Highly tunable topological system based on PbTe-SnTe binary alloy

Topological semimetals have been attracting great interest for their superb potentials. While many theoretical and experimental investigations have been performed for topological semimetals, their materials platform is still in demand. Here, we report a highly tunable materials system for topological semimetal, indium (In)-doped $\mathrm{P}{\mathrm{b}}_{1-x}\mathrm{S}{\mathrm{n}}_x\mathrm{Te}$. By exploring the crystals with varying Pb/Sn ratios and In doping levels, a phase formation with low carrier concentration, high mobility, and large anomalous Hall effect is found for a finite area of the composition between topological crystalline insulator and normal insulator at ambient pressure. Furthermore, the in-plane anomalous Hall effect as a hallmark of Berry-curvature generation is also observed at low temperatures, where optical second-harmonic generation reveals the breaking of inversion symmetry. These results show that there is a finite range of topological semimetal phase in the PbTe-SnTe binary alloy, providing a promising materials platform to investigate the versatile nature of topological semimetals.

Figure 1

Electrical transport properties of In doped ${\left(\mathrm{P}{\mathrm{b}}_{0.5}\mathrm{S}{\mathrm{n}}_{0.5}\right)}_{1-y}\mathrm{I}{\mathrm{n}}_y\mathrm{Te}$. (a) Temperature-dependent resistivity of samples with different In doping concentrations. (b) Schematic phase diagram for the band evolution between normal insulator (NI; PbTe) and topological crystalline insulator (TCI; SnTe). By In doping for reducing the carrier density, topological semimetallic (TSM) features are expected to show up. (c) Hole-type carrier concentration $p\left(2\mathrm{K}\right)$ plotted against In concentration. (d) Mobility $\mu \left(2\mathrm{K}\right)$ plotted with respect to In concentration $y$ for nominal Pb/Sn ratio of $1\left(x=0.5\right)$. The analyzed Pb/Sn ratios are shown for each sample. Samples with actual Pb/Sn ratios within $1.00\pm 0.06$ are in the violet region. Only samples with Pb/Sn ratios off unity exhibits a large enhancement of μ (indicated by the green area).

Figure 2

Charge-transport characterization of single crystals ${\left(\mathrm{P}{\mathrm{b}}_{1-x}\mathrm{S}{\mathrm{n}}_x\right)}_{1-y}\mathrm{I}{\mathrm{n}}_y\mathrm{Te}$ prepared with various compositions of Pb/Sn and In. (a)–(d) Position-dependent composition characterization of a long single crystalline rod with the nominal values of $x=0.5$; $y=0.06$. Concentrations of (a) In $y$, (b) $\mathrm{Sn}x\left(1-y\right)$, and $\mathrm{Pb}\left(1-x\right)\left(1-y\right)$ determined by EDX (see text), (c) hole-type carrier concentration $p\left(2\mathrm{K}\right)$ and (d) mobilities $\mu \left(2\mathrm{K}\right)$ characterized piece by piece along the growth direction of the single crystalline rod shown on top of panel (a). The sample position is defined as the distance $d$ measured from the top position of the as-grown crystal rod. The reddish area indicates the intermediate range of the crystal pieces exhibiting enhanced mobility values. (e) Hole-type carrier concentration $p\left(2\mathrm{K}\right)$ of all the samples from different crystal rods (including some rods with a Pb/Sn ratio larger than 1) The contour map is spanned by concentrations of In $y$ and $\mathrm{Pb}\left(1-x\right)\left(1-y\right)$. (f) The corresponding mobilities $\mu \left(2\mathrm{K}\right)$ of all these samples are summarized in the contour map.

Figure 3

Temperature dependence of charge transport properties on the three representative samples with slightly different compositions. (a)–(c) Temperature dependence of resistivity ρ for the three typical samples, S33, S35, and S40 [see Figs. 2 and 2] for their accurate compositions. S33 and S35 exhibit semimetallic features at low temperatures. The inset of panel (c) shows a logarithmic-scale resistivity versus temperature, signifying the insulating behavior in sample S40. (d)–(f) Temperature dependence of carrier concentration $p$ (blue lines) and mobility μ (red lines). S35 exhibits a large enhancement of mobility below 100 K.

Figure 4

In-plane anomalous Hall effect as a signature of Berry curvature of the topological semimetal candidate crystal. (a)–(c) Out-of-plane $\left(H\right|\left|\mathit{c}\right)$ and in-plane $\left(H\right|\left|\mathit{b}\right)$ Hall effects of sample S33, S35, and S40, respectively. The inset in panel (a) shows the applied current and magnetic field configuration. Only sample S35 exhibits simultaneously an obvious out-of-plane and in-plane anomalous Hall signal at 2 K. (d) Temperature dependence of the in-plane $\left(H\right|\left|\mathit{b}\right)$ anomalous Hall effect for sample S35. (e) Temperature dependence of the ratio of the in-plane Hall conductivity to carrier concentration, ${\sigma }_{xy}^{\mathrm{in}-\mathrm{plane}}\left(3\mathrm{T}\right)/p$, for sample S35. This quantity is predicted to be proportional to the Berry curvature $\langle {\mathrm{\Omega }}_z\rangle$, see Eq. (1), showing a large enhancement below 100 K. The inset shows temperature dependent polar plots of the second harmonic generation (SHG) signal with normal incident fundamental laser light (1.5 eV with pulse duration of 120 fs) on the $\mathit{a}\mathit{b}$ plane of S35, indicating the polarity generation along the ⟨100⟩ axes. The thick pink line is a guide to the eyes.