[Wannier] ab initio based Tight binding model

[Jonathan Yates]

On 7 Apr 2010, at 15:46, Elie Moujaes wrote:

> Dear Wannier90 users,
>
> I have two simple questions:
>
> (1)  What is the difference between the ab initio Tight binding  
> model (derived using the Wannier90 localized functions) and the  
> usual Tight binding model based on number of nearest or next nearest  
> neighbours..etc?

In terms of the formalism, they are very similar.

The Wannier approach provides one way to obtain a set of TB matrix  
elements. The idea is to obtain the matrix elements such that the ab- 
initio results are reproduced for a given atomic configuration - even  
if this may require a large number of nearest neighbours.


>  (2) Would the band structure (say of graphene) differ using ab  
> initio TB model (WANNIER90 code) from the one obtained using PW code  
> although both start with self consistent calculations.

Figure 3 of Computer Physics Communications 178, 685 (2008) shows a  
comparison of a graphite band structure from W90 and from PWSCF.

In the limit of MLWF obtained from an ab-initio calculation with  
infinite k-point sampling they would be identical. At finite k-point  
sampling (ie any practical calculation) the band structures will  
differ - however, the difference will decrease exponentially as the k- 
point sampling is increased.

  This is discussed in Phys. Rev. B 75, 195121 (2007) - particularly  
the appendix.

Yours
   Jonathan

-- 
Department of Materials, University of Oxford, Parks Road, Oxford, OX1  
3PH, UK
tel: +44 (0)1865 612797                http://users.ox.ac.uk/~oums0549/