pythtb.models.kane_mele#
- kane_mele(delta, t, soc, rashba)[source]#
Kane-Mele tight-binding model.
Added in version 2.0.0.
This function creates a Kane-Mele tight-binding model with the specified parameters. 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:
\[\mathbf{r}_1 = \frac{1}{3} \mathbf{a}_1 + \frac{1}{3} \mathbf{a}_2, \quad \mathbf{r}_2 = \frac{2}{3} \mathbf{a}_1 + \frac{2}{3} \mathbf{a}_2\]The Hamiltonian in second-quantized form is given by:
\[\begin{split}H = \Delta \sum_{i} c_i^\dagger c_i + t \sum_{\langle i,j \rangle} ( c_i^\dagger c_j + h.c.) + \lambda_{SO} \sum_{\langle \langle i,j \rangle \rangle} ( c_i^\dagger \sigma_z c_j + \text{h.c.}) + \\ \lambda_{R} \sum_{\langle i,j \rangle} ( c_i^\dagger \mathbf{\sigma} \times \mathbf{\hat{d}}_{\langle i,j \rangle} c_j + \text{h.c.})\end{split}\]- Parameters:
- onsitefloat
On-site energy.
- tfloat, complex
Hopping parameter.
- socfloat, complex
Spin-orbit coupling strength.
- rashbafloat, complex
Rashba coupling strength.
- Returns:
- TBModel
An instance of the model.
Notes
The Kane-Mele model describes a two-dimensional topological insulator with spin-orbit coupling. It is defined on a honeycomb lattice and includes both intrinsic and Rashba spin-orbit coupling [kane-mele].
References
[kane-mele]Kane, C. L., & Mele, E. J. (2005). Quantum Spin Hall Effect in Graphene. Physical Review Letters, 95(22), 226801.