A rigorous proof of the Landau-Peierls formula and much more

Philippe Briet (1, 2) , Horia D. Cornean (3) , Baptiste Savoie (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 MATH. DEPT., AALBORG UNIVERSITY - Institut for Matematiske Fag, Aalborg university

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Gaz Quantiques [cond-mat.quant-gas]; Mécanique statistique [cond-mat.stat-mech]

Philippe Briet, Horia D. Cornean, Baptiste Savoie. A rigorous proof of the Landau-Peierls formula and much more. Annales Henri Poincaré, 2012, 13 (1), pp.1-40. ⟨10.1007/s00023-011-0128-x⟩. ⟨hal-00540577v2⟩