English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We develop a theory for the analytic computation of the free energy of bandinsulators in the presence of a uniform and constant electric field. The twokey ingredients are a perturbation-like expression of the Wannier-Stark energyspectrum of electrons and a modified statistical mechanics approach involving alocal chemical potential in order to deal with the unbounded spectrum andimpose the physically relevant electronic filling. At first order in the field,we recover the result of King-Smith, Vanderbilt and Resta for the electricpolarization in terms of a Zak phase - albeit at finite temperature - and, atsecond order, deduce a general formula for the electric susceptibility, orequivalently for the dielectric constant. Advantages of our method are thevalidity of the formalism both at zero and finite temperature and the easycomputation of higher order derivatives of the free energy. We verify ourfindings on two different one-dimensional tight-binding models.

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators