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arXiv:cond-mat/0007484 · Physical Review Letters

Conductivity of Doped Two-Leg Ladders

Eugene H. Kim

Published Feb 12, 2001• 6 citations
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Abstract

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.

DOI
10.1103/physrevlett.86.1315

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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 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 current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudogaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the ddd-wavelike pairing correlations in the hole-doped state, at least up to a doping of 10%. Thus we conclude that no phase with CC order or dominant CC fluctuations occur in the three-band model of two-leg CuO ladders at low doping.
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.
Here we report results of a density-matrix-renormalization-group calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This model allows us to study the effects of hole and electron doping on a system that is a charge-transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes and with electrons.
In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.
Using density matrix renormalization group calculations, we compare results obtained for the $t\ensuremath{-}J,$ one-band Hubbard, and three-band Hubbard models of a two-leg CuO ladder. Spin and charge gaps, pair binding energies, and effective pair hoppings are calculated for a wide range of parameters. All three models have an insulating state at a filling corresponding to one hole per Cu site. For physically relevant parameters their spin gaps are similar in size but they exhibit quite different charge gaps. We find that the binding energy of a pair of doped holes is of the order of the undoped ladder spin gap for all three models. The main difference between the models is the size of the effective pair hopping, which is significantly larger in the three-band model with parameters appropriate for CuO materials than in the other two models.