Quasiparticle interference on the surfaces of the of the layered topological superlattice Bi$_{4}$Se$_{3}$

Three-dimensional topological insulators (TIs) host robust surface states with massless Dirac-like dispersion and helical spin texture. The possibility of layering TIs with other materials in a superlattice is especially intriguing, as exotic phenomena are predicted to occur at their boundary. Here, we present scanning tunneling microscopy and spectroscopy (STM/STS) results on one of the simplest such superlattices, Bi$_{4}$Se$_{3}$, which consists of alternating layers of a three-dimensional TI, Bi$_{2}$Se$_{3}$, and a two-dimensional TI, Bi$_{2}$. STM topographs reveal two distinct, alternating surfaces, each of which harbors dispersing surface states. By using Fourier-transform STS, we characterize the dispersion of these states, which is considerably more complex than that of the single Dirac cone found in prototypical three-dimensional TIs. In addition, we show that the surface states of Bi$_{4}$Se$_{3}$ are strongly influenced by proximity to atomic defects.