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A surface of a strong topological insulator (STI) is characterized by an oddnumber of linearly dispersing gapless electronic surface states. It is wellknown that such a surface cannot be described by an effective two-dimensionallattice model (without breaking the time-reversal symmetry), which oftenhampers theoretical efforts to quantitatively understand some of the propertiesof such surfaces, including the effect of strong disorder, interactions andvarious symmetry-breaking instabilities. Here we formulate a lattice model thatcan be used to describe a {\em pair} of STI surfaces and has an odd number ofDirac fermion states with wavefunctions localized on each surface. TheHamiltonian consists of two planar tight-binding models with spin-orbitcoupling, representing the two surfaces, weakly coupled by terms that removethe extra Dirac points from the low-energy spectrum. We illustrate the utilityof this model by studying the magnetic and exciton instabilities of the STIsurface state driven by short-range repulsive interactions and show that thisleads to results that are consistent with calculations based on the continuummodel as well as three-dimensional lattice models. We expect the modelintroduced in this work to be widely applicable to studies of surface phenomenain STIs.

Lattice model for the surface states of a topological insulator with applications to magnetic and exciton instabilities