gftool.honeycomb_dos

gftool.honeycomb_dos(eps, half_bandwidth)

DOS of non-interacting 2D honeycomb lattice.

The DOS diverges at eps=±half_bandwidth/3. The Green’s function and therefore the DOS of the 2D honeycomb lattice can be expressed in terms of the 2D triangular lattice gftool.lattice.triangular.dos, see [horiguchi1972].

Parameters:

epsfloat np.ndarray or float

DOS is evaluated at points eps.

half_bandwidthfloat

Half-bandwidth of the DOS, DOS(| eps | > half_bandwidth) = 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.honeycomb.dos_mp

Multi-precision version suitable for integration.

gftool.lattice.triangular.dos

References

[horiguchi1972]

Horiguchi, T., 1972. Lattice Green’s Functions for the Triangular and Honeycomb Lattices. Journal of Mathematical Physics 13, 1411–1419. https://doi.org/10.1063/1.1666155

Examples

>>> eps = np.linspace(-1.5, 1.5, num=501)
>>> dos = gt.lattice.honeycomb.dos(eps, half_bandwidth=1)

>>> import matplotlib.pyplot as plt
>>> for pos in (-1/3, 0, +1/3):
...     _ = 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()

(png, pdf)