A tight binding and $$\overrightarrow{{\boldsymbol{k}}}\cdot \overrightarrow{{\boldsymbol{p}}}$$ k → ⋅ p → study of monolayer stanene

Stanene is a single layer of tin atoms which has been discovered as an emerging material for quantum spin Hall related applications. In this paper, we present an accurate tight-binding model for single layer stanene near the Fermi level. We parameterized the onsite and hopping energies for the nearest, second nearest, and third nearest neighbor tight-binding method, both without and with spin orbital coupling. We derived the analytical solution for the $$\overrightarrow{{\boldsymbol{\Gamma }}}$$ Γ → and $$\overrightarrow{{\boldsymbol{K}}}$$ K → points and numerically investigated the buckling effect on the material electronic properties. In these points of the reciprocal space, we also discuss a corresponding $$\overrightarrow{{\boldsymbol{k}}}\cdot \overrightarrow{{\boldsymbol{p}}}$$ k → ⋅ p → description, obtaining the value of the $$\overrightarrow{{\boldsymbol{k}}}\cdot \overrightarrow{{\boldsymbol{p}}}$$ k → ⋅ p → parameters both analytically from the tight-binding ones, and numerically, fitting the ab-initio dispersion relations. Our models provide a foundation for large scale atomistic device transport calculations.