Dear Gabriel,
These matrix elements do not give you access to the density of states
inside the system.
All what you might have access to is the Transmission via the Fisher-Lee
formula or the density of states at the interface.
I hope this helps,
Adel
On Mon, Oct 2, 2023 at 8:58 PM Gabriel Garcia <gqgarci...@gmail.com> wrote:
> Hi devs,
>
> I have been studying Kwant, specifically, Green’s functions. I am trying
> to obtain the electron density from the definition of the correlation
> function. The code follows below,
>
> -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> data3 = []
> energies2 = []
>
> Es = np.linspace(0, 30, 100)
>
> for ie in Es:
> E = ie * 0.01
> G = kwant.greens_function(fsyst, E)
>
> # Funcoes de Green retardada indo da lead0 para lead1
> G_r = G.submatrix(1,0)
>
> # Funcao de Green avancada
> G_a = conj((G_r).T)
>
> # Self-energy da lead 0
> SigmaL_r = lead_0.selfenergy(E) # Retardada
> SigmaL_a = conj((SigmaL_r).T) # Avancada
>
> # Self-energy da lead 1
> SigmaR_r = lead_1.selfenergy(E) # Retardada
> SigmaR_a = conj((SigmaR_r).T) # Avancada
>
> # Matriz de Alargamento
> Gamma_L = 1j*(SigmaL_r-SigmaL_a) # referente a lead_0
> Gamma_R = 1j*(SigmaR_r-SigmaR_a) # referente a lead_1
>
> # Funcao de distribuicao de Fermi-Dirac em T=0
> f_L = np.heaviside(mu_L - E, 1)
> f_R = np.heaviside(mu_R - E, 1)
>
> # Funcao inscattering
> Sigma_in = (f_L)*(Gamma_L) + (f_R)*(Gamma_R)
>
> # Funcao de correlacao
> G_n = np.dot(np.dot(G_r, Sigma_in), G_a)
>
> data3.append(imag(np.trace(G_n)))
> energies2.append(E)
>
> plt.figure()
> plt.plot(energies2, data3)
> plt.xlabel("energy [eV]")
> plt.ylabel("electron density")
> plt.show()
>
> -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> >From this definition, is it possible to obtain this electron density as a
> function of the sites position? How can I do that?
>
> Best,
> Gabriel
>
--
Abbout Adel
