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.
The optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of a doped two-leg $t\ensuremath{-}J$ ladder is calculated for an electric field polarized parallel to the legs of the ladder. The low- and high-electron-density regimes behave differently, exhibiting Tomonaga-Luttinger-like and Luther-Emery-like behavior, respectively. We concentrate on the hole-doped region where the conductivity has a Drude weight proportional to the hole doping and an apparent threshold for absorption (a pseudogap) which may be associated with the energy to break a pair. This pseudogap in $\ensuremath{\sigma}(\ensuremath{\omega})$ is present even though the pairs have a modified ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like wave function because the geometry of the ladder leads to quasiparticle states which probe the gap along an antinode.
The optical conductivity of the one-band Hubbard model is calculated using the ``dynamical cluster approximation'' implementation of dynamical mean-field theory for parameters appropriate to high-temperature copper-oxide superconductors. The calculation includes vertex corrections and the result demonstrates their importance. At densities of one electron per site, an insulating state is found with gap value and above-gap absorption consistent with measurements. As carriers are added the above-gap conductivity rapidly weakens and a three component structure emerges, with a low-frequency ``Drude'' peak, a mid-infrared absorption, and a remnant of the insulating gap. The mid-infrared feature obtained at intermediate dopings is shown to arise from a pseudogap structure in the density of states. On further doping the conductivity evolves to the Drude peak plus weakly frequency dependent tail structure expected for less strongly correlated metals.
On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard model. For reasonable parameter sets appropriate for the cuprate superconductors, the single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2\ifmmode\times\else\texttimes\fi{}2 unit-cell system. The optical results, which are the first quantitative calculations performed for realistic parameters of the three-band Hubbard model, clearly show three allowed optical transitions: (i) itinerant motion of the Cu-O singlets, having (for doping concentrations x\ensuremath{\ne}0) a spectral Drude distribution around \ensuremath{\omega}=0 with spectral weight proportional to x; (ii) unbinding of the O hole from the Cu spin in the singlet. This gives, in particular, a strong absorption peak due to singlet\ensuremath{\rightarrow}nonbonding oxygen transitions, again with relative weight \ensuremath{\sim}x.It is roughly centered at \ensuremath{\omega}\ensuremath{\sim}
JKondo, where
JKondo is the Kondo coupling and \ensuremath{\Delta} the bare Cu-O charge-transfer energy. It is this singlet unbinding that results in the by far dominant absorption structure between Drude and higher-energy Cu-O transitions and not the often discussed ``mid-infrared'' absorption due to transitions between different singlet states. (iii) Cu-O charge-transfer processes at energy \ensuremath{\sim}\ensuremath{\Delta}+
Upd. They show a pronounced excitonic effect due to the p-d interaction
Upd and have a reduced spectral weight shifted to higher energies for increased dopings. Findings (i)--(iii) are in general accordance with recent experimental data. Our study of the low-energy absorption is complemented with a numerical scaling analysis of the Drude weight in 1D, where, in particular, we find an interesting violation of Lenz's law for 4n-site Hubbard rings. Finally, the magnetic structure factor is calculated for the 2D case. For finite doping it contains a peak at 2
JKondo, which should be detectable in experiment.
In the framework of this thesis the infrared spectra of two-leg spin ladders were measured. This study presents the first determination of the magnetic contribution to the optical conductivity of spin ladders. A comparison between experiment and new theoretical calculations provided a comprehensive understanding of the magnetic spectrum of the undoped telephone-number compounds La(y)Ca(14-y)Cu(24)O(41). To be able to study the weak magnetic contribution to the spectra, it was necessary to measure not only the reflectance but in particular the transmittance of thin single crystals. When both quantities are known, one can directly calculate the optical conductivity. The low-temperature spectra were compared with results of three different theoretical approaches in close collaboration with the theory groups of Uhrig et al. from the University of Cologne and of Kopp et al. from the University of Augsburg. The excellent agreement between theory and experiment allowed us to identify the two sharp peaks in the mid-infrared range unambiguously as the signature of a true bound state of two triplets. The occurrence of bound states in spin ladders had been predicted already by several groups, but we provided the first experimental verification. Further spectral weight at higher frequencies was attributed to the multi-triplet continuum. The exchange couplings were derived, and the importance of the four-spin cyclic exchange was demonstrated. With increasing temperature especially the line shape for polarization along the legs changes considerably. The spectral weight of the continuum strongly grows, whereas the bound-state peaks lose weight. The resemblance between the measured room-temperature data of the S=1/2 ladder and theoretical results for the S=1 Haldane chain was discussed. The corresponding calculations were performed by Nunner et al. in Augsburg. Another main part of this thesis was to examine the influence of doping on the infrared spectra. We observed the same bound-state features in Sr(14)Cu(24)O(41) as in the undoped compounds, but we found additional structure in the spectra. Several scenarios were discussed in order to explain the new features, including the modulation of the exchange coupling along the legs due to the incommensurate structure and due to the charge order in the chains.
In the nested limit of the spin-fermion model for the cuprates, one-dimensional physics in the form of half-filled two-leg ladders emerges. We show that the renormalization group flow of the corresponding ladder is towards the
d-Mott phase, a gapped spin-liquid with short-ranged
d-wave pairing correlations, and reveals an intermediate $\mathrm{SO}(5)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)$ symmetry. We use the results of the renormalization group in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hot spot region dominate the transport. We argue that umklapp processes play a major role. For finite temperatures, we determine the resistivity in the zero-frequency (dc) limit. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a nonuniversal power law. A comparison to experimental data supports our assumption that the conductivity is dominated by the antinodal contribution above the pseudogap.
The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped
high-Tc cuprate superconductors is studied using exact diagonalization of effective $t\ensuremath{-}J\text{-like}$ Hamiltonians describing low energy electronic excitations of the
CuO2 plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu
3d, Ni
3d, and O
2p orbitals. Our main findings are: (i) The width ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ of the pseudogap occurring in the many body density of states, and manifesting itself also in the
c-axis infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is---for realistic values of the model parameters---weakly bound to the Ni site. This causes a slight increase of ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ with respect to the pure case. (iii) Based on this result and further results for 1--2 holes and 1--2 Ni impurities, we suggest that in the real Ni substituted
CuO2 plane ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the
c-axis infrared conductivity data of Zn and Ni substituted (Sm,Nd)${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystals.