Abstract:
An improved version of SU(2) slave-boson approach is applied to study the in-plane optical conductivity of the two dimensional systems of high Tc cuprates. We investigate the role of fluctuations of both the phase and amplitude of order parameters on the (Drude) peak-dip-hump structure in the in-plane conductivity as a function of hole doping concentration and temperature. The mid-infrared(MIR) hump in the in-plane optical conductivity is shown to originate from the antiferromagnetic spin fluctuations of short range(the amplitude fluctuations of spin singlet pairing order parameters), which is consistent with our previous U(1) study. However the inclusion of both the phase and amplitude fluctuations is shown to substantially improve the qualitative feature of the optical conductivity by showing substantially reduced Drude peak widths for entire doping range. Both the shift of the hump position to lower frequency and the growth of the hump peak height with increasing hole concentration is shown to be consistent with observations.

Abstract:
The single-site dynamical mean-field approximation is used to solve a model of high-Tc cuprate superconductors which includes both d_{x^2-y^2} and d_{3z^2-r^2} orbitals on the Cu as well as the relevant oxygen states. Both T (with apical oxygen) and T' (without apical oxygen) crystal structures are considered. In both phases, inclusion of the d_{3z^2-r^2} orbital is found to broaden the range of stability of the charge transfer insulating phase. For equal charge transfer energies and interaction strengths, the T' phase is found to be less strongly correlated than the T phase. For both structures, d-d excitons are found within the charge-transfer gap. However, for all physically relevant dopings the Fermi surface is found to have only one sheet and the admixture of d_{3z^2-r^2} into ground state wave function remains negligible (<5%). Inclusion of the extra orbitals is found not to resolve the discrepancy between computed and observed conductivity in the insulating state.

Abstract:
We present a generalized Drude analysis of the in-plane optical conductivity $\sigma_{ab}$($T$,$\omega$) in cuprates taking into account the effects of in-plane anisotropy. A simple ansatz for the scattering rate $\Gamma$($T$,$\omega$), that includes anisotropy, a quadratic frequency dependence and saturation at the Mott-Ioffe-Regel limit, is able to reproduce recent normal state data on an optimally doped cuprate over a wide frequency range. We highlight the potential importance of including anisotropy in the full expression for $\sigma_{ab}$($T$,$\omega$) and challenge previous determinations of $\Gamma$($\omega$) in which anisotropy was neglected and $\Gamma$($\omega$) was indicated to be strictly linear in frequency over a wide frequency range. Possible implications of our findings for understanding thermodynamic properties and self-energy effects in high-$T_c$ cuprates will also be discussed.

Abstract:
We study AC conductivities in high-Tc cuprates, which offer us significant information to reveal the true electronic ground states. Based on the fluctuation-exchange (FLEX) approximation, current vertex corrections (CVC's) are correctly taken into account to satisfy the conservation laws. We find the significant role of the CVC's on the optical Hall conductivity in the presence of strong antiferromagnetic (AF) fluctuations. This fact leads to the failure of the relaxation time approximation (RTA). As a result, experimental highly unusual behaviors, (i) prominent frequency and temperature dependences of the optical Hall coefficient, and (ii) simple Drude form of the optical Hall andge for wide range of frequencies, are satisfactorily reproduced. In conclusion, both DC and AC transport phenomena in (slightly under-doped) high-Tc cuprates can be explained comprehensively in terms of nearly AF Fermi liquid, if one take the CVC's into account.

Abstract:
The graphite conductivity is evaluated for frequencies between 0.1 eV, the energy of the order of the electron-hole overlap, and 1.5 eV, the electron nearest hopping energy. The in-plane conductivity per single atomic sheet is close to the universal graphene conductivity $e^2/4\hbar$ and, however, contains a singularity conditioned by peculiarities of the electron dispersion. The conductivity is less in the $c-$direction by the factor of the order of 0.01 governed by electron hopping in this direction.

Abstract:
In certain materials with strong electron correlations a quantum phase transition (QPT) at zero temperature can occur, in the proximity of which a quantum critical state of matter has been anticipated. This possibility has recently attracted much attention because the response of such a state of matter is expected to follow universal patterns defined by the quantum mechanical nature of the fluctuations. Forementioned universality manifests itself through power-law behaviours of the response functions. Candidates are found both in heavy fermion systems and in the cuprate high Tc superconductors. Although there are indications for quantum criticality in the cuprate superconductors, the reality and the physical nature of such a QPT are still under debate. Here we identify a universal behaviour of the phase angle of the frequency dependent conductivity that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a QPT in the cuprates close to optimal doping, although of an unconventional kind.

Abstract:
We calculate the optical conductivity using several models for unparticle or scale-invariant matter. Within a Gaussian action for unparticles that is gauged with Wilson lines, we find that the conductivity computed from the Kubo formalism with vertex corrections yields no non-trivial deviation from the free-theory result. This result obtains because at the Gaussian level, unparticles are just a superposition of particle fields and hence any transport property must be consistent with free theory. Beyond the Gaussian approach, we adopt the continuous mass formulation of unparticles and calculate the Drude conductivity directly. We show that unparticles in this context can be tailored to yield an algebraic conductivity that scales as $\omega^{-2/3}$ with the associated phase angle between the imaginary and real parts of $\arctan\frac{\sigma_2}{\sigma_1}=60^\circ$ as is seen in the cuprates. Given the recent results\cite{Donos2014,Rangamani2015,Langley} that gravitational crystals lack a power-law optical conductivity, this constitutes the first consistent account of the $\omega^{-2/3}$ conductivity and the phase angle seen in optimally doped cuprates. Our results indicate that at each frequency in the scaling regime, excitations on all energy scales contribute. Hence, incoherence is at the heart of the power-law in the optical conductivity in strongly correlated systems such as the cuprates.

Abstract:
Applying the recently developed spin-charge gauge theory for the pseudogap phase in cuprates, we propose a self-consistent explanation of several peculiar features of the far-infrared in-plane AC conductivity, including a broad peak as a function of frequency and significant anisotropy at low temperatures, along with a similar temperature-dependent in-plane anisotropy of DC conductivity in lightly doped cuprates. The anisotropy of the metal-insulator crossover scale is considered to be responsible for these phenomena. The obtained results are in good agreement with experiments. An explicit proposal is made to further check the theory.

Abstract:
A review is given of the experimental status of the interlayer coupling energy in the cuprates. A second c-axis plasmon is identified in the double layer compound Y123 for various dopings. The anomalous transport properties along the c-direction and in the planar directions are compared to model calculations based on strongly anisotropic scattering. An excellent description of the optical data at optimal doping is obtained if an anomalously large anisotropy of the scattering rate between cold spots and hot spots is assumed. This raises questions as to the physical meaning of these parameters.

Abstract:
The doping and temperature dependent conductivity of electron-doped cuprates is analysed. The variation of kinetic energy with doping is shown to imply that the materials are approximately as strongly correlated as the hole-doped materials. The optical spectrum is fit to a quasiparticle scattering model; while the model fits the optical data well, gross inconsistencies with photoemission data are found, implying the presence of a large, strongly doping dependent Landau parameter.