pythtb.models.haldane#
- haldane(delta, t1, t2, phi=1.5707963267948966)[source]#
Haldane tight-binding model.
Added in version 2.0.0.
This function creates a Haldane 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,
\[\mathbf{a}_1 = (1, 0), \quad \mathbf{a}_2 = \left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)\]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:
\[H = \Delta \sum_i (-)^i c_i^\dagger c_i + t_1 \sum_{\langle i,j \rangle} (c_i^\dagger c_j + \text{h.c.}) + t_2 \sum_{\langle\langle i,j \rangle\rangle} (ic_i^\dagger c_j + \text{h.c.})\]- Parameters:
- deltafloat
Onsite mass term. Opposite sign for the two sublattices.
- t1float
Nearest neighbor hopping amplitude.
- t2float
Next-nearest neighbor hopping amplitude. Peierls phase is included.
- Returns:
- TBModel
An instance of the model.
Notes
The Haldane model describes a two-dimensional topological insulator with a non-trivial band structure. It is characterized by a finite Chern number and exhibits edge states that are protected by time-reversal symmetry [haldane].
References
[haldane]Haldane, F. D. M. (1988). O(3) Nonlinear \(\sigma\) Model and the Quantum Hall Effect in Two Dimensions. Physical Review Letters, 61(20), 2015–2018.