gftool.lattice.honeycomb.gf_z

gftool.lattice.honeycomb.gf_z(z, half_bandwidth)

Local Green’s function of the 2D honeycomb lattice.

The Green’s function of the 2D honeycomb lattice can be expressed in terms of the 2D triangular lattice gftool.lattice.triangular.gf_z, see [horiguchi1972].

The Green’s function has singularities at z=±half_bandwidth/3.

Parameters

zcomplex np.ndarray or complex

Green’s function is evaluated at complex frequency z.

half_bandwidthfloat

Half-bandwidth of the DOS of the honeycomb lattice. The half_bandwidth corresponds to the nearest neighbor hopping \(t=2D/3\).

Returns

gf_zcomplex np.ndarray or complex

Value of the honeycomb lattice Green’s function

See also

gftool.lattice.triangular.gf_z

References

horiguchi1972

Horiguchi, T., 1972. Lattice Green’s Functions for the Triangular and Honeycomb Lattices. Journal of Mathematical Physics 13, 1411–1419. https://doi.org/10.1063/1.1666155

Examples

>>> ww = np.linspace(-1.5, 1.5, num=501, dtype=complex) + 1e-64j
>>> gf_ww = gt.lattice.honeycomb.gf_z(ww, half_bandwidth=1)

>>> import matplotlib.pyplot as plt
>>> _ = plt.axhline(0, color='black', linewidth=0.8)
>>> _ = plt.plot(ww.real, gf_ww.real, label=r"$\Re G$")
>>> _ = plt.plot(ww.real, gf_ww.imag, '--', label=r"$\Im G$")
>>> _ = plt.ylabel(r"$G*D$")
>>> _ = plt.xlabel(r"$\omega/D$")
>>> _ = plt.xlim(left=ww.real.min(), right=ww.real.max())
>>> _ = plt.legend()
>>> plt.show()

(png, pdf)