Zero modes of tight binding electrons on the honeycomb lattice

Details Zero modes of tight binding electrons on the honeycomb lattice Zero modes of tight binding electrons on the honeycomb lattice

2006-04-19

arxiv.org/abs/cond-mat/0604433v1

Phys. Rev. B 74, 033413 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 6 figures

Scientific paper

10.1103/PhysRevB.74.033413

Tight binding electrons on the honeycomb lattice are studied where nearest neighbor hoppings in the three directions are $t_a,t_b$ and $t_c$, respectively. For the isotropic case, namely for $t_a=t_b=t_c$, two zero modes exist where the energy dispersions at the vanishing points are linear in momentum $k$. Positions of zero modes move in the momentum space as $t_a,t_b$ and $t_c$ are varied. It is shown that zero modes exist if $||\frac{t_b}{t_a}| -1| \leq |\frac{t_c}{t_a}| \leq ||\frac{t_b}{t_a}|+1|$. The density of states near a zero mode is proportional to $|E|$ but it is propotional to $\sqrt{|E|}$ at the boundary of this condition.

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