Disorder, when strong enough, generally localizes all electrons. An exception is electrons at the surfaces of topological insulators, which due to their nontrivial topological properties manage to avoid localization. This property can, in fact, be used as a definition of a topological insulators.

We were at the forefront of demonstrating this for the case a 2D Dirac fermions, as realized on the surface of 3D topological insulators. In particular, we have shown that disorder always drives the surface of a strong topological insulator metallic -- sometimes referred to as supermetal. A strong topological insulator has an odd number of Dirac fermions in its surface; a weak topological insulator, in contrast, has an even number. Surprisingly, as we have shown, the weak topological insulator also avoids localization under rather general conditions.

In order to demonstrate these and other transport phenomena of Dirac fermions, we have developed a numerical technique based on the transfer matrix formalism in momentum space. This was needed to avoid the *fermion doubling theorem*, which states that an odd number of Dirac fermions can not be realized on a lattice in two dimensions.

For further reading see:

- Jens H. Bardarson, Joel E. Moore, Rep. Prog. Phys.
**76**, 056501 (2013). - E. Rossi, J. H. Bardarson, M. S. Fuhrer, S. Das Sarma, Phys. Rev. Lett.
**109**, 096801 (2012). - Roger S. K. Mong, Jens H. Bardarson, Joel E. Moore Phys. Rev. Lett.
**108**, 076804 (2012). - J. H. Bardarson, M. V. Medvedyeva, J. Tworzydlo, A. R. Akhmerov, C. W. J. Beenakker, Phys. Rev. B
**81**, 121414(R) (2010). - J. H. Bardarson, J. Tworzydło, P. W. Brouwer, C. W. J. Beenakker, Phys. Rev. Lett.
**99**, 106801 (2007)