Pulling apart the atoms of a topological insulator Consider a topological insulator. In order to destroy a topological phase, the band gap of the bulk system should close at some point (passing thru a conducting state), but if the atoms that make up the topological insulator start to be pulled apart, I would assume that the system would become more and more insulating in the bulk (and therefore it would never go thru the conducting state). 
If the assumption is correct, this implies that the topological phase is not destroyed and we cannot get to a system of simply isolated atoms by pulling apart the system. 
What does this mean? Does this mean that this a reversible process?
What happens to the edge modes when the atoms are far apart?
In which (measurable) sense would this final system be different from a system of isolated atoms? 
What would happen if the atoms were put together again in the same phase/system but with the positions (of identical atoms) interchanged?
E. J. Mele says something about this at min 15:29.
 A: That's a very interesting question, thank you.
I'm not sure I have the answer but I would like to offer some points for consideration:
Consider the easiest case, which is the Landau Hamiltonian. For an electron governed by the Landau Hamiltonian, there are no atoms at all. It's just kinetic energy in a magnetic field. Yet there is a topologically non-trivial phase (each Landau level has Chern number equal to $-1$). 
It would seem to me that as long as you have a magnetic field, and you start from a topological phase, and then you start pulling the atoms apart, (assuming the magnetic field is stronger than the binding to the atom cores) what you'll get is just the Landau Hamiltonian.
Note that this idea also goes through for the SSH model:
Take the SSH model with $S^1\ni k\mapsto H(k) \equiv \begin{bmatrix}0&t+t'\exp(\mathrm{i}k) \\
 t+t'\exp(-\mathrm{i}k)&0\end{bmatrix}.$ We know that there is a well-defined phase if $|t/t'|\neq 1$ and furthermore it is $1$ if $|t/t'|<1$. But nothing stops us from slowly taking $t\to0$, the effect of which is to pull the dimers apart from each other. Yet you can clearly calculate that the winding number of this model stays $1$ (and well-defined) as you take $t\to0$. The gap also stays open throughout and the functions are smooth in $k$.
