Hall effect above ${\mathit{T}}_{\mathit{c}}$ in untwinned single-crystal ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$: Normal-state behavior and superconducting fluctuations

We present a measurement of the Hall coefficient ${\mathit{R}}_{\mathit{H}}$ for an untwinned single crystal of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$. The crystal was produced by a method that does not involve thermomechanical detwinning, and has a resistivity along the copper-oxide chains of only 29 μΩ cm at 100 K, indicating high sample quality. The in-plane resistivity and 1/${\mathit{R}}_{\mathit{H}}$ become linear in temperature as T rises significantly above ${\mathit{T}}_{\mathit{c}}$. Near ${\mathit{T}}_{\mathit{c}}$ we observe deviation from this linearity, and we interpret it as indicating thermodynamic fluctuations in a layered superconductor. Fits of this model to both the resistivity and Hall-effect data yield physically reasonable values for the fitting parameters. Evidence is obtained that the two copper-oxide planes in each unit cell are tightly coupled, acting as one superconducting layer. Surprisingly, the best fits indicate that the Hall-effect fluctuations are dominated by the Maki-Thompson process rather than the Aslamazov-Larkin process.