gftool.lattice.kagome.dos
- gftool.lattice.kagome.dos(eps, half_bandwidth)[source]
DOS of non-interacting 2D kagome lattice.
The delta-peak at eps=-2*half_bandwidth/3 is ommited and must be treated seperately! Without it, the DOS integrates to 2/3.
Besides the delta-peak, the DOS diverges at eps=0 and eps=2*half_bandwidth/3.
The Green’s function and therefore the DOS of the 2D kagome lattice can be expressed in terms of the 2D triangular lattice
gftool.lattice.triangular.dos
, see [kogan2021]. Omitting the non-dispersive peak, it corresponds togftool.lattice.honeycomb.dos
shifted by half_bandwidth/3.- Parameters:
- epsfloat np.ndarray or float
DOS is evaluated at points eps.
- half_bandwidthfloat
Half-bandwidth of the DOS, DOS(eps < -2/3`half_bandwidth`) = 0, DOS(4/3`half_bandwidth` < eps) = 0. The half_bandwidth corresponds to the nearest neighbor hopping \(t=2D/3\).
- Returns:
- float np.ndarray or float
The value of the DOS.
See also
gftool.lattice.kagome.dos_mp
Multi-precision version suitable for integration.
gftool.lattice.triangular.dos
gftool.lattice.honeycomb.dos
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
>>> eps = np.linspace(-1.5, 1.5, num=1001) >>> dos = gt.lattice.kagome.dos(eps, half_bandwidth=1)
>>> import matplotlib.pyplot as plt >>> for pos in (-2/3, 0, +2/3): ... _ = plt.axvline(pos, color='black', linewidth=0.8) >>> _ = plt.plot(eps, dos) >>> _ = plt.xlabel(r"$\epsilon/D$") >>> _ = plt.ylabel(r"DOS * $D$") >>> _ = plt.ylim(bottom=0) >>> _ = plt.xlim(left=eps.min(), right=eps.max()) >>> plt.show()