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Lecture notes in physics

Spin-Charge Separation and Confinement in Ladder Systems and in High-T C Superconductors

M. Yu. Kagan

Published Jan 1, 2013• 1 citation
Publisher
DOI
10.1007/978-94-007-6961-8_13

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Pseudogap in the c -axis (along the ladder) optical conductivity of t − J ladders and its quasiparticle interpretation

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Motivated by similarities between cuprate superconductors and two-leg ladder copper-oxide compounds and in order to obtain a better understanding of optical properties of cuprate superconductors we have studied the c-axis (along the ladder) optical conductivity [Formula: see text] of a doped [Formula: see text] two-leg ladder. Using exact diagonalization, we have calculated the conductivity and related quantities for cyclic ladders of up to 13 rungs. In agreement with results of an early study by Hayward and coworkers (Hayward et al 1996 Phys. Rev. B 53 8863) we find that [Formula: see text] consists of a Drude peak at zero frequency and an absorption band in the infrared region that is separated from the former by a pseudogap. The width of the pseudogap [Formula: see text] increases with increasing J/t, in parallel with an increase of the magnitude [Formula: see text] of the gap in the quasiparticle excitation spectra. Our central finding is that [Formula: see text], where [Formula: see text] is the magnitude of the gap in the spin excitation spectra. We demonstrate that this approximate relation can be understood in terms of a phenomenological model involving a superconducting ladder and a coupling between charged quasiparticles and spin excitations. The relation is remarkably similar to the one between experimental values of the energy scale of a dip in the in-plane optical conductivity, the superconducting gap [Formula: see text] and the energy of the spin-resonance in cuprate superconductors (for a recent discussion of the optical data, see Šopík et al 2015 New J. Phys. 17 053022). Our findings support the point of view that low energy infrared active excited states of cuprate superconductors can be viewed as consisting of two charged quasiparticles connected with pair-breaking and a spin excitation.

Journal of Physics Condensed Matter•Jan 9, 2019•1 citation
Fractionalization of an electronic quasiparticle into spin, charge, and orbital parts is a fundamental and characteristic property of interacting electrons in one dimension. However, real materials are never strictly one dimensional and the fractionalization phenomena are hard to observe. Here we studied the spin and orbital excitations of the anisotropic ladder material CaCu_{2}O_{3}, whose electronic structure is not one dimensional. Combining high-resolution resonant inelastic x-ray scattering experiments with theoretical model calculations, we show that (i) spin-orbital fractionalization occurs in CaCu_{2}O_{3} along the leg direction x through the xz orbital channel as in a 1D system, and (ii) no fractionalization is observed for the xy orbital, which extends in both leg and rung direction, contrary to a 1D system. We conclude that the directional character of the orbital hopping can select different degrees of dimensionality. Using additional model calculations, we show that spin-orbital separation is generally far more robust than the spin-charge separation. This is not only due to the already mentioned selection realized by the orbital hopping, but also due to the fact that spinons are faster than the orbitons.
Motivated by similarities between cuprate superconductors and two-leg ladder copper-oxide compounds and in order to obtain a better understanding of optical properties of cuprate superconductors we have studied the c-axis (along the ladder) optical conductivity [Formula: see text] of a doped [Formula: see text] two-leg ladder. Using exact diagonalization, we have calculated the conductivity and related quantities for cyclic ladders of up to 13 rungs. In agreement with results of an early study by Hayward and coworkers (Hayward et al 1996 Phys. Rev. B 53 8863) we find that [Formula: see text] consists of a Drude peak at zero frequency and an absorption band in the infrared region that is separated from the former by a pseudogap. The width of the pseudogap [Formula: see text] increases with increasing J/t, in parallel with an increase of the magnitude [Formula: see text] of the gap in the quasiparticle excitation spectra. Our central finding is that [Formula: see text], where [Formula: see text] is the magnitude of the gap in the spin excitation spectra. We demonstrate that this approximate relation can be understood in terms of a phenomenological model involving a superconducting ladder and a coupling between charged quasiparticles and spin excitations. The relation is remarkably similar to the one between experimental values of the energy scale of a dip in the in-plane optical conductivity, the superconducting gap [Formula: see text] and the energy of the spin-resonance in cuprate superconductors (for a recent discussion of the optical data, see Šopík et al 2015 New J. Phys. 17 053022). Our findings support the point of view that low energy infrared active excited states of cuprate superconductors can be viewed as consisting of two charged quasiparticles connected with pair-breaking and a spin excitation.