Statistical mechanics approach to the electric polarization and dielectric constant of band insulators
Abstract
We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbationlike expression of the WannierStark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling. At first order in the field, we recover the result of KingSmith, Vanderbilt, and Resta for the electric polarization in terms of a Zak phase—albeit at finite temperature—and, at second order, deduce a general formula for the electric susceptibility, or equivalently for the dielectric constant. Advantages of our method are the validity of the formalism both at zero and finite temperature and the easy computation of higher order derivatives of the free energy. We verify our findings on two different onedimensional tightbinding models.
 Publication:

Physical Review B
 Pub Date:
 October 2016
 DOI:
 10.1103/PhysRevB.94.155109
 arXiv:
 arXiv:1605.03013
 Bibcode:
 2016PhRvB..94o5109C
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics
 EPrint:
 15 pages, 4 figures