Theory of quasiparticle interference on the surface of a strong topological insulator

Electrons on the surface of a strong topological insulator, such as ${\text{Bi}}_2{\text{Te}}_3$ or ${\text{Bi}}_{1-x}{\text{Sb}}_x$, form a topologically protected helical liquid whose excitation spectrum contains an odd number of massless Dirac fermions. A theoretical survey and classification is given of the universal features, observable by the ordinary and spin-polarized scanning tunneling spectroscopy, in the interference patterns resulting from the quasiparticle scattering by magnetic and nonmagnetic impurities in such a helical liquid. Our results confirm the absence of backscattering from nonmagnetic impurities observed in recent experiments and predict new interference features, uniquely characteristic of the helical liquid, when the scatterers are magnetic.

Figure 1

(Color online) (a) Dirac dispersion and spin orientation in helical liquid on the surface of a strong topological insulator. (b) FT-STS response $\mathfrak{I}{\Lambda }_{00}\left(\mathbf{q},\omega \right)$ as a density plot in the $\left(q_x,q_y\right)$ plane (top), cut along the $q_x$ direction (bottom).

Figure 2

Spin-resolved FT-STS response $\mathfrak{I}{\Lambda }_{ij}\left(\mathbf{q},\omega \right)$ to magnetic impurities. Top row gives the density plot in the $\left(q_x,q_y\right)$ plane in channel $\left(ij\right)$ indicated in the upper left corner. Bottom row shows the corresponding cuts along the indicated lines parametrized by $q_x$.