gftool.triangular_dos

gftool.triangular_dos(eps, half_bandwidth)

DOS of non-interacting 2D triangular lattice.

The DOS diverges at -4/9*half_bandwidth. The DOS is evaluated as complete elliptic integral of first kind, see [kogan2021].

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 \(t=4D/9\).

Returns:

float np.ndarray or float

The value of the DOS.

See also

gftool.lattice.triangular.dos_mp

Multi-precision version suitable for integration.

References

[kogan2021]

Kogan, E. and Gumbs, G. (2021) 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=1000)
>>> dos = gt.lattice.triangular.dos(eps, half_bandwidth=1)

>>> import matplotlib.pyplot as plt
>>> _ = plt.axvline(-4/9, color='black', linewidth=0.8)
>>> _ = plt.axvline(0, 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()

(png, pdf)