Direct spectroscopic evidence for mixed-valence Tl in the low carrier-density superconductor ${\mathrm{Pb}}_{1-x}{\mathrm{Tl}}_x\mathrm{Te}$

Upon doping with Tl the narrow band-gap semiconductor PbTe exhibits anomalously high-temperature superconductivity despite a very low carrier-density as well as signatures of the Kondo effect despite an absence of magnetic moments. These phenomena have been explained by invoking $2e$ fluctuations of the valence of the Tl dopants, but a direct measurement of the mixed valency implied by such a mechanism has not been reported to date. In this work we present the unambiguous observation of multiple valences of Tl in Tl-doped PbTe via photoemission spectroscopy measurements. It is shown via a quantitative analysis that the suppression of the carrier density in compositions exhibiting superconductivity and Kondo-like behavior can be accounted for by mixed valency, thus arguing against a self-compensation scenario proposed elsewhere for this material and strengthening the case for valence fluctuation models. In addition to the identification of ${\mathrm{Tl}}^{+}$ and ${\mathrm{Tl}}^{3+}$ a possible third intermediate local charge-density is suggested by full fits to the data, the origins of which are also discussed but remain unclear.

Figure 1

Core level analysis of ${\mathrm{Pb}}_{1-x}{\mathrm{Tl}}_x\mathrm{Te}$ by PES. Panel (a) shows a typical wide-energy-range spectra for the core levels of ${\mathrm{Pb}}_{1-x}{\mathrm{Tl}}_x\mathrm{Te}$ showing the spin-orbit split Te $4d$ and Pb $5d$ levels. The more dilute Tl $5d$ levels are located in the red box, which has been expanded in panel (b). It can be seen in panel (b) that both the Tl $5d_{3/2}$ and Tl $5d_{5/2}$ core levels of ${\mathrm{Pb}}_{1-x}{\mathrm{Tl}}_x\mathrm{Te}$ have multiple peaks. For comparison, the blue curve is a spectrum of metallic thallium, and the red curve a spectrum of ${\mathrm{Tl}}_2\mathrm{Te}$ (${\mathrm{Tl}}^{+}$). These data were taken at temperatures between 10 and 40 K using a ${\mathrm{Pb}}_{1-x}{\mathrm{Tl}}_x\mathrm{Te}$ sample with $x=1.39\%\pm 0.10\%$.

Figure 2

Examples of fits to the Tl $5d_{3/2}$ core levels, shown here for $x=0.29\%\pm 0.10\%, x=0.69\%\pm 0.10\%$, and $x=1.39\%\pm 0.10\%$ [panels (a)–(c), respectively]. Black circles show the raw data, gray lines are the polynomial background, red curves are the full fitting results, blue (orange) solid lines mark the peak corresponding to ${\mathrm{Tl}}^{+}$ (${\mathrm{Tl}}^{3+}$) ions, and green lines mark an unexpected third peak that is consistent with the presence of a third population of Tl ions if intrinsic.

Figure 3

(a) A phase diagram illustrating the evolution of the low-temperature electrical transport properties as a function of Tl concentration in ${\mathrm{Pb}}_{1-x}{\mathrm{Tl}}_x\mathrm{Te}$. In compositions where $x<x_c$ the electrical transport is consistent with a single-band conventional metallic state, but at Tl concentrations above $x_c$, superconductivity, Kondo-like phenomenology, and resonant impurity states at the Fermi level are observed [3, 6, 18]. Values of the superconducting critical temperature in single crystals as determined by resistivity and heat capacity (solid black squares and circles, respectively) are reproduced from Ref. [4]. Values for thin films and polycrystaline samples (open circles and squares, respectively) are reproduced from Refs. [2, 22]. (b) The evolution as a function of Tl concentration of the integrated areas of the Lorentzian fits, such as those illustrated in Fig. 2. The areas of the peaks are proportional to the densities of Tl dopants in each valence and normalized such that the total area (total Tl density) matches the measured $x$. The solid blue line indicates the known presence of monovalent ${\mathrm{Tl}}^{+}$ at $x<x_c$, and the dotted blue and orange lines show the expected trends of the ${\mathrm{Tl}}^{+}$ and ${\mathrm{Tl}}^{3+}$ as implied by the measured carrier density in a two valence model. Note that, coincidentally, all three peak areas are almost identical at $x=0.29\%\pm 0.10\%$. (c) A comparison between the carrier density as measured by the Hall effect (gray symbols from Refs. [4, 18]) and the carrier density implied by the observed peak areas in this study (red stars). The black dashed line indicates the expected behavior in each Tl contributed a single charge carrier; the gray dot-dashed line is a guide to the eye. In all plots the vertical black dotted line marks the doping at which the superconducting phase and signatures of the Kondo effect emerge, $x_c=0.30\%\pm 0.10\%$.