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 $


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

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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

  • 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


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