The direction of effective mass analysis

[guodudu]

Hi, everyone

I saw that the two directions for calculating the effective mass in this tutorial are (101) and (110), and I think 101 is due to the fact that the X point is (1/2 0 1/2) in the article High-throughput electronic band structure calculations: Challenges and tools (DOI: 10.1016/j.commatsci.2010.05.010), but I can't understand the choice of the other direction, because the effective mass is related to the bandstructrue., so I think we should take the coordinates of the point L,since it is another point close to Γ. So it's 1/2, 1/2, 1/2 in fractional coordinates, it's 1, 1, 1.

 If I understand wrong, please point out my problem, I will be very grateful.Thank you very much.

[guodudu]

This is the k-points of the cell in the article and bandstructrue.

[Anders Blom]

No, the two masses are both computed at the X point. The 101 is for the longitudinal mass, as this direction points along G-X. The other direction is the transverse mass. To find the direction perpendicular to G-X you have to look in Cartesian space, and you can see directly from the two screenshots in the tutorial that "fractional 101" is along Cartesian [010], while "fractional 011" (equivalent to 110) is along Cartesian [100]. The L point is never involved in this example.

[guodudu]

Thank you very much.

So if i want to calculate the effective mass in the direction of the armchair and the zigzag, I just need to fill in the Cartesian coordinates of (0, 1, 0) and (1, 0, 0). It is a very simple question, but I still want to confirm it.

Thank you again.

[Anders Blom]

Well, just to be clear (for others reading this) my earlier comment was related to the representation of coordinates in reciprocal space only, which can be fractional (in units of the reciprocal lattice vectors) or Cartesian (in units of 1/x, 1/y, 1/z).

But yes, you are right of course, for an orthogonal cell it's all quite easy, esp. for the directions along the (reciprocal) cell axes.