gftool.square_dos

gftool.square_dos(eps, half_bandwidth)

DOS of non-interacting 2D square lattice.

Has a van Hove singularity (logarithmic divergence) at eps = 0.

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=D/4.

Returns:

float np.ndarray or float

The value of the DOS.

See also

gftool.lattice.square.dos_mp

Multi-precision version suitable for integration.

References

[economou2006]

Economou, E. N. Green’s Functions in Quantum Physics. Springer, 2006.

Examples

>>> eps = np.linspace(-1.1, 1.1, num=500)
>>> dos = gt.lattice.square.dos(eps, half_bandwidth=1)

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

(png, pdf)