Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features?
See e.g. the article
Xiao-Liang Qi and Shou-Cheng Zhang, The quantum spin Hall effect and topological insulators. The pdf file is available here.
They provide an effective Hamiltonian in the box on page 36 for a mercury telluride topological insulator. It's easy to find the eigenstates and dispersion. How do you find the gapless edge states as shown in fig. 2b of the same paper?