Extrinsic or intrinsic conduction in cuprates: Anisotropy, weak, and strong links.

Abstract

The layered structure of superconducting cuprates is the origin of the anisotropic conductivity in the normal state and the anisotropic energy gap and anisotropic critical current density ${\mathit{j}}_{\mathit{c}}$ in the superconducting state. The anisotropic, quasi-two-dimensional conduction in the ${\mathrm{CuO}}_{2}$ planes is close to the metal-insulator transition. Defects can either initiate insulating or conducting behavior depending on the position of the defects and orientation of the current. For example, defects may enhance the small conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\perp}}}$ perpendicular to the planes, whereas defects reduce the strong conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\parallel}}}$ along the planes. That is, defects make the cuprate superconductors more isotropic. Due to the layered structure defects are often organized in planes, usually of reduced conductivity, which are named ``weak links'' (WL). The effect of WL on the dc conductivity and superconductivity, especially as function of temperature and field, allows their classification and quantification. Their grain-boundary resistances ${\mathit{R}}_{\mathit{b}\mathit{n}}^{\mathrm{\ensuremath{\parallel}}}$\ensuremath{\ge}${10}^{\mathrm{\ensuremath{-}}7}$--${10}^{\mathrm{\ensuremath{-}}9}$ \ensuremath{\Omega} ${\mathrm{cm}}^{2}$ are several orders of magnitude larger than the metallic Sharvin resistance, proving that WL are insulating interruptions. They contain localized states carrying current across by resonant tunneling. Such WL deteriorate the metallic conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\parallel}}}$, the superconducting critical current ${\mathit{j}}_{\mathit{c}}^{\mathrm{\ensuremath{\parallel}}}$, and the energy gap ${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{\mathrm{\ensuremath{\parallel}}}$, but enhance the leakage current ${\mathit{j}}_{\mathit{b}\mathit{l}}^{\mathrm{\ensuremath{\parallel}}}$.Localized states between ${\mathrm{CuO}}_{2}$ double planes enhance the ``insulating'' ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{j}}_{\mathit{c}}^{\mathrm{\ensuremath{\perp}}}$ and deteriorate ${\mathrm{\ensuremath{\Delta}}}_{\mathit{s}}^{\mathrm{\ensuremath{\perp}}}$. For Y cuprates such states are due to oxygenation in the Cu chains. For Bi cuprates such states are caused by oxidation of the Bi oxide layers (overdoping). The intergranular ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{j}}_{\mathit{c}}^{\mathrm{\ensuremath{\perp}}}$ in grain-aligned material are different for Y and Bi cuprates because Y cuprate surfaces decay above 70 K whereas the Bi-O surface stays stable up to 400 K containing even localized states. So ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{j}}_{\mathit{c}}^{\mathrm{\ensuremath{\perp}}}$ are enhanced in grain-aligned Bi cuprates, which is the base of the brick-wall model. For all cuprates the ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\parallel}}}$ and ${\mathit{j}}_{\mathit{c}}^{\mathrm{\ensuremath{\parallel}}}$ degradation by WL is similar, due to the common two-dimensional nature.