Electromagnetic response of static and fluctuating stripes in cuprate superconductors

dc Resistivity of Quantum Critical, Charge Density Wave States from Gauge-Gravity Duality

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high T_{c} superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

Optical studies of high-temperature superconducting cuprates

The optical studies of high-temperature superconducting cuprates (HTSC) are reviewed. From the doping dependence of room temperature spectra, a dramatic change of the electronic state from a Mott (charge transfer) insulator to a Fermi liquid has been revealed. Additionally, the unusual 2D nature of the electronic state has been found. The temperature dependence of the optical spectra provided a rich source of information on the pseudogap, superconducting gap, Josephson plasmon, transverse Josephson plasma mode and precursory superconductivity. Among these issues, Josephson plasmons and transverse Josephson plasma mode were experimentally discovered by optical measurements, and thus are unique to HTSC. The effect of the spin/charge stripe order is also unique to HTSC, reflecting the conducting nature of the stripe order in this system. The pair-breaking due to the stripe order seems stronger in the out-of-plane direction than in the in-plane one.

Observation of momentum-resolved charge fluctuations proximate to the charge-order phase using resonant inelastic x-ray scattering

In strongly correlated electron systems, enhanced fluctuations in the proximity of the ordered states of electronic degrees of freedom often induce anomalous electronic properties such as unconventional superconductivity. While spin fluctuations in the energy-momentum space have been studied widely using inelastic neutron scattering, other degrees of freedom, i.e., charge and orbital, have hardly been explored thus far. Here, we use resonant inelastic x-ray scattering to observe charge fluctuations proximate to the charge-order phase in transition metal oxides. In the two-leg ladder of Sr_14−xCa_xCu₂₄O₄₁, charge fluctuations are enhanced at the propagation vector of the charge order (q_CO) when the order is melted by raising temperature or by doping holes. In contrast, charge fluctuations are observed not only at q_CO but also at other momenta in a geometrically frustrated triangular bilayer lattice of LuFe₂O₄. The observed charge fluctuations have a high energy (~1 eV), suggesting that the Coulomb repulsion between electrons plays an important role in the formation of the charge order.

Implications of charge ordering in high Tc cuprate superconductors in far-infrared spectroscopy

We addressed the issue of the absence of far-infrared signatures pertaining to charge ordering in the published far-infrared reflectivity data of La2-xSrxCuO4 single crystals while other experimental probes reveal that charge ordering is a hallmark of superconducting cuprates. Through direct comparison of the far-infrared data reported by various groups side by side and also with the Raman scattering data, we found that the inconsistencies stem from the failure in capturing delicate spectral features embedded in the close-to-perfect ab-plane far-infrared reflectivity of La2-xSrxCuO4 single crystals by misidentifying the reflectivity as the Drude-like metallic reflectivity. The analysis of the close-to-true reflectivity data reveals that only a small fraction (<3%) of the total doping-induced charge carriers (electrons) are itinerant on the electron lattice made up with the rest of the electrons (>97%) at all doping levels up to 16%. We conclude that the far-infrared reflectivity study is far from being ready to construct a coherent picture of the ubiquitous charge ordering phenomenon and its relationship with the high Tc superconductivity.

Simulation of a hump structure in the optical scattering rate within a generalized Allen formalism and its application to copper oxide systems

We propose a possible way to simulate a hump structure in the optical scattering rate. The optical scattering rate of correlated charge carriers can be defined within an extended Drude model formalism. When some electron- and hole-doped copper oxide systems are in spin density or charge density wave phases they show hump structures in their optical scattering rates. The hump structures have not yet been simulated or clearly understood. We are able to simulate the hump structure by using a peak followed by a dip feature in the normalized density of states within a generalized Allen formalism. We observe that reversing the order of the dip and peak gives completely different features in the optical scattering rate; a peak-dip (dip-peak) results in a hump (a valley) in the scattering rate. We also obtain the real parts of the optical conductivity and reflectance spectra from the simulated optical scattering rate and compare them with published experimental spectra. From these comparisons we conclude that the peak-dip order can give the hump structure that is observed experimentally in copper oxide systems. Finally we fit two published optical spectra with our new model and discuss our results and the possible origin of the dip or peak features in the normalized density of states.

Bandwidth tuning triggers interplay of charge order and superconductivity in two-dimensional organic materials

We observe charge-order fluctuations in the quasi-two-dimensional organic superconductor β''-(BEDT-TTF)2SF5CH2CF2SO3, both by means of vibrational spectroscopy, locally probing the fluctuating charge order, and by investigating the in-plane dynamical response by infrared reflectance spectroscopy. The decrease of the effective electronic interaction in an isostructural metal suppresses both charge-order fluctuations and superconductivity, pointing to their interplay. We compare the results of our experiments with calculations on the extended Hubbard model.

