Quasiparticle interference on the surface of the topological crystalline insulator Pb${}_{1-x}$Sn${}_x$Se

Topological crystalline insulators represent a novel topological phase of matter in which the surface states are protected by discrete point group symmetries of the underlying lattice. Rock-salt lead-tin-selenide alloy is one possible realization of this phase, which undergoes a topological phase transition upon changing the lead content. We used scanning tunneling microscopy (STM) and angle resolved photoemission spectroscopy (ARPES) to probe the surface states on (001) Pb${}_{1-x}$Sn${}_x$Se in the topologically nontrivial ($x=0.23$) and topologically trivial ($x=0$) phases. We observed quasiparticle interference with STM on the surface of the topological crystalline insulator and demonstrated that the measured interference can be understood from ARPES studies and a simple band structure model. Furthermore, our findings support the fact that Pb${}_{0.77}$Sn${}_{0.23}$Se and PbSe have different topological nature.

Figure 1

(a) STM topographic image ($V_{\mathrm{bias}}=400$ mV and $I=25$ pA) of a 450 $\text{Å}$-by-450 $\text{Å}$ cleaved surface of Pb${}_{0.77}$Sn${}_{0.23}$Se. (b) Schematic illustration of the (001) termination of the rocksalt crystal structure. (c) High spatial resolution topographic image of the same area at $V_{\mathrm{bias}}=-10$ meV ($I=150$ pA) and at $V_{\mathrm{bias}}=-50$ meV ($I=200$ pA). Topographies (d), (e) and spatially averaged $dI/dV$ spectra (f), (g) on Pb${}_{0.77}$Sn${}_{0.23}$Se and undoped PbSe. Insets show the schematic surface band dispersion as a function of the momentum along $\overline{\Gamma }\overline{X}$ direction.

Figure 2

(a) Fourier transform of a conductance map taken at $V_{\mathrm{bias}}=-100$ meV and $I=40$ pA over an area of 820 $\text{Å}\times$820 $\text{Å}$. Red lines mark the boundary of the FSBZ. (b) ARPES intensity map at $E=-100$ meV on Pb${}_{0.77}$Sn${}_{0.23}$Se reveals overall four surface pockets in the inner side and four other pockets on the outer side of $\overline{X}$ points. White square indicates the location of the FBZ. (c) Energy-momentum dispersion relation measured by ARPES on Cs doped Pb${}_{0.85}$Sn${}_{0.15}$Se in the $\overline{\Gamma }\overline{X}$ direction. Green lines show the highest intensity obtained from the theoretical model. (d) ARPES intensity maps of Cs doped Pb${}_{0.85}$Sn${}_{0.15}$Se around the ${\overline{X}}_2$ point.

Figure 3

Fourier transform of the QPI patterns on the surface of Pb${}_{0.77}$Sn${}_{0.23}$Se at different energies superimposed with the calculated JDOS (third and fourth quarters of $q$ space). In the figures, two different isocontours are shown corresponding to two different intensity values: the intensity of the green contours is an order of magnitude higher than the intensity of purple contours. Insets display the corresponding calculated Fermi surfaces around the $\overline{X}$ point.

Figure 4

Energy-momentum structure of the surface states of Pb${}_{0.77}$Sn${}_{0.23}$Se along (a) $\overline{\Gamma }\overline{X}$ and (b) $\overline{\Gamma }\overline{M}$ directions. White dashed line indicates the position of the Bragg peak, while red dotted lines as guides to the eye enclose the relevant high intensity regions of the STM data. The isocontours correspond to the same intensity values as on Fig. 3.