You may wish to consult the attached review article by MZ Hasan and CL Kane (Rev. Mod. Phys. 82, 3045 (2010)).

http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.3045

Ps. Professor Charles Kane of University of Pennsylvania (the second author of the above-mentioned review article) has a number of lectures on topological band theory, which are available on YouTube. I attach below the URL of a YouTube search on 'Topological band theory'.

https://www.youtube.com/results?search_query=Topological+band+theory

http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.3045

https://www.youtube.com/results?search_query=Topological+band+theory

     Let me try to distinguish the main different insulators.

    Band insulator is the usual well known insulator having a great band gap of energy. There are several kinds of band insulators: covalent insulator with energy gap around 1 eV as GaAs, solid insulator as where the energy gap is around 10 eV as in Ar liquid (electronic transitions between 3p to 4s orbitals) or Dirac vacuum where the transition is positron-electron which needs an excitation (energy gap around 1 MeV).

   A topological insulator is a covalent band insulator which has a non trivial topology associated to the band structure which makes it to have metallic behaviour in their surface. Examples are quantum wells as HgTe, alloys as BiSb and crystals as Bi2 Se3

   But there are insulators which do not follow the criterium of the band theory and needs to consider the strong correlated electrons interaction as it happens for the Mott insulators. Notice that in this case the usual electronic screening, they consider mainly materials 3d. Others are the charge transfer inslulators where the usual bands fail also due to an anomalous transfer of electrons as it happens in NiO between 2p (oxigen) to 3d (nitrogen).

   I hope that this can help.

You may wish to consult the attached review article by MZ Hasan and CL Kane (Rev. Mod. Phys. 82, 3045 (2010)).

http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.3045

Ps. Professor Charles Kane of University of Pennsylvania (the second author of the above-mentioned review article) has a number of lectures on topological band theory, which are available on YouTube. I attach below the URL of a YouTube search on 'Topological band theory'.

https://www.youtube.com/results?search_query=Topological+band+theory

http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.3045

https://www.youtube.com/results?search_query=Topological+band+theory