Dear Juan,
I'm not sure what you mean by shape. Are you asking why it's lifted off
the horizontal axis?
It is lifted off the horizontal axis to ensure that the Green's function
behaves smoothly away from the real axis, allowing for a nice numerical
scheme for the integration. You give the distance as a number of poles
of the Fermi-Dirac distribution because Cauchy's theorem tells you that
the integral of a contour is the sum of the enclosed residues, which are
determined by the poles in the integrand.
This is pretty much the discussion Brandbyge has in the PRB paper you
cite, on pages 4 and 5.
If the complex integration is troubling you, you may want to read up on
Cauchy's theorem. Also, the important thing about the Fermi-Dirac
distribution, in this case, is just the location of its poles, which
should be evident by inspection of the function.
Hope this helps,
-Jonathan
On 06/01/2012 10:09 AM, Juan Manuel Aguiar wrote:
Dear Users,
Can I assume that nobody understands this issue or knows a reference?
Sincerely
Juan Manuel
On Thu, May 31, 2012 at 4:47 PM, Juan Manuel Aguiar
<[email protected]> wrote:
Dear Siesta Users,
I'm trying to understand the particular shape chosen for the contour
integration for the density matrix in transiesta. I've already read
the paper where the method is explained [Phys. Rev. B 65, 165401
(2002); pag 5, fig 2] but there the contour is only mentioned, not
explained. I didn't find this contour in the literature I've found
about contour integration in NEGF calculations.
I think that the answer must be very easy for the well documented
user, so I ask you to share with me your knowledge or a reference
where this particular shape for the contour integration is justified.
Regards
Juan Manuel
