Electron polarizability of crystalline solids in quantizing magnetic fields and topological gap numbers

Pavel Streda (1) , Thibaut Jonckheere (2, 3) , Thierry Martin (2, 3)

1 Institute of Physics
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. It is argued that The polarizability is strongly affected by non-dissipative Hall currents induced by the presence of crossed electric and magnetic fields: these can even change its sign. Results are illustrated in detail for a two dimensional square lattice. The polarizability and the Hall conductivity are respectively linked to the two topological quantum numbers entering the so--called Diophantine equation. These numbers could in principle be detected in actual experiments.

Mots clés: quantum hall effect; polarizability; topological gap numbers; tight-binding

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

Pavel Streda, Thibaut Jonckheere, Thierry Martin. Electron polarizability of crystalline solids in quantizing magnetic fields and topological gap numbers. Physical Review Letters, 2008, 100, pp.146804. ⟨10.1103/PhysRevLett.100.146804⟩. ⟨hal-00184637⟩