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2007

Chiral Decomposition in the Electronic Structure of Graphene Multilayers

Min, Hongki, MacDonald, A. H.

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We show that the low-energy electronic structure of arbitrarily stacked graphene multilayers with nearest-neighbor interlayer tunneling consists of chiral pseudospin doublets.

Although the number of doublets in an $N$-layer system depends on the stacking sequence, the pseudospin chirality sum is always $N$.
$N$-layer stacks have $N$ distinct Landau levels at E=0 for each spin and valley, and quantized Hall conductivity $\sigma_{xy} = \pm(4 e^2/h)(N/2+n)$ where $n$ is a non-negative integer.

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For recent technical and popular reviews see A. K. Geim and K. S. Novoselov, Nature Mat. 6
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The velocity of the J = 1 J=1 doublets is determined by the strength of the coupling between the odd-length chain zero-energy state and isolated states on the sublattice opposite to the chain ends. For a chain of length 2 N − 1 2N-1 , the chain’s zero-energy state has nonzero amplitude on the N N odd-index sites. The velocity is reduced from the single sheet velocity by a factor of M / N \sqrt{M/N} , where M M is the number of isolated sites opposite to the N N odd-index sites. In a similar manner, higher J J doublet Hamiltonians are sometimes altered by a multiplicative factor by perturbative coupling to smaller J J doublets as in the single reversed layer example

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