gftool.fcc_dos

gftool.fcc_dos(eps, half_bandwidth)

DOS of non-interacting 3D face-centered cubic lattice.

Has a van Hove singularity at z=-half_bandwidth/2 (divergence) and at z=0 (continuous but not differentiable).

Parameters:

epsfloat np.ndarray or float

DOS is evaluated at points eps.

half_bandwidthfloat

Half-bandwidth of the DOS, DOS(eps < -0.5*`half_bandwidth`) = 0, DOS(1.5*`half_bandwidth` < eps) = 0. The half_bandwidth corresponds to the nearest neighbor hopping t=D/8.

Returns:

float np.ndarray or float

The value of the DOS.

See also

gftool.lattice.fcc.dos_mp

Multi-precision version suitable for integration.

References

[morita1971]

Morita, T., Horiguchi, T., 1971. Calculation of the Lattice Green’s Function for the bcc, fcc, and Rectangular Lattices. Journal of Mathematical Physics 12, 986–992. https://doi.org/10.1063/1.1665693

Examples

>>> eps = np.linspace(-1.6, 1.6, num=501)
>>> dos = gt.lattice.fcc.dos(eps, half_bandwidth=1)

>>> import matplotlib.pyplot as plt
>>> _ = plt.axvline(0, color='black', linewidth=0.8)
>>> _ = plt.axvline(-0.5, 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)