Frequency and magnetic-field dependence of the dielectric constant and conductivity of La sub 2 CuO sub 4+ y

Detailed measurements are reported of the conductivity and dielectric constant at frequencies up to 20 MHz for single crystals of La{sub 2}CuO{sub 4+{ital y}}, with {ital y} varied in the range 0.001--0.01. The hole concentration is determined for each {ital y} by Hall measurements. The conductivity shows a power-law dependence on frequency ({omega}{sup {ital s}}), which is typical of thermally assisted tunneling between localized states. The exponent {ital s}{lt}1 decreases with increasing temperature and increasing oxygen content. The dielectric constant decreases with increasing frequency at low frequency with the power law {omega}{sup {ital s}{minus}1}, showing that it is dominated by the same hopping mechanism. At high frequency the dielectric constant saturates and, for the electric field parallel to the CuO{sub 2} layers, the saturation value increases with oxygen content. From the polarizability at low acceptor concentration the radius of the bound hole is found to be {similar to}8 A, a value that is consistent with a simple hydrogenic model of the impurity state. The small binding energy of the hole to the impurity, 35 meV as determined from Hall measurements, together with this radius of 8 A, requires that the mass of the hole be fairly small, {similar to}2{ital m}{submore » {ital e}}. The growth of the localization length with hole density is almost purely two dimensional, implying that there is no true insulator-to-metal transition, but rather a crossover from strong to weak localization. From studies of the magnetic-field dependence of the frequency-dependent conductivity and dielectric constant one finds new evidence for the strong coupling of the excess holes to the antiferromagnetically ordered Cu spins.« less