  The hexagonal warping effect on transport properties and Goos-H\"anchen (GH)
lateral shift of electrons on the surface of a topological insulator with a
potential barrier is investigated theoretically. Due to the warped Fermi
surface for incident electron beams, we can expect two propagating transmitted
beams corresponding to the occurrence of double refraction. The transmitted
beams have spin orientations locked to their momenta so one of the spin
directions rotates compared to the incident spin direction. Based on a
low-energy Hamiltonian near the Dirac point and considering Gaussian beams, we
derive expressions for calculating lateral shifts in the presence of warping
effect. We study the dependence of transmission probabilities and GH shifts of
transmitted beams on system parameters in detail by giving an explanation for
the appearance of large peaks in the lateral shifts corresponding to their
transmission peaks. It is shown that the separation between two transmitted
beams through their different GH shifts can be as large as a few micrometers,
which is large enough to be observed experimentally. Finally, we propose a
method to measure the GH shift of electron beams based on the transverse
magnetic focusing technique in which, by tuning an applied magnetic field, a
detectable resonant path for electrons can be induced.
