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arXiv:cond-mat/0107550 · Journal of Physics Condensed Matter

Bound states in d-density-wave phases

Carsten Honerkamp A, Manfred Sigrist

Published Nov 30, 2001• 1 citation
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Abstract

We investigate the quasiparticle spectrum near surfaces in a two-dimensional system with d-density-wave order within a mean-field theory. For Fermi surfaces with perfect nesting for the ordering wavevector (π,π) of the d-density wave, a zero-energy bound state occurs at 110 surfaces, in close analogy with the known effect in d-wave superconducting states or graphite. When the shape of the Fermi surface is changed by doping, the bound-state energy moves away from the Fermi level. Furthermore, away from half-filling we find inhomogeneous phases with domain walls of the d-density-wave order parameter. The domain walls also support low-energy bound states. These phenomena might provide an experimental test for hidden d-density-wave order in the high- T c cuprates.

DOI
10.1088/0953-8984/13/50/326

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We investigate the quasiparticle spectrum near surfaces in a two-dimensional system with d-density-wave order within a mean-field theory. For Fermi surfaces with perfect nesting for the ordering wavevector (π,π) of the d-density wave, a zero-energy bound state occurs at 110 surfaces, in close analogy with the known effect in d-wave superconducting states or graphite. When the shape of the Fermi surface is changed by doping, the bound-state energy moves away from the Fermi level. Furthermore, away from half-filling we find inhomogeneous phases with domain walls of the d-density-wave order parameter. The domain walls also support low-energy bound states. These phenomena might provide an experimental test for hidden d-density-wave order in the high- T c cuprates.
We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi-1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain mean-field theory. The resulting critical temperatures of the SC phases generically exhibit a power-law scaling with the coupling constants of the array, instead of the essential singularity found in weak-coupling BCS-type theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles.
The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.
Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here, we focus on variational approaches, but comparisons with both quantum cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the quantum cluster method. An interesting trend is found by comparing gap parameters Δ (antiferromagnetic or superconducting) obtained with different variational wave functions. Δ varies by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.
We examine the quasiparticle lifetime and spectral weight near the Fermi surface in the two-dimensional Hubbard model. We use the FLEX approximation to self-consistently generate the Matsubara Green's functions and then we analytically continue to the real axis to obtain the quasiparticle spectral functions. We compare the spectral functions found in the nearest neighbor hopping only Hubbard model with those found when second neighbor hopping is included. This separates the effects of nesting, the Van Hove singularity and the short-ranged antiferromagnetic correlations. The quasiparticle scattering rate is enhanced along the (0,pi) to (pi,pi) Brillouin zone diagonal. When the density is close to half-filling these 'hot-spots' lie on the Fermi surface and the scattering rate increases with decreasing temperature. For the next-nearest neighbor hopping scenario we observe a large range of doping where there is no antiferromagnetism but the scattering rate has a linear temperature dependence. On decreasing the interaction this non-Fermi liquid behavior is confined to doping levels where the Fermi energy lies near to the Van Hove singularity. We conclude that the 'hot-spots' are associated with the antiferromagnetic phase transition while the linear temperature dependence of the scattering rate is associated with the Van Hove singularity.
We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional ddd-wave superconductors using an exact real-space method, incorporating realistic details known about the cuprates. Random on-site energy and pointlike unitary impurity models are found to give rise to a vanishing DOS at the Fermi energy for narrow distributions and low concentrations, respectively, and lead to a finite, but suppressed, DOS at unrealistically large levels of disorder. Smooth disorder arising from impurities located away from the copper-oxide planes meanwhile gives rise to a finite DOS at realistic impurity concentrations. For the case of smooth disorder whose average potential is zero, a resonance is found at zero energy for the quasiparticle DOS at large impurity concentrations. We discuss the implications of these results on the computed low-temperature specific heat, the behavior of which we find is strongly affected by the amount of disorder present in the system. We also compute the localization length as a function of disorder strength for various types of disorder and find that intermediate- and high-energy states are quasiextended for low disorder, and that states near the Fermi energy are strongly localized and have a localization length that exhibits an unusual dependence on the amount of disorder. We comment on the origin of disorder in the cuprates and provide constraints on these based on known results from scanning tunneling spectroscopy and specific heat experiments.
We examine the effects of a van Hove singularity (vHs) in the density of states (DOS) of a two dimensional, t−t′−Ut-t'-Ut−t′−U Hubbard model within the local approximation. Within our approximation the non-interacting Fermi surface is always retained away from half-filling; and we find that the vHs in the DOS survives, and for hole doping is nearly "pinned" to the Fermi level due to the enhancement of the effective mass, m∗m^*m∗. We discuss the electron-hole asymmetry of this phenomena and its relevance to the electron and hole doped cuprates. At optimal (hole) doping, with the Fermi level at the vHs, we find that the single particle damping rate ΓΓΓ, and the resistivity ρdcρ_{dc}ρdc​, scale as TTT for moderately low temperatures (T≳100T \gtrsim 100T≳100K), while for the electron doped system ΓΓΓ and ρdc∼T2ρ_{dc} \sim T^2ρdc​∼T2.