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these days I have been trying to understand the essentials of the so-called topological insulators (TBI), such as Bi2Te3, which seem very hot in current research. As i understand, these materials should possess at the same time gapped bulk bands but gapless surface bands, and spin-orbit coupling (SO) is neccessary. Within the usual Bloch treatment, by which one uses periodic boundary conditions, no distinction between bulk and surface bands can be made. Thus, to model TBI properly, one must take into realistic surface conditions, i.e., the system is finite and terminated at the surface. Is it so ?

These surface states are quite similar to the edge states found in quantum Hall systems. Those edge states result from the presence of strong magnetic field, which splits the edge states off from the bulk states. So, may I say, SO in TBI plays an analogous role as the magnetic field in quantum Hall systems ?

Further, can anyone suggest a simple lattice model that supports TBI phenomena ?

I'll be very glad and grateful if anyone gives me a response :)

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# Is the topological insulators a result of boundary conditions with SO coupling ?

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