pythtb.models.checkerboard

checkerboard(delta, t)

Checkerboard tight-binding model.

Added in version 2.0.0.

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

\[\mathbf{a}_1 = (1, 0), \quad \mathbf{a}_2 = (0, 1)\]

and the orbital positions are given by,

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

The second-quantized Hamiltonian can be written as:

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

Parameters:

tfloat

Nearest neighbor hopping amplitude.

deltafloat

On-site energy. Positive for one sublattice, negative for the other.

Returns:

TBModel

An instance of the model.