unit of transmission spectrum and DOS

[jchang]

Hi,

I have a question about the unit of transmission in the example below.

https://docs.quantumwise.com/tutorials/transmission_gr_mos2/transmission_gr_mos2.html

In this example, we calculate transmission of rectangular unit cell of graphene and MoS2.
In the graphene example, it shows how transmission spectrum changes with the number of k-points in the transverse modes.
And my question is what is the unit of Transmission.
Since it is a periodic structure in the transverse direction, transmission unit should be #/m or #/um, but the picture showing transmission it is not clear.

Is the default unit in the transmission spectrum just # or #/m?
If it is just #, then I guess we need to divide it with the length of rectangular unit cell in the transverse direction (y-direction).


I also have similar question for DOS calculation.
If I calculate DOS for 2-D material, then the unit for the calculated DOS in ATK is just #/eV or is it normalized with area?

Thanks.
jiwon

[Petr Khomyakov]

Transmission coefficient is unitless physical quantity, and it is computed per lateral unit cell of the scattering region, i.e., if you, for instance, double the lateral unit cell size in your transport calculations, the transmission will then increase by factor of 2. 

In the Landauer-Buttiker formalism for the electron transport, total transmission can also be seen as conductance in units of G_0, https://en.wikipedia.org/wiki/Conductance_quantum.       

DOS is given in # of states per eV (per unit cell, not unit cell area). Integration of DOS  x Fermi-Dirac distribution (at a given temperature and Fermi energy) over the  energy should  give you the number of electrons (per unit cell) in the system.   

[jchang]

Thanks for the fast response.
So, you are saying that the transmission and DOS value from ATK is not normalized by length or area.

Thanks.
jiwon

[Petr Khomyakov]

Yes, that is correct.