gftool.lattice.kagome.gf_z

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

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

The Green’s function of the 2D kagome lattice can be expressed in terms of the 2D triangular lattice gftool.lattice.triangular.gf_z, and a non-dispersive peak, see [kogan2021]. Omitting the non-dispersive peak, it corresponds to gftool.lattice.honeycomb.gf_z shifted by half_bandwidth/3.

The Green’s function has singularities for z/half_bandwidth in [-2/3, 0, 2/3].

Parameters:

zcomplex np.ndarray or complex

Green’s function is evaluated at complex frequency z.

half_bandwidthfloat

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

Returns:

complex np.ndarray or complex

Value of the kagome lattice Green’s function.

See also

gftool.lattice.triangular.gf_z

References

[varm2013]

Varma, V.K., Monien, H., 2013. Lattice Green’s functions for kagome, diced, and hyperkagome lattices. Phys. Rev. E 87, 032109. https://doi.org/10.1103/PhysRevE.87.032109

[kogan2021]

Kogan, E., Gumbs, G., 2020. Green’s Functions and DOS for Some 2D Lattices. Graphene 10, 1–12. https://doi.org/10.4236/graphene.2021.101001

Examples

>>> ww = np.linspace(-1.5, 1.5, num=1001, dtype=complex) + 1e-4j
>>> gf_ww = gt.lattice.kagome.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.ylim(bottom=-5, top=5)
>>> _ = plt.legend()
>>> plt.show()

(png, pdf)