Versatile electronic states in epitaxial thin films of (Sn-Pb-In)Te: From topological crystalline insulator and polar semimetal to superconductor

Epitaxial thin films of ${\left({\mathrm{Sn}}_x{\mathrm{Pb}}_{1-x}\right)}_{1-y}{\mathrm{In}}_y\mathrm{Te}$ were successfully grown by molecular-beam epitaxy in a broad range of compositions ($0\le x\le 1$, $0\le y\le 0.23$). We investigated electronic phases of the films by the measurements of electrical transport and optical second-harmonic generation. In this system, one can control the inversion of the band gap, the electric polarization that breaks the inversion symmetry, and the Fermi-level position by tuning the Pb/Sn ratio and In composition. A plethora of topological electronic phases is expected to emerge, such as the topological crystalline insulator, the topological semimetal, and superconductivity. For the samples with large Sn compositions $(x>0.5)$, hole density increases with In composition $\left(y\right)$, which results in the appearance of superconductivity. On the other hand, for those with small Sn compositions $(x<0.5)$, an increase in In composition reduces the hole density and changes the carrier type from $p$ type to $n$ type. In a narrow region centered at $\left(x,y\right)=\left(0.16,0.07\right)$ where the $n$-type carriers are slightly doped, charge transport with high mobility exceeding $5000\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{\text{–}1}{\mathrm{s}}^{\text{–}1}$ shows up, representing the possible semimetal states. In those samples, the optical second-harmonic generation measurement showing the breaking of inversion symmetry along the out-of-plane [111] direction, which is a necessary condition for the emergence of the polar semimetal state. The thin films of ${\left({\mathrm{Sn}}_x{\mathrm{Pb}}_{1-x}\right)}_{1-y}{\mathrm{In}}_y\mathrm{Te}$ material systems with a variety of electronic states would become a promising materials platform for the exploration of novel quantum phenomena.

Figure 1

(a) Schematic of the sample structure. (b) XRD patterns in 2θ-ω scans for ${\mathrm{Sn}}_x{\mathrm{Pb}}_{1-x}\mathrm{Te}$ thin films with various $x$'s. (c) Cubic lattice constant evaluated from the (222) diffraction peak in (b). Dashed lines represent the bulk values for the lattice constant of PbTe and SnTe. (d) Temperature dependence of resistivity for ${\mathrm{Sn}}_x{\mathrm{Pb}}_{1-x}\mathrm{Te}$ thin films with several $x$'s. (e) and (f) Sn composition $x$ dependence of resistivity ${\rho }_{xx}$ (e) and hole carrier density $p$ (f) at $T=2\mathrm{K}$.

Figure 2

(a) Temperature dependence of longitudinal resistivity ${\rho }_{xx}$ for several ${\left({\mathrm{Sn}}_x{\mathrm{Pb}}_{1-x}\right)}_{1-y}{\mathrm{In}}_y\mathrm{Te}$ samples with various $x$'s ($x>0.5$) and $y$'s ($y\le 0.23$) values. (b) $y$ dependence of hole density ($p$) at $T=5\mathrm{K}$ for series of samples with different $x$'s. Filled circles indicate the samples that show superconductivity. (c) $p$ dependence of onset temperature of superconductivity $T_{\mathrm{c}}^{\mathrm{onset}}$ for series of samples with different $x$'s. The inset shows the definition of $T_{\mathrm{c}}^{\mathrm{onset}}$ for the sample with $\left(x,y\right)=\left(0.63,0.23\right)$.

Figure 3

(a) Temperature dependence of resistivity under out-of-plane magnetic field for $\left(x,y\right)=\left(0.63,0.23\right)$ sample. (b) Temperature dependence of upper critical field ${\mu }_0{H}_{\mathrm{c}2}$ (red) and temperature-linear fitting (black line).

Figure 4

(a) Temperature dependence of longitudinal resistivity ${\rho }_{xx}$ for several ${\left({\mathrm{Sn}}_x{\mathrm{Pb}}_{1-x}\right)}_{1-y}{\mathrm{In}}_y\mathrm{Te}$ samples with various $x$ ($x<0.5$) and $y$ ($y\le 0.23$) values. (b) $y$ dependence of electron (blue circles) and hole (red circles) density ($n$ and $p$, respectively) at $T=2\mathrm{K}$ for series of samples with different $x$. (c) and (d) Color maps of carrier density (c) and mobility (d) as functions of $x$ and $y$. The measured data points are overlaid on the color map with small gray circles.

Figure 5

Temperature dependence of resistivity (a) and electron density (b) for $\left(x,y\right)=\left(0.16,0.09\right)$ sample.

Figure 6

(a) Incident light polarization dependence of $p$-polarized SH intensity for six samples with various $x$(Sn) and $y$(In) values. (b) Temperature dependence of the SH intensity with $p_{\mathrm{in}}-p_{\mathrm{out}}$ geometry.

Figure 7

(a) and (b) Reciprocal space maps of x-ray diffraction peaks around (a) InP (222) and (b) InP (513) Bragg peaks for SPIT sample with $\left(x,y\right)=\left(0.16,0.02\right)$. In-plane and out-of-plane reciprocal lattice vectors, respectively, are along the $\left[1\overline{1}0\right]$ and [111] directions. (c) Crystal structure of (Sn,Pb,In)Te with in-plane lattice constant $a_{\parallel }$, out-of-plane lattice constant $c$, corner angle α, and rhombohedral/cubic lattice parameter $a_0$. These parameters satisfy the geometrical relations $sin\frac{\alpha }{2}=\frac{a_{\parallel }}{2a_0}$ and $3a_0=\sqrt{c^2+3a_{\parallel }^2}$.