gftool.lattice.lieb.gf_z

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

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

The Green’s function of the 2D Lieb lattice can be expressed in terms of the 2D square lattice gftool.lattice.square.gf_z, and a non-dispersive peak, see [kogan2021].

The Green’s function has singularities for z/half_bandwidth in [-2**-0.5, 0, 2**-0.5].

Parameters

zcomplex np.ndarray or complex

Green’s function is evaluated at complex frequency z.

half_bandwidthfloat

Half-bandwidth of the DOS of the Lieb lattice. The half_bandwidth corresponds to the nearest neighbor hopping t=D * 2**1.5.

Returns

gf_zcomplex np.ndarray or complex

Value of the Lieb lattice Green’s function

See also

gftool.lattice.square.gf_z

References

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.lieb.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=-5.0, top=5.0)
>>> _ = plt.legend()
>>> plt.show()

(png, pdf)