field lines/boundary condition

[Dipankar Saha]

Hi,
In atomically thin materials... field lines extend into the free space (unlike bulk materials).  Now, when we incorporate sufficiently large vacuum along the thickness as well as do consider the periodic boundary condition... what exactly happens  at the  material-vacuum interface (and, beyond)? Does it consider Laplace's equation in the ambient?

Best_
Dipankar   

[Petr Khomyakov]

If you impose periodic boundary conditions for a 2D system in the out-of-plane direction, you solve the Poisson equation for a distribution of positive (ions) and negative (electrons) charges with periodic boundary conditions, where the period of the electrostatic potential and charge density is given by the unit cell size in the out-of-plane direction.

In the ATK, you may also solve the Poisson equation on multigrid, imposing (non-periodic) boundary conditions such as Dirichlet, Neumann or mixed boundary conditions.

[Dipankar Saha]

where the period of the electrostatic potential and charge density is given by the unit cell size in the out-of-plane direction

Did you mean that the distribution of the charge (in the out-of-plane direction) is essentially confined by the cell size ??

Thanks and Regards_
Dipankar

[Jess Wellendorff]

That's right. If the vacuum region is too small, periodic BCs will lead to a periodic electron density that does not correctly vanish above/below a 2D sheet. If Dirichlet BCs are used, too small vacuum region will artificially "squeeze" the electron density above&/below the 2D sheet in order to force the density to zero at the boundary.

[Dipankar Saha]

Thank you Jess...