gftool.lattice.lieb.gf_z
- gftool.lattice.lieb.gf_z(z, half_bandwidth)[source]
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:
- complex np.ndarray or complex
Value of the Lieb lattice Green’s function.
See also
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()