Quasiparticle interference on the surface of the topological insulator ${\text{Bi}}_2{\text{Te}}_3$

The quasiparticle interference of the spectroscopic imaging scanning tunneling microscopy has been investigated for the surface states of the large gap topological insulator ${\text{Bi}}_2{\text{Te}}_3$ through the $T$-matrix formalism. Both the scalar-potential scattering and the spin-orbit scattering on the warped hexagonal isoenergy contour are considered. While backscatterings are forbidden by time-reversal symmetry, other scatterings are allowed and exhibit strong dependence on the spin configurations of the eigenfunctions at $\vec{k}$ points over the isoenergy contour. The characteristic scattering wave vectors found in our analysis agree well with recent experiment results.

Figure 1

(Color online) (a)The isoenergy contour near the $\Gamma$ point for $E=1.5E^{\ast }$ with snow-flake shape. The $\widehat{x}$ and $\widehat{y}$ axes are chosen to be the $\Gamma \text{-K}$ and $\Gamma \text{-M}$ directions, respectively, and $k_c=\sqrt{v/\lambda }$. The red (gray) and brown (dark gray) dots refer to the valley and the tip points on the contour, and the arrows indicates six representative scattering wave vectors. $k_L$ and $k_U$ are solutions of $E_{+}\left(k_L,\theta =0\right)=E_{+}\left(k_U,\theta =\pi /2\right)=E$ which are the boundary of the truncation for the $\vec{k}$ integration used in this paper. (b) The spin orientations of the eigenfunctions for ${\alpha }_{+}$ band at valley and tip points. The dotted lines refer to the mirror-symmetric lines $\left(\Gamma \text{-M}\right)$, and the system has a threefold rotational symmetry. The arrow indicate the spin configuration in the $xy$ plane and the solid circle (cross) refers to $S_z$ being along $+\widehat{z}\left(-\widehat{z}\right)$. At the cusp points the spin lies only on the $xy$ plane while $S_z$ has the largest magnitude at the valley points with staggered signs.

Figure 2

(Color online) The quasiparticle interference image for (a) $c=0$ and (b) $c=0.5$ with $E=1.5E^{\ast }$ and $V_0/E^{\ast }=0.1$. In this case, $k_L/k_c=1.029$ and $k_U/k_c=1.5$. (a) The strongest large $\vec{q}$ scatterings are ${\vec{q}}_5$ and ${\vec{q}}_2$ indicated by the red (dark gray) and green (light gray) circles (and their symmetric points). ${\vec{q}}_3$ (indicated by the white circle) is too weak to be seen. (b) For $c=0.5$, new QPI features with large momenta are visible.