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arXiv:0903.2347 · New Journal of Physics

Influence of non-magnetic impurities on hole-doped two-leg Cu–O Hubbard ladders

Piotr Chudziński, M. Gabay, Thierry Giamarchi

Published May 29, 2009• 4 citations
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Abstract

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.

DOI
10.1088/1367-2630/11/5/055059

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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.
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 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.
Recently, conductivity measurements were performed on the hole-doped two-leg ladder material S(r14-x)Ca(x)Cu(24)O(41). In this work, we calculate the conductivity for doped two-leg ladders using a model of hole pairs forming a strongly correlated liquid. Quantum interference effects are handled using renormalization group methods. We find that our model can account for the low-energy features of the experiments. However, at higher energies there are deviations from the predictions of this model. Using the results of our calculations as well as results on the ground state of doped two-leg ladders, we suggest a scenario to explain the experimental results.
We investigate the physical consequences of orbital current patterns (OCP) in doped two-leg Cu-O Hubbard ladders. The internal symmetry of the pattern, in the case of the ladder structure, differs slightly from that suggested so far for cuprates. We focus on this OCP and look for measurable signatures of its existence. We compute the magnetic field produced by the OCP at each lattice site and estimate its value in view of a possible experimental detection. Using a renormalization-group (RG) analysis, we determine the changes that are caused by the SU(2) spin rotational symmetry breaking which occurs when the OCP is present in the ground-state phase diagram. The most significant one is an in-plane spin-density wave gap opening in an otherwise critical phase, at intermediate dopings. We estimate the value of this gap, give an analytic expression for the correlation functions and examine some of the magnetic properties of this new phase which can be revealed in measurements. We compute the conductance in the presence of a single impurity using an RG analysis. A discussion of the various sources of SU(2) symmetry breaking underscores the specificity of the OCP-induced effects.
We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit ($t\text{\ensuremath{-}}J$ model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust, but immediately acquires algebraic transverse (i.e., along rungs) current correlations which are commensurate with the 4kF4{k}_{F}4kF​ density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio J∕tJ∕tJ∕t: we found strong anomalies at low J∕tJ∕tJ∕t only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and 1∕21∕21∕2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a 4kF4{k}_{F}4kF​ charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.