intermediate carrier concentrations (well inside the bands) where the ground state consists of an incommensurate pattern of orbital currents plus a spin density wave structure.

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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

{p}_{x}

and

{p}_{y}

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.

d

-wave-like superconducting

(\mathrm{SC}d)

state into density-wave states, with increasing nearest-neighbor repulsions and/or decreasing doping rate. The competition between the

\mathrm{SC}d

state and the charge-density-wave state coexisting with the

p

-density-wave state becomes noticeable on the critical point, at which the gap for magnetic excitations vanishes. Based on the Majorana-fermion description of the effective theory, we calculate the temperature dependence of the magnetic response such as the spin susceptibility and the NMR relaxation rate, which exhibit unusual properties due to two kinds of spin excitation modes. On the quantum critical point, the spin susceptibility shows paramagnetic behavior with logarithmic corrections and the NMR relaxation rate also exhibits anomalous power-law behavior. We discuss the commensurability effect due to the umklapp scattering and relevance to the two-leg ladder compounds ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$.