gftool.fcc_dos¶
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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
- dosfloat np.ndarray or float
The value of the DOS.
See also
gftool.lattice.fcc.dos_mpmulti-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()
