  The protected surface states of topological insulators (TIs) form gapless
Dirac cones corresponding non-degenerate eigenstates with helical spin
polarisation. The presence of a warping term deforms the isotropic cone of the
most simple model into snowflake Fermi surfaces as in Bi2Se3 and Bi2Te3. Their
features have been identified in STM quasiparticle interference (QPI)
experiments on isolated surfaces. Here we investigate the QPI spectrum for the
TI thin-film geometry with finite tunnelling between the surface states. This
leads to a dramatic change of spectrum due to gapping and a change in spin
texture that should leave distinct signatures in the QPI pattern. We consider
both normal and magnetic exchange scattering from the surface impurities and
obtain the scattering t-matrix in Born approximation as well as the general
closed solution. We show the expected systematic variation of QPI snowflake
intensity features by varying film thickness and study, in particular, the
influence on backscattering processes. We predict the variation of the QPI
spectrum for Bi2Se3 thin films using the observed gap dependence from ARPES
results.
