Tuesday, March 1, 2011

What is a topological insulator?

Today Tony Wright is giving the weekly Quantum Science Seminar on Topological Insulators. Some people consider this new state of matter one of the most important discoveries and achievements of condensed matter theory in the past decade [see this Nature News feature]. Basically they are metallic states which occur on the surfaces of insulators as a result of topological effects associated with the band structure of the solid.
A really helpful introduction, The birth of topological insulators, by Joel Moore appeared in Nature last year.
I think a more accurate and helpful name for this class of materials might be something like "topological surface metals" or "topological metals". What do others think?


  1. Regarding the name:

    The defining property of these systems are
    1) Gap over the ground state,
    2) Non-trivial topology (under a suitable definition of topological equivalence),
    so I think that "topological insulators" (or topological superconductors, for the classes with particle-hole symmetry) covers both of these aspects.

    "Topological surface metals" on the other hand would be a little misleading for several reasons from a theoretical points of view:
    1) the topological property does not depend on the surface. The bulk by itself contains the topological 'non-trivialness' and therefore the topology of the system can be analyzed without a surface,
    2) gapless (metallic) surface states are not, in my opinion, the truly fundamental thing here. Gapless states can be bound to various kinds of topological defects (which ones depend on the universality class), for example vortices, hedgehogs, line defects, domain walls etc... In this regard, surfaces are not special. These metallic states exist because the bulk gap closes continuously between two topologically distinct regions (for example trivial and non-trivial regions separated by a surface) See http://arxiv.org/abs/1006.0690 .

    Thus in my opinion it is the bulk that contains the true topological properties, and since the bulk is insulating: topological insulator.

    Heidar Moradi

  2. Obviously, I forgot "non-interacting system" in the defining properties.

  3. Hi Heidar,

    Thanks for the clarifying comments. You have helped me understand the issues much better and your points are well taken. I now agree topological insulator is better terminology than my proposed alternative.
    This is why I like blogging. Because I can have my misunderstandings corrected so quickly!