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 <gqgarcia99@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()
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>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