transmission spectrum and transmission coefficients

[kaypu]

i'm a rookie
canyou tell me the diffenence between the transmission spectrum and transmission coefficients
i think the transmission coefficients is calculated in a fixed energy (such as E=0),but the transmission spectrum is calculated in a energy range(such as -2ev to 2ev),if i choose the energy range from 0ev to 0ev. at this time, are they equal to each other??
 thank you

[Nordland]

Yes, with a small but. You have to add all the transmission coefficients together to get the full transmission which is calculated in the transmission spectrum.

[Anders Blom]

Sometimes a formula helps. The transmission spectrum T(E) is the integrated transmission coefficients T(E,k) over the 2D Brillouin zone of incident wave vectors k. That is,

[tex]T(E)=\int d\mathbf{k} T(E,\mathbf{k})[/tex]

Of course, in reality the integral is performed as a sum over k-points, that's why you specify the k-point sampling for the transmission spectrum.

[pengdou]

The transmission spectrum T(E) is the integrated transmission coefficients T(E,k) over the 2D Brillouin zone of incident wave vectors k.

Dear Anders Blom,

   I have just recently raised a similar question on one dimensional transport problem("http://quantumwise.com/forum/index.php?topic=896.0"). Both kstokbro and zh explained that  for me.  In my unstanding about their two explanations, the transmission spectrum T(E) is the integrated transmission coefficients T(E,k) not only over the 2D Brillouin zone, but also over the kz direction which is perpendicular to the  2D Brillouin zone.
   So in one dimensional transport problem, the electron tunnel only through the gamma point which is degenerated from the 2D Brillouin zone, but the transmission spectrum T(E) is the integrated transmission coefficients over the kz direction(from 0 to [tex]\pi[/tex]/Lz)?

[Anders Blom]

You could say that, provided you only pick those kz points which give the specific energy E in the band structure E(kz). However, you cannot define a transmission coefficient for a specific kz, since there is no periodicity in the Z direction and hence kz is not a good quantum number. So the picture you paint is only useful when trying to figure out which states in the electrode band structure that contribute to the transport.

[pengdou]

You could say that, provided you only pick those kz points which give the specific energy E in the band structure E(kz). However, you cannot define a transmission coefficient for a specific kz, since there is no periodicity in the Z direction and hence kz is not a good quantum number. So the picture you paint is only useful when trying to figure out which states in the electrode band structure that contribute to the transport.

   I see. Thanks a lot!

[1ight0ne]

Hello! Can you tell me why coef. T(E) in this example above 1 and its 3 ?

[Anders Blom]

T(E) is not restricted to be less than one. Each eigenchannel can at most contribute 1, but there may be several channels (px and py orbitals for instance) at any given energy.