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Abstract: It is nowadays a quite diffuse idea that variations of electronicpolarisation, as introduced by Resta1, in condensed matter theory are relatedto a -Berry phase-2, as shown by Vanderbilt. The derivation of the lattergeometric phase is correct and the periodic gauge2 is used for itsderivation, aside not allowing for its calculations in finite electromagneticfields. Its derivation has not been demonstrated in the general case of anexternal homogeneous electric field interacting with the electronic field. Inthe present paper we give a brief derivation of the algorithm for thecalculations of polarisation differences in a general manner than in2defining it even in the presence of an external electric field interacting withthe electronic field and writing equations in a way directly implementable inmodern first principles codes1,2



Author: Simone Selenu

Source: https://arxiv.org/







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