Dynamical electron-ion coupling in the ionic conductor $\alpha -\mathrm{NaSn}$

Dynamical electron-ion coupling in an ionic solid NaSn at high temperatures is studied by ab initio molecular dynamics simulation. The cooperative ion dynamics of the migration of ${\mathrm{Na}}^{+}$ ions and the deformations of $({\mathrm{Sn}}_4{)}^{4-}$ tetrahedra are clarified. The band gap fluctuates between metallic and semiconducting values, and is strongly coupled with the ion dynamics. When the band gap vanishes, the character of the highest occupied eigenfunction changes from bonding to nonbonding within a tetrahedron, and it is caused by the deformations of the tetrahedra. The mechanism of the rapid rise of conductivity experimentally observed is discussed in light of our results.