Kondo-hole conduction in the La-doped Kondo insulator ${\mathrm{Ce}}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$

The resistivity, Hall constant, specific heat, and magnetic susceptibility of the doped Kondo insulator ${\left({\mathrm{Ce}}_{1-x}{\mathrm{La}}_x\right)}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$ are studied as a function of temperature and $x$. Already at $x=0.006$, the alloy behaves like a metal, so that the metal-insulator transition in the impurity band must occur at a lower concentration. Our data allow to determine the effective mass $m^{*}$ and the carrier concentration $n$ separately. After a strong initial increase of $n\left(x\right)$, the carrier concentration remains nearly constant between $x=0.1$ and 0.5. The effective mass in the metallic state initially increases with $x$ and reaches a maximum of $m^{*}\approx 100m_0$ at $x=0.3$. The scattering time $\tau$ as determined from the Drude formula decreases drastically between $x=0.006$ and 0.1, has a minimum at about $x=0.1$, and then a maximum at $x=0.3$. Surprisingly, $m^{*}∕\tau$ is nearly constant for the entire alloy range for $x⩾0.1$.

Figure 1

(Color online) The resistivity $\rho$ for ${\left({\mathrm{Ce}}_{1-x}{\mathrm{La}}_x\right)}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$ as a function of $T$ normalized to its value at room-temperature ${\rho }_{300}$ for various La concentrations. Note that in the upper panel, the scale of $\rho$ is logarithmic, while in the lower panel, this scale is linear.

Figure 2

(Color online) Logarithm of the normalized resistivity $\rho ∕\rho \left(300\mathrm{K}\right)$ as a function of $T^{-1}$ for various La concentrations $x$. The slopes of the curves correspond to the activation energy. The corresponding values of $T$ are indicated on the upper horizontal axis.

Figure 3

(Color online) Carrier density $n$ plotted logarithmically as a function of $T^{-1}$, determined from the Hall constant measured in a magnetic field of $5\mathrm{T}$ for several La concentrations $x$. The corresponding values of $T$ are indicated on the upper horizontal axis.

Figure 4

Comparison of properties of ${\left({\mathrm{Ce}}_{1-x}{\mathrm{La}}_x\right)}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$: (a) Conductivity $\tilde{\sigma }$ at $2.5\mathrm{K}$ normalized to the conductivity at room temperature, (b) carrier concentration $n$ extrapolated to $T\to 0$ (from Fig. 3), and (c) linear specific-heat coefficient $\gamma$, as a function of the La concentration $x$. In order to facilitate the direct comparison with $n$, $\gamma$ is given in units of $\mathrm{J}∕{\mathrm{K}}^2{\mathrm{m}}^3$. For ${\mathrm{Ce}}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$ $(x=0)$, $1000\mathrm{J}∕{\mathrm{K}}^2{\mathrm{m}}^3$ correspond to $0.459\mathrm{J}∕{\mathrm{K}}^2\mathrm{mol}$ ${\mathrm{Ce}}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$. The solid curves are a guide for the eye. Inset in (a) shows $\tilde{\sigma }$ vs $x^{1∕3}$ for $x⩽0.3$.

Figure 5

(a) Effective mass of the quasiparticles in the Kondo-hole impurity band in units of the free electron mass and (b) the Drude scattering time $\tau$ at low $T$ as a function of the La concentration $x$. See the text for the definition of these quantities. The solid curves are a guide for the eye.

Figure 6

(Color online) The magnetic dc susceptibility, ${\chi }_{dc}=M∕B$, of ${\left({\mathrm{Ce}}_{1-x}{\mathrm{La}}_x\right)}_3{\mathrm{Bi}}_4{\mathrm{Pt}}_3$ as a function of temperature for several La concentrations $x$. The data in (a) were obtained for single crystal with $x=0$, while those in (b) were obtained for polycrystalline samples for various $x$.