I am having trouble understanding how to calculate the energy dispersion relation $E(\vec{k})$ in a given direction within the first Brillouin zone.I can find the vectors in the reciprocal lattice. Any pointers?
Thank you
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$\begingroup$ Did the answer helped or not? $\endgroup$– LaurierCommented Apr 7, 2023 at 12:53
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1 Answer
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If I understand your question correctly; you'll have to compute de value of $E(\mathbf{k})$ for a given vector composed of $k_{i}$ (i=x,y,z), as the result will be the energy and the $k_{i}$ the direction.
An example would be the square lattice of size $a\times a$ with a dispersion relation of $E(\mathbf{k}) = -\frac{E_{0}}{4} (\cos(k_{x}a) +\sin(k_{y} a))$ gives
Hope it helps, cheers
