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I am trying to understand how to find the $k$-Path of high symmetry points in the 1st Brillouin Zone. Can someone explain to me what does $$\Gamma-X-U \space|\space K-\Gamma-L-W-X $$ mean for the case of FCC's Irreducible Brillouin Zone?

  • 3
    $\begingroup$ There is no unique choice for K-paths along the high-symmetry points. It's often a matter of choice. For example for the fcc crystal system of Si/Ge, they often choose a k-path with only L,$\Gamma$,X because these are the lowest conduction bands of interest. $\endgroup$
    – Simon
    Feb 19, 2021 at 19:59
  • $\begingroup$ I see. Thank you. $\endgroup$
    – C.C.
    Feb 20, 2021 at 8:48

1 Answer 1


The high symmetry points are labelled in the Table in your screenshot in the fourth column. $\Gamma$-X-U means the path going from $\Gamma$ to X and then on to U. In the reference you took the screenshot from (Setyawan Curtarolo), you can look up the definition of the reciprocal lattice vectors b1,b2,b3. Then you can determine explicitly the points along the high symmetry path $\Gamma$-X-U.


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