Relationship between Conductivity and Phase Coherence Length in Cuprates

The large (10 2 − 10 5) and strongly temperature dependent resistive anisotropy η = (σ ab /σc) 1/2 of cuprates perhaps holds the key to understanding their normal state in-plane σ ab and out-of-plane σc conductivities. It can be shown that η is determined by the ratio of the phase coherence lengths ℓ i in the respective directions: σ ab /σc = ℓ 2 ab /ℓ 2 c. In layered crystals in which the out-of-plane transport is incoherent, ℓc is fixed, equal to the interlayer spacing. As a result, the T-dependence of η is determined by that of ℓ ab , and vice versa, the in-plane phase coherence length can be obtained directly by measuring the resistive anisotropy. We present data for hole-doped Y Ba 2 Cu 3 Oy (6.3 < y < 6.9) and Y 1−x P rxBa 2 Cu 3 O 7−δ (0 < x ≤ 0.55) and show that σ ab of crystals with different doping levels can be well described by a two parameter universal function of the in-plane phase coherence length. In the electron-doped N d 2−x CexCuO 4−y , the dependence σ ab (η) indicates a crossover from incoherent to coherent transport in the c-direction.