Rectangular supercell bandstucture error

[ams_nanolab]

The band structure of strained monolayer MoS2 in rectangular unit cell in the paper by

P. Lu, X. Wu, W. Guo, and X.C. Zeng, Physical Chemistry Chemical Physics : PCCP 14, 13035 (2012). (doi:10.1039/C2CP42181J)

shows the CB minima and the VB maxima for the unstrained case somewhere between the G and M points. Looking at the structure i feel the process of mapping the symmetry points for the rectangular supercell to the G-M-K-G path for hexagonal may not be equivalent to the G-M-K-G path of the original hexagonal unit cell.

This is more true for the strained case as the symmetry points G-M-K-G and G-M'-K'-G (Fig-1) would no longer be equivalent in such a case.

Thus if we use the script in
http://quantumwise.com/forum/index.php?topic=2096.msg9927#msg9927
to override the symmetry points, then the mapping would not be accurate. 

(I have also verified it by simulating uniaxial strain for the hexagonal and the rectangular unit cells using the override script mentioned, and the results clearly show the mapping of G-M-K-G path no longer holds. see Fig-2)

This is also corroborated by the paper
T. Li, Phys Rev B., 85, 235407(2012) (DOI: 10.1103/PhysRevB.85.235407)
where even after applying strain the CM min and the VB max remain at the K points of the BZ, and the bandstructure is shown for the
M'-G-M-K-G-K' path (Fig. -3)


Could you kindly make a script so as to map the points M' and K' correctly? Or do we have to use hexagonal cell only?

[ams_nanolab]

Could you provide me the exact co-ordinates of the G,M,K,M' and K' in ATK, then I can myself make a script.

[Anders Blom]

This whole task is quite tricky, I've been thinking about it but haven't had time to go deeper.

The coordinates of the symmetry points are universal and not different in ATK than anywhere else:

G = (0,0,0)
M = (0,1/2,0)
M' = (1/2,0,0)
K = (1/3,1/3,0)
K' = (-1/3,1/3,0)

[ams_nanolab]

Okay I'll make a script and post it for ur consideration. 

[ams_nanolab]

I'm trying with this script to set the path, for hexagonal cell it works fine but with supercell things still seem to go awry. 

[zh]

The high symmetry k points for hexagonal unit cell cannot be directly used in the band structure calculation of a rectangular unit cell.

If the rectangular unit cell is taken with the following  unit vectors: a1 = (sqrt(3)* a, 0, 0); a2=(0, 3*a, 0); a3=(0, 0, c), where a is the lattice constant of graphene sheet, the line along Gamma---> Y (0.0, 0.5, 0.0) in the BZ of rectangular unit cell is parallel to the line along Gamma--M' (0.0, 0.5, 0.0) in the BZ of a hexagonal unit cell, also the line along Gamma--->X(0.5, 0.0, 0.0) in the BZ of  rectangular unit cell is parallel to the line along Gamma-->K(2/3, -1/3, 0) in the BZ of a hexagonal unit cell. Here the fractional coordinates of M' and K in the BZ of a hexagonal unit cell [a1= (a, 0, 0); a2= (-1/2 *a, sqrt(3)/2 *a, 0); a3=(0,0,c)] are given according to the BZ in Fig1-1.jpg. To map the coordinates of k points of rectangular unit cell with those of a hexagonal unit cell, it may be better to first transform the above fractional coordinates of k points  to their Cartesian coordinates, and then to use
them in the band structure calculations.

[ams_nanolab]

I am attaching the two configurations herewith, could you kindly make a script so I get the same type bandstructure from the two?