[DFTB-Plus-User] R: DOS and Transmission units

Alessandro Pecchia alessandro.pecchia at cnr.it
Wed Feb 17 12:49:54 CET 2021


Dear  Théo Giverne,

'Transmission' is already a dimensionless quantity. It is the transmission of all travelling states at a given energy, E. 
Mind however that, as defined in most literature of transport, T(E) is the quantity entering the Landauer formula for current, J = 2e/h Integral[ T(E) (f1(E) - f2(E)) dE ].  This means that the T(E) contains the number of states. For a perfectly ideal system it counts the number of bands at a given energy. This also means that T(E) is size-dependent. It depends on cross-section of the conductor.

Concerning the density of states computed by TunnelingAndDos, this is the "trace" of the Retarded Green's function on the central region.  DOS(E) = -1/pi Im{Trace[GR(E)]}

The PDOS is the projection on given atoms/orbitals obtained by sub-tracing the matrix on related atoms/orbitals, such that for instance:
PDOS(atom==n, E) = -1/pi Im{ Sum_i GR_ii(E)},   where i are the orbitals of atom n.

HOWEVER, it should be noted that integrating this quantity over E does *not* give back exactly the number of electrons in the central region. In order to sum-up to N, the correct formula should be:
PDOS(atom==n, E) = -1/pi Im{ Sum_i Sum_j GR_ij(E) S_ji}, where S_ij is the overlap matrix.

This was not done because internally GR is restricted to the central region, whereas the sum over j should extend to overlapping regions between central and contacts. In order to get the overlapping parts of GR more computations are needed. Note that such an extra work was done for the density matrix in order to compute correct SCC charges.  

It should be said that the DOS computed neglecting the overlap reproduces the main information needed to correlate the transmission to the electronic states and localization. 

Regards,

A Pecchia






 


  


-----Messaggio originale-----
Da: DFTB-Plus-User [mailto:dftb-plus-user-bounces at mailman.zfn.uni-bremen.de] Per conto di Théo Giverne
Inviato: mercoledì 17 febbraio 2021 10:58
A: User list for DFTB+ related questions
Oggetto: Re: [DFTB-Plus-User] DOS and Transmission units

Dear users,

Where can I find in what unit are normalised DOS and Transmission. Without this information the DOS and Transmission are practically useless as they can’t be que quantitatively but only qualitatively.
Your answer will be greatly appreciate, thank you,

Sincerely,

Théo Giverne

theo.giverne at etu.u-bordeaux.fr



> Le 11 févr. 2021 à 11:05, Théo Giverne <theo.giverne at etu.u-bordeaux.fr> a écrit :
> 
> Dear users,
> 
> I am currently using the DOS and Transmission results from DFTB+ do obtain some electronic properties.
> However I need to know in what units DFTB+ gives the DOS and the Transmission, I couldn’t find any information on this matter, does anyone have a clue ?
> 
> Thank you,
> 
> Sincerely,
> 
> Théo Giverne
> 
> theo.giverne at etu.u-bordeaux.fr
> 
> 
> 
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