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,
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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