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 ${({\mathrm{Sn}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x})}_{1\ensuremath{-}y}{\mathrm{In}}_{y}\mathrm{Te}$ were successfully grown by molecular-beam epitaxy in a broad range of compositions ($0\ensuremath{\le}x\ensuremath{\le}1$, $0\ensuremath{\le}y\ensuremath{\le}0.23$). 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 $(xg0.5)$, hole density increases with In composition $(y)$, which results in the appearance of superconductivity. On the other hand, for those with small Sn compositions $(xl0.5)$, 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 $(x,y)=(0.16,0.07)$ where the $n$-type carriers are slightly doped, charge transport with high mobility exceeding $5000\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\text{--}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\text{--}1}$ 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 ${({\mathrm{Sn}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x})}_{1\ensuremath{-}y}{\mathrm{In}}_{y}\mathrm{Te}$ material systems with a variety of electronic states would become a promising materials platform for the exploration of novel quantum phenomena.