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Maximally localized Wannier functions: existence and exponential localization

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Geometric Partial Differential Equations proceedings

Part of the book series: CRM Series ((CRMSNS,volume 15))

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Abstract

We describe recent results proved in [32] in collaboration with G.Panati, concerning a periodic Schrodinger operator and the maximally localized (composite) Wannier functions corresponding to a relevant family of its Bloch bands. More precisely, we discuss the minimization problem for the associated localization functional introduced in [22] and we review some rigorous results about the existence and exponential localization of its minimizers, in dimension d ≤ 3. The proof combines ideas and methods from the Calculus of Variations and the regularity theory for harmonic maps between Riemannian manifolds.

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Authors
  1. Adriano Pisante
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Editors and Affiliations

  1. CMAP, Ecole Polytechnique, CNRS, 91128, Palaiseau Cedex, France

    Antonin Chambolle

  2. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italia

    Matteo Novaga

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Pisante, A. (2013). Maximally localized Wannier functions: existence and exponential localization. In: Chambolle, A., Novaga, M., Valdinoci, E. (eds) Geometric Partial Differential Equations proceedings. CRM Series, vol 15. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-473-1_12

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