gftool.sc_dos

gftool.sc_dos(eps, half_bandwidth=1)

Local Green’s function of 3D simple cubic lattice.

Has a van Hove singularity (continuous but not differentiable) at abs(eps) = D/3.

Parameters

epsfloat np.ndarray or float: DOS is evaluated at points eps.
half_bandwidthfloat: Half-bandwidth of the DOS of the simple cubic lattice. The half_bandwidth corresponds to the nearest neighbor hopping \(t=D/6\).

Returns

float np.ndarray or float: The value of the DOS.

Notes

Around eps=0 the expansion Eq. (5.4) using Eq. (7.37) from [joyce1973] is used. Otherwise, it is identical to -gf_z.imag/np.pi

References

economou2006: Economou, E. N. Green’s Functions in Quantum Physics. Springer, 2006.
joyce1973: G. S. Joyce, Phil. Trans. of the Royal Society of London A, 273, 583 (1973). https://www.jstor.org/stable/74037
katsura1971: S. Katsura et al., J. Math. Phys., 12, 895 (1971). https://doi.org/10.1063/1.1665663

Examples

>>> eps = np.linspace(-1.1, 1.1, num=501)
>>> dos = gt.lattice.sc.dos(eps)

>>> import matplotlib.pyplot as plt
>>> _ = plt.axhline(0, color="black", linewidth=0.8)
>>> _ = plt.axvline(-1/3, color="black", linewidth=0.8)
>>> _ = plt.axvline(+1/3, color="black", linewidth=0.8)
>>> _ = plt.plot(eps, dos)
>>> _ = plt.xlabel(r"$\epsilon/D$")
>>> _ = plt.ylabel(r"DOS * $D$")
>>> _ = plt.xlim(left=eps.min(), right=eps.max())
>>> plt.show()

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