Dear Mohammad - well, this is a nice simple exercise in direct/reciprocal cells.
Let "a" be the C-C distance (as assumed in the the small-supercell input), then the supercell translation vectors (in the graphene plane) are: AA = [3a,0]; BB = [0, 2a*sqrt(3)] and the reciprocal lattice vectors : AA_inv = [2*pi/(3*a), 0]; BB_inv = [0, pi/(a*sqrt(3))]. Whereas translation vectors of the graphene primitive cell in the same setting, not moving any atoms and not rotating anything, are, for example: A = a/2[3, sqrt(3)]; B=a/2[-3, sqrt(3)]. Their respective reciprocal vectors are: A_inv = (2*pi)/(3*a)[1, sqrt(3)]; B_inv = (2*pi)/(3*a)[-1, sqrt(3)]. With these, you can draw the Brillouin zone and check where the K points are. There are six around Gamma: (2*pi)/(3*a)[(+/-)1, (+/-)1/sqrt(3)] and (2*pi)/(3*a)[0, (+/-)2/sqrt(3)]. They are expressed in terms of the supercell reciprocal vectors as follows: (+/-)AA_inv (+/-)2/3*BB_inv and (+/-)4/3*BB_inv . In other words, the K points are mapped onto (+/-)1/3*BB_inv. So if your k-lattice division includes (0, 1/3) without shift it will for sure hit a K-point. Now, a solution to your problem: - Choose the number of divisions along BB_inv [the third line in the setting chosen, as the graphene plane is (y,z)] divisible by 3; - To get an isotrope k-sampling in the (y,z) plane, choose the number of divisions along AA_inv [the third line] larger than that along BB_inv - not 2 times larger than in your case, just ~2/sqrt(3); - add no shift. Good luck. Andrei Postnikov > Dear all, > > I would be thankful if you help me with this question. Namely, I am > studying a graphene TranSIESTA example located at > http://dipc.ehu.es/frederiksen/tstutorial/index.php/Graphene. A > tarball is provided there which contains two folders to calculate the > transmission of graphene sheet. My question is regarding the > calculations in the "small-supercell" folder. Particularly, after the > scattering calculation is finished, when I use tbtrans to calculate > the transmission, if I change the Monkhorst-Pack sampling in the .fdf > file to the following: > > %block kgrid_Monkhorst_Pack > 1 0 0 0.0 > 0 20 0 0.0 > 0 0 10 0.0 > %endblock Kgrid_Monkhorst_Pack > > the transmission "does not come to zero at zero energy". But "it comes > to zero when using the original Monkhorst-Pack grid", i.e. : > > %block kgrid_Monkhorst_Pack > 1 0 0 0.0 > 0 20 0 0.5 > 0 0 10 0.5 > %endblock Kgrid_Monkhorst_Pack > > As can be seen, I have only changed the values of displacements in the > %block kgrid_Monkhorst_Pack and nothing else was changed in the .fdf > file. Apparently, by changing the displacements, I have missed the K > point of graphene but I can not figure out the mechanism of this. Any > help to clarify what is going on is indeed welcome. > > Bests, > Mohammad, >
