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I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by

$$H=-t\sum_\vec{R}|\vec R\rangle\langle \vec R+\vec \tau|+|\vec R\rangle\langle \vec R+\vec a+\vec \tau|+|\vec R\rangle\langle \vec R+\vec b+\vec \tau|+\text{h.c.}$$ where $t>0$ is a constant, $\vec a$ and $\vec b$ are the unit cell vectors for a two-atom unit cell, and $\vec \tau$ is the position of the second atom in the basis, the first atom being at the origin of the unit cell. The position of $\vec\tau$ is $\frac13(a,b)$ generalized over all space.

How can I interpret the different terms in the Hamiltonian as hopping processes?

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Hi mshossain12, this is a homework-like question and I've edited it to add the homework tag. You need to explain what you've done / tried and do your best to convert this to a conceptual question. –  Brandon Enright Nov 19 '13 at 21:35
    
What are $a$, $b$, and $\tau$? –  leongz Nov 20 '13 at 4:36
    
Sorry i should have made it clearer. a and b are the unit cell vectors. Its a two atom unit cell and Tau is the position of the second atom in the basis, the first atom being at the origin of the unit cell. tau's position is 1/3(a,b) generalized over all space. –  mshossain12 Nov 20 '13 at 14:08

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