# 1D topological insulator

This question is inspired by another one about the simplest model of topological insulator, where 4tnemele showed a nice two band model in the answer.

I read that and am wondering if we and push that to one dimension.

For example, by analogy to the graphene case, if we have a Hamiltonian in 1D (say x) as $H(k_x)=(k_x-k_0)+m$ for $k_x>0$. When $k_x=k_0$, one has $m>0$. $H(k_x)=(k_x+k_0)+m$ for $k_x<0$. When $k_x=-k_0$, one has $m<0$. A smooth connection in between, we will have a conductive edge (two ends in the 1D structure), right?

If I want to make a intuitive picture like below, is it correct?

Any suggestion for real materials show this behavior?

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I can't say anything too insightful as an answer to your actual question, but I think it's interesting to note that novel "edge modes" on the free ends of 1D systems are actually quite generic, two beautiful examples being emergent spin-1/2 excitations at the tips of S=1 Heisenberg magnets (see also the AKLT chain) or Majorana fermion modes on the ends of the Kitaev chain. –  wsc Feb 26 '11 at 4:01