# How can one localize the massless fermions in Dirac materials?

I noticed that finite electric potential cannot localize the low energy excitations in a graphene sheet. Is it possible to localize the massless fermions in the surface band of topological insulators with a magnetic field?

I found a paper dealing with a similar problem: http://apl.aip.org/resource/1/applab/v98/i16/p162101_s1

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What do you mean "localize"? Do you mean make bound states? –  Ron Maimon Sep 16 '11 at 19:02
Yes. That is what I mean. –  Z.Sun Sep 16 '11 at 19:50

This issue is a well known problem in high energy physics which is called " Neutrino Billiards". You can find a full description about it in:

Ref: Berry, M.V. and R.J. Mondragon, Neutrino Billiards: Time-Reversal Symmetry-Breaking Without Magnetic Fields. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1987. 412(1842): p. 53-74.

And in the case of graphene C.W.J. Beenakker have a good paper about this problem: Physical Review Letters, 2006. 96(24): p. 246802. or it's Arxiv:0603315 counterpart.

in summary: for making bound states from massless Dirac fermions you must use a mass term in each bound instead of electric potentials. So the probability of Klein tunneling set to zero and fermions became confined.

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