pythtb.models.graphene

graphene(delta, t)

Graphene tight-binding model.

Added in version 2.0.0.

This function creates a graphene tight-binding model with the specified hopping parameters and on-site energy. The model is defined on a 2D honeycomb lattice with two sublattices. The lattice vectors are given by,

\[\mathbf{a}_1 = a(1, 0), \quad \mathbf{a}_2 = a\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right),\]

and the orbital positions are given by,

\[\mathbf{\tau}_1 = \frac{1}{3} \mathbf{a}_1 + \frac{1}{3} \mathbf{a}_2, \quad \mathbf{\tau}_2 = \frac{2}{3} \mathbf{a}_1 + \frac{2}{3} \mathbf{a}_2\]

The second-quantized Hamiltonian can be written as:

\[H = \Delta \sum_i n_i + t \sum_{\langle i,j \rangle} (c_i^\dagger c_j + \text{h.c.})\]

Parameters:

deltafloat

On-site energy difference between the two orbitals.

tfloat

Hopping parameter between nearest neighbor orbitals.

Returns:

TBModel

An instance of the model.