Hi there, I am reading the book "Condensed Matter Physics" second edition by Michael P. Marder. It stated in page 9 that one basis of the the honeycomb lattice is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\vec{v}_1 = a [0 \ 1/(2\sqrt{3})], \qquad

\vec{v}_2 = a [0 \ -1/(2\sqrt{3})]

[/tex]

which is based on figure 1.5(B) in page 10. But in that case when two (vertical) atoms are bind together, so should this basis be

[tex]

\vec{v}_1 = a [0 \ \sqrt{3}/2], \qquad

\vec{v}_2 = a [0 \ -\sqrt{3}/2]

[/tex]

By the way, why the primitive vectors are given as that in 1.6a and 1.6b

[tex]

\vec{v}_1 = (1/6 \ 1/6) , \qquad \vec{v}_2 = (-1/6 \ -1/6)

[/tex]

it said [tex](\vec{a}_1 + \vec{a}_2)/6 = \vec{v}_1[/tex]

But

[tex]

\vec{a}_1 = a(1 \ 0), \qquad \vec{a}_2 = a (1/2 \ \sqrt{3}/2)

[/tex]

why [tex](\vec{a}_1 + \vec{a}_2)/6 = \vec{v}_1[/tex]?

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# About basis of the honeycomb lattice

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