Test of the Wiedemann-Franz Law in an Optimally Doped Cuprate

We present a study of heat and charge transport in ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CuO}}_{6+\delta }$ focused on the size of the low-temperature linear term of the thermal conductivity at optimal-doping level. In the superconducting state, the magnitude of this term implies a $d$-wave gap with an amplitude close to what has been reported. In the normal state, recovered by the application of a magnetic field, measurement of this term and residual resistivity yields a Lorenz number $L={\kappa }_N{\rho }_0/T=1.3\pm 0.2L_0$. The departure from the value expected by the Wiedemann-Franz law is thus slightly larger than our estimated experimental resolution.

Figure 1

Renormalized Hall coefficient in a ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CuO}}_{6+\delta }$ sample compared with the values reported for La-214 [10] for two different doping levels. The inset shows the temperature dependence of resistivity.

Figure 2

(a) Subkelvin thermal conductivity in three different Bi-2201 single crystals. (b) Temperature dependence of the zero-field resistivity in the three samples. (c) A comparison between the doping dependence of ${\kappa }_0/T$ (open circles) and of $L_0/{\rho }_0$ (solid circles). Lines are to guide the eye.

Figure 3

Upper and lower panels: The effect of magnetic field on subkelvin thermal conductivity in two Bi-2201 samples with different doping levels. Solid lines represent the extrapolated low-temperature behavior and arrows show the expected WF magnitude. The insets display the resistivity data for the two samples.