k points sampling and system size

[huge]

Dear all,
    I have two questions about the k points sampling when calculating the transmission.
    1.According to the Bloch theorem, Does the number of k points in one direction(such as x direction) depend on the number of the unit cells in x? 
    2.Can the number of k points sampled in calculation reflect the system size(the number of the unit cells), or just affect the precision of calculation?

      Could you give me some advises?

Thanks in advance for your help,
Huge

[zh]

The denseness (or size of grid) of k point sampling depends on the size of  Brillouin zone, which is reciprocal to the size of unit cell. In practice, the denseness of k point sampling is not automatically chosen by the computational code and it is alternatively chosen by the user according to the desired accuracy. Therefore, the size of k point sampling used in the calculation cannot reflect the system size.

[huge]

Mr.Zh,
   Thank you for your instructive reply.
     
    In a finite system, The period boundary condition(PBC) and Bloch's theorem tell us the number of allowed k points is related to the system size. If I calculate a very large system(such as 100*100 unit cells in transverse plane) ,whose supercell is too large to calculate directly,can I just build a bulk model and sample  the k points by 100*100 to estimate the result? Of course the boundary influence is ignored here.
     Thanks a lot!
     Huge
   

[zh]

For a finite system,  it can be simulated by a supercell with sufficiently large lattice constant or by an isolated system with open boundary condition for the electrostatic potential. In the former case,  only one k point (e.g., usually Gamma point) is enough . There is no k point sampling in the latter case.

" If I calculate a very large system(such as 100*100 unit cells in transverse plane) ,whose supercell is too large to calculate directly,can I just build a bulk model and sample  the k points by 100*100 to estimate the result?"

You cannot.

As already pointed out, the size of k point sampling does not reflect the simulated system size.