0
$\begingroup$

I am trying to calculate numerically a current from the given Green's function. I am aware that to calculate density of states of a Green's function I must do the integral as follows:

$ \tag1\ DOS(E) =\frac{ -1 }{2*\pi^2}*Im*\int_{-\pi}^{\pi}G(E,k)*dk $

and,

$ \tag2\ G(E) =\frac{ 1 }{E-i*n-2*cos(k)} $

enter image description here

is a Green's advanced function. Equation (1) and (2) shows how to calculated DOS using the integral. To calculate current for simple two contacts model of quantum transport I assume the following equation:

$ \tag3\ I(V) =\frac{ 2*e }{h}*Re\int_{-\infty}^{\infty}T(E)*(F(E-V)-F(E))*dE $

and T(E) is the transmitance function expressed in terms of Gamma's and Retarded/Advanced Green's function. My question is that in order to calculate current numerically do I have to do one integral over dE and keeping k constant at some value or do I have to do double integral (first one over dk and second integral over dE)? Both give me same results in curve plot (I-V line going through (0,0) but amplitudes are different)

enter image description here

$ \tag4\ I(V) =\frac{ 2*e }{h}*Re\int_{-\infty}^{\infty}T(E)*(F(E-V)-F(E))*dE, and: k-constant$

enter image description here

$ \tag5\ I(V) =\frac{ 2*e }{h}*Re\int_{-\infty}^{\infty}*(\int_{-\pi}^{\pi}T(E)*(F(E-V)-F(E))*dk)*dE$

enter image description here

$\endgroup$
2
  • 1
    $\begingroup$ I'm not used to see such codings on this website, perhaps could you present your question with the physical concepts instead of a code? $\endgroup$
    – gingras.ol
    Jul 7, 2017 at 21:11
  • $\begingroup$ @gingras.ol, Thanks for reply. I removed the code and added physical concepts as you suggested. $\endgroup$
    – Aschoolar
    Jul 8, 2017 at 16:06

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.