gftool.sc_dos¶
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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.
Implements Eq. 7.37 from [joyce1973] for the special case of eps = 0, otherwise identical to -gf_z.imag/np.pi.
- 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
- dosfloat np.ndarray or float
The value of the DOS.
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()
