Wednesday, February 6, 2013

Definitive evidence for a topological insulator

Last Friday I had a nice meeting at IISc Bangalore with Subroto Mukerjee.
One thing he emphasized to me is that if you see evidence of surface states with a Dirac cone (e.g. in ARPES or quantum oscillations) it is not unambiguous evidence that you have a topological insulator. That requires seeing an odd number of Dirac cones.


  1. Very true. If I'm not mistaken, this is one reason people are so interested in samarium hexaboride. I remember hearing that its status as a topological insulator is less ambiguous.

  2. This is true.

    If you see a Dirac cone at a high symmetry point in the Brillouin zone, such as the Gamma point or one of the zone edges, then this condition is necessarily fulfilled though, isn't it? Unless they're degenerate bands, and you're doing arpes for example, then perhaps you think you're seeing one band but you're actually seeing two.

    Nevertheless, I remember Charlie Kane saying that he spent a summer looking for topological materials by going through band structures of known materials, and the best he found was one with 5 Dirac cones. But in the same period S.C. Zhang and friends found that Bismuth based (BiSe or BiTe I can't remember) materials could have just one, so that's better, though equivalent.

  3. Tony wrote:

    >Unless they're degenerate bands, and you're
    >doing arpes for example, then perhaps you think
    >you're seeing one band but you're actually >seeing two.

    They won't be degenerate. These are generally materials with strong SO coupling and so the states a the surface will split except at time-reversal invariant momenta

  4. Hi Peter,

    Naturally you're right about spin splitting. But they can be degenerate for many other reasons right? Call it a pseudo-spin, and it can be anything at all! You can trivially write down a Hamiltonian with degenerate bands. And you can easily write down a Hamiltonian with degenerate low energy bands at, say, the Gamma point. All I'm saying is that arpes won't give you this information.

    However perhaps you're implicitly right, and that degenerate bands in crystals are quite uncommon. I wouldn't have a clue about this.