Origin of anomalous low-temperature downturns in the thermal conductivity of cuprates

We show that the anomalous decrease in the thermal conductivity of cuprates below $300\mathrm{mK}$, as has been observed recently in several cuprate materials including ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{7-\delta }$ in the field-induced normal state, is due to the thermal decoupling of phonons and electrons in the sample. Upon lowering the temperature, the phonon-electron heat transfer rate decreases and, as a result, a heat current bottleneck develops between the phonons, which can in some cases be primarily responsible for heating the sample, and the electrons. The contribution that the electrons make to the total low-$T$ heat current is thus limited by the phonon-electron heat transfer rate, and falls rapidly with decreasing temperature, resulting in the apparent low-$T$ downturn of the thermal conductivity. We obtain the temperature and magnetic field dependence of the low-$T$ thermal conductivity in the presence of phonon-electron thermal decoupling and find good agreement with the data in both the normal and superconducting states.

Figure 1

A simple picture of the experimental configuration for thermal conductivity measurements. The thermal resistance to phonon and electron heat currents that occurs before the current enters the sample are represented by $R_{\mathit{ph}\left(c\right)}$ and $R_{\mathit{el}\left(c\right)}$, respectively. The thermal resistance to phonon and electron heat flow through the sample are represented by $R_{\mathit{ph}}$ and $R_{\mathit{el}}$, respectively. The electron-phonon heat transfer rate is associated with $R_{\mathit{el}\text{−}\mathit{ph}}$. Temperatures at different positions have been labeled.

Figure 2

The electronic thermal conductivity ${\kappa }_{el}∕T$ measured (Ref. 1) for normal state ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{7-\delta }$ is plotted versus $T$ along with the result of Eq. (5).

Figure 3

${\kappa }_{el}∕T$, normalized to its high-$T$ value, determined by Eq. (5) is plotted versus $T$ for various values of the “contact” resistance $r$.

Figure 4

The electronic thermal conductivity ${\kappa }_{el}∕T$ versus $T$ measured (Ref. 5) for ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ in the superconducting state in zero field and in a field of $13\mathrm{T}$ applied perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes along with the results of Eq. (5).

Figure 5

Main panel: ${\kappa }_{el}∕T$, normalized to its high-$T$ zero-field value, versus $T$ in varying magnetic fields as given by Eq. (15). From the bottom, the curves are for fields of 0, 0.05, 0.1, and 0.2 $H_{C2}$ applied perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes. Inset: The same quantity plotted versus $H$ at various temperatures. From the bottom, the curves are for temperatures of 0.1, 1, and 10 $T_D$.