Spectral and optical properties in the antiphase stripe phase of the cuprate superconductors

We investigate the superconducting order parameter, the spectral and optical properties in a stripe model with spin-(charge-) domain-derived scattering potential V(s) (V(c)). We show that the charge-domain-derived scattering is less effective than the spin scattering on the suppression of superconductivity. For [Formula: see text], the spectral weight concentrates on the (π,0) antinodal region and a finite energy peak appears in the optical conductivity with the disappearance of the Drude peak. But for V(s)≈V(c), the spectral weight concentrates on the (π/2,π/2) nodal region and a residual Drude peak exists in the optical conductivity without the finite energy peak. These results consistently account for the divergent observations in the ARPES and optical conductivity experiments in several high- T(c) cuprates and suggest that the 'insulating' and 'metallic' properties are intrinsic to the stripe state, depending on the relative strength of the spin- and charge-domain-derived scattering potentials.

Probing the superconducting energy gap from infrared spectroscopy on a Ba0.6K0.4Fe2As2 single crystal with Tc=37 K

We performed optical spectroscopy measurement on a superconducting Ba0.6K0.4Fe2As2 single crystal with T{c}=37 K. Formation of the superconducting energy gaps in the far-infrared reflectance spectra below T{c} is clearly observed. A flat and close to unity reflectance is observed roughly below 150 cm;{-1} for T<<T{c}, following an s-wave pairing line shape. A more rapid decrease occurs near 200 cm;{-1}, leading to a peak in the ratio of the reflectance at T<<T{c} over that for T>or=T{c}. We determined the absolute value of the penetration depth at 10 K as lambda approximately 2000+/-80 A. A spectral weight analysis shows that the Ferrell-Glover-Tinkham sum rule is satisfied at low energy scale, less than 6Delta.

Charge order, metallic behavior, and superconductivity in La2-xBaxCuO4 with x=1/8

The ab-plane optical properties of a cleaved single crystal of La2-xBaxCuO4 for x=1/8 (Tc approximately =2.4 K) have been measured over a wide frequency and temperature range. The low-frequency conductivity is Drude-like and shows a metallic response with decreasing temperature. However, below approximately =60 K, corresponding to the onset of charge-stripe order, there is a rapid loss of spectral weight below about 40 meV. The behavior is quite different from that typically associated with the pseudogap in the normal state of the cuprates. Instead, the gapping of the normal-state single-particle excitations looks surprisingly similar to that observed in superconducting La2-xSrxCuO4, including the presence of a residual Drude peak with reduced weight.

Charge-fluctuation contribution to the Raman response in superconducting cuprates

We calculate the Raman response contribution due to soft collective modes, finding a strong dependence on the photon polarizations and on the characteristic wave vectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, La2-xSrxCuO4 and (Y1.97Ca0.3)Ba2CuO6.05, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks can naturally arise from charge collective excitations at finite wavelength.

Dynamical properties of charged stripes in La2-xSrxCuO4

Inelastic light-scattering spectra of underdoped La2-xSrxCuO4 single crystals are presented which provide direct evidence of the formation of quasi-one-dimensional charged structures in the two-dimensional CuO2 planes. The stripes manifest themselves in a Drude-like peak at low energies and temperatures. The selection rules allow us to determine the orientation to be along the diagonals at x=0.02 and along the principal axes at x=0.10. The electron-lattice interaction determines the correlation length which turns out to be larger in compound classes with lower superconducting transition temperatures. Temperature is the only scale of the response at different doping levels demonstrating the importance of quantum critical behavior.

Josephson plasmon and inhomogeneous superconducting state in La2-xSrxCuO4

We report on the interlayer far infrared response for a series of La2-xSrxCuO4 crystals with 0.08<x<0.20 focusing on the survey of the Josephson plasmon resonance (JPR). The analysis of the JPR mode provides information on the local variation of the superfluid density within the CuO2 planes thus empowering one with a tool for "microscopy" on the superconducting condensate. Our results uncover the presence of regions with characteristic length of approximately 100-200 A within which superconductivity is strongly depressed or completely depleted. An examination of the doping trends suggests that development of superconducting inhomogeneities is triggered by the formation of the unidirectional spin density wave state in La2-xSrxCuO4 at x=1/8.

Anisotropic electromagnetic response of lightly doped La2-xSrxCuO4 within the CuO2 planes

Using infrared spectroscopy, we show that spin self-organization in untwinned La2-xSrxCuO4 (LSCO) crystals has profound consequences for the dynamical conductivity sigma(omega). The electronic response of CuO2 planes acquires significant anisotropy in the spin ordered state with enhancement of the conductivity along the direction of the diagonal spin stripes by up to a factor of 2. An examination of the anisotropic response indicates that the diagonal spin texture in weakly doped LSCO is also accompanied by the modulation of charge density. The electronic response of the charge stripes is found to be gapless consistent with the hypothesis of the metallic ground state. Our experiments directly show that the striped ordered systems reveal new degrees of freedom not present in ordinary one-dimensional conductors.

Phase diagram of La2-xSrxCuO4 probed in the infared: imprints of charge stripe excitations

While there is increasing evidence for antiferromagnetic (AF) ordering in the Cu-O planes of high-T(c) superconductors, either static or fluctuating, there is no direct evidence so far for the charge stripes that should separate the AF domains. By investigating the optical response of La2-xSrxCuO4 for 0<or=x<or=0.26 and 30<or=T<or=295 K, we identify strong far infrared peaks whose energy, width, and intensity are consistent with a scenario of charge stripe dynamics in the Cu-O planes.