QuantumATK Forum

QuantumATK => General Questions and Answers => Topic started by: Cyrille on November 10, 2015, 14:12

Title: Adding a small imaginary part to Self-energy
Post by: Cyrille on November 10, 2015, 14:12

dear all

I was wondering if there was a "simple way" to tweak atk in order to add an imaginary part to the self-energies.
This could be a poorman solution to deal with various scattering processes...

thanks in advance

Cyrille

Title: Re: Adding a small imaginary part to Self-energy
Post by: Anders Blom on November 13, 2015, 11:10

Yes, I think we can make this quite easily. But, to verify it will fulfill your needs - would it be sufficient to have an imaginary external (diagonal) potential?

Title: Re: Adding a small imaginary part to Self-energy
Post by: Cyrille on November 13, 2015, 11:25

I was thinking that in a first very simple approximation I could just increase the "infinitesimal" value for the calculation of the self-energies.
If I understand well  it should add a constant (in energy but diagonal in "space") term.
Of course the next step could be to add a term that also depends on the energy!

Cyrille

Title: Re: Adding a small imaginary part to Self-energy
Post by: Cyrille on November 13, 2015, 14:57

One more question:

Is the infinitesimal parameter added only in the calculation of the Leads self-energies or is it also added in the calculation of the Central part Green function.
More precisely do you have
GC=(ES-H-SigmaL-SigmaR)^-1
or
GC=((E+i epsilon)S-H-SigmaL-SigmaR)^-1

Cyrille

Title: Re: Adding a small imaginary part to Self-energy
Post by: Jess Wellendorff on November 17, 2015, 12:08

The second equation looks right; the infinitesimal parameter enters the Green's function through the overlap matrix. But according to the ATK Reference Manual, this parameter has nothing to do with the the electrode self energy calculations, which are simply done using direct diagonalization or recursion: http://www.quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/chap.negf.html#sect1.negf.intro (http://www.quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/chap.negf.html#sect1.negf.intro)

Title: Re: Adding a small imaginary part to Self-energy
Post by: Cyrille on November 17, 2015, 15:51

Let me put my question more precise.
Where does the Infinitesimal parameter (set to 10^-6eV by default) enter?

If I am correct it enters as a small imaginary part in the calculation of the "surface"  Green functions used to obtain the self-energies.
But it does not enter in the Central Green function?

which reads:
GC(z=E+i epsilon)=1/(E-Sigma(E+i epsilon) )
and not
GC(z=E+i epsilon)=1/(E+i epsilon-Sigma(E+i epsilon) )

Cyrille