Optical symmetries and anisotropic transport in high-Tc superconductors

A simple symmetry analysis of in-plane and out-of-plane transport in a family of high temperature superconductors is presented. It is shown that generalized scaling relations exist between the low frequency electronic Raman response and the low frequency in-plane and out-of-plane conductivities in both the normal and superconducting states of the cuprates. Specifically, for both the normal and superconducting state, the temperature dependence of the low frequency $B_{1g}$ Raman slope scales with the $c-$axis conductivity, while the $B_{2g}$ Raman slope scales with the in-plane conductivity. Comparison with experiments in the normal state of Bi-2212 and Y-123 imply that the nodal transport is largely doping independent and metallic, while transport near the BZ axes is governed by a quantum critical point near doping $p\sim 0.22$ holes per CuO$_{2}$ plaquette. Important differences for La-214 are discussed. It is also shown that the $c-$ axis conductivity rise for $T\ll T_{c}$ is a consequence of partial conservation of in-plane momentum for out-of-plane transport.Comment: 16 pages, 8 Figures (3 pages added, new discussion on pseudogap and charge ordering in La214

Interlayer tunneling spectroscopy of layered CDW materials

We have measured intrinsic tunneling spectra of charge density wave (CDW) materials NbSe$_3$ and o-TaS$_3$ in sub-micron scale mesa structures. Beyond the interband tunneling across the CDW gap, $2\Delta$, we observe intragap states at the voltage $V\approx 2\Delta/3$ which we associate with creation of the amplitude soliton. The onset of the tunneling occurs only above a threshold voltage $V_t\approx 0.1\Delta$ followed by a quasi-periodic staircase spectrum. We interpret that behavior as the CDW phase decoupling between neighboring layers via the formation of a grid of dislocation lines. In NbSe$_3$, the application of a high magnetic field (up to 27 T) yields a strong suppression of the tunneling density of states within the CDW gap indicating a possible field induced metal-insulator transition