gftool.lattice.lieb.dos

gftool.lattice.lieb.dos(eps, half_bandwidth)

DOS of non-interacting 2D Lieb lattice.

The delta-peak at eps=0 is ommited and must be treated seperately! Without it, the DOS integrates to 2/3.

Besides the delta-peak, the DOS diverges at eps=±half_bandwidth/2**0.5.

The Green’s function and therefore the DOS of the 2D Lieb lattice can be expressed in terms of the 2D square lattice gftool.lattice.square.dos, see [kogan2021].

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 * 2**1.5.

Returns:

float np.ndarray or float

The value of the DOS.

See also

gftool.lattice.lieb.dos_mp

Multi-precision version suitable for integration.

gftool.lattice.square.dos

References

[kogan2021]

Kogan, E., Gumbs, G., 2020. Green’s Functions and DOS for Some 2D Lattices. Graphene 10, 1–12. https://doi.org/10.4236/graphene.2021.101001

Examples

>>> eps = np.linspace(-1.5, 1.5, num=1001)
>>> dos = gt.lattice.lieb.dos(eps, half_bandwidth=1)

>>> import matplotlib.pyplot as plt
>>> for pos in (-2**-0.5, 0, +2**-0.5):
...     _ = plt.axvline(pos, 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)