Experimental Observation of Dirac-like Surface States and Topological Phase Transition in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}(111)$ Films

The surface of a topological crystalline insulator (TCI) carries an even number of Dirac cones protected by crystalline symmetry. We epitaxially grew high-quality ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}(111)$ films and investigated the TCI phase by in situ angle-resolved photoemission spectroscopy. ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}(111)$ films undergo a topological phase transition from a trivial insulator to TCI via increasing the Sn/Pb ratio, accompanied by a crossover from $n$-type to $p$-type doping. In addition, a hybridization gap is opened in the surface states when the thickness of the film is reduced to the two-dimensional limit. The work demonstrates an approach to manipulating the topological properties of TCI, which is of importance for future fundamental research and applications based on TCI.

Figure 1

MBE growth of ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}(111)$ films. The growth dynamics is very similar to that of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ [12, 13, 14]. High-quality single crystalline thin film is achieved under the Te-rich condition (flux ratio $\mathrm{Te}/\mathrm{Sn}>5$) and $T_{\mathrm{Sn}(\mathrm{Pb})}>T_{\mathrm{sub}}>T_{\mathrm{Te}}$, where $T_{\mathrm{Sn}(\mathrm{Pb})}$, $T_{\mathrm{sub}}$, and $T_{\mathrm{Te}}$ are the temperatures of the Sn(Pb) cell, substrate, and Te cell, respectively. The growth rate is typically $\sim 0.25\text{monolayer}/\sec$ ($\mathrm{ML}/\mathrm{s}$) at $T_{\mathrm{Sn}}=1020°\mathrm{C}$, $T_{\mathrm{sub}}=310°\mathrm{C}$, and $T_{\mathrm{Te}}=300°\mathrm{C}$. The ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ buffer layer is 7 nm thick. (a) Crystal structure of Sn(Pb)Te along the [111] direction. (b) The bulk and the projected (111) Brillouin zones of ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$. (c) Schematic illustration of topological phase transition in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ system. TSS stands for topological surface states. (d) RHEED pattern along the $[1\overline{1}0]$ ($\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{K}}$) direction of a SnTe(111) film that is 30 nm thick. (e) STM image of SnTe(111) film acquired at 77 K. The inset is the atomically resolved image. (f) X-ray diffraction pattern of SnTe film. Only the (2,2,2) Bragg peak is clearly seen.

Figure 2

Electronic structure of the ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}(111)$ film (30 nm thick) in the vicinity of the $\overline{\mathrm{\Gamma }}$ point. (a) and (b) ARPES and TB calculation of SnTe. (c) and (d) ARPES and TB calculation of ${\mathrm{Pb}}_{0.25}{\mathrm{Sn}}_{0.75}\mathrm{Te}$. (e) and (f) ARPES and TB calculation of ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Te}$. (g) and (h) ARPES and TB calculation of PbTe. The red and white dashed lines indicate the relative shift between the Fermi level of the doped sample observed by ARPES and that of the intrinsic sample given by the calculation.

Figure 3

Electronic structure of ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}(111)$ film (30 nm thick) in the vicinity of the $\overline{M}$ point. (a) to (d) ARPES of SnTe, ${\mathrm{Pb}}_{0.25}{\mathrm{Sn}}_{0.75}\mathrm{Te}$, ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Te}$, and PbTe. (e)–(h) The corresponding TB calculation, which agrees well with the observed spectra. The spin texture is the same as previous calculations [8, 10] and not shown here. The red and white dashed lines indicate the relative shift between the Fermi level of the doped sample observed by ARPES and that of the intrinsic sample given by the calculation.

Figure 4

ARPES of (a) 1.1 nm and (b) 30 nm ${\mathrm{Pb}}_{0.25}{\mathrm{Sn}}_{0.75}\mathrm{Te}(111)$ films.