1. RRI Digital Repository
  2. 07. Theoretical Physics
  3. Research Papers (TP)
Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/8035
Full metadata record
DC FieldValueLanguage
dc.contributor.authorVyas, Vivek M.-
dc.contributor.authorRoy, Dibyendu-
dc.date.accessioned2023-02-03T04:41:47Z-
dc.date.available2023-02-03T04:41:47Z-
dc.date.issued2023-01-30-
dc.identifier.citationApplied Mathematics, 2023, Vol.14,p82en_US
dc.identifier.issn2152-7393-
dc.identifier.issn2152-7385-
dc.identifier.urihttp://hdl.handle.net/2289/8035-
dc.descriptionOpen Access, licensed under Creative Commons Attribution International License (CC BY 4.0)en_US
dc.description.abstractHere the notion of geometric phase acquired by an electron in a one-dimensional periodic lattice as it traverses the Bloch band is carefully studied. Such a geometric phase is useful in characterizing the topological properties and the electric polarization of the periodic system. An expression for this geometric phase was first provided by Zak, in a celebrated work three decades ago. Unfortunately, Zak’s expression suffers from two shortcomings: its value depends upon the choice of origin of the unit cell, and is gauge dependent. Upon careful investigation of the time evolution of the system, here we find that the system displays cyclicity in a generalized sense wherein the physical observables return in the course of evolution, rather than the density matrix. Recognition of this generalized cyclicity paves the way for a correct and consistent expression for the geometric phase in this system, christened as Pancharatnam-Zak phase. Pancharatnam-Zak geometric phase does not suffer from the shortcomings of Zak’s expression, and correctly classifies the Bloch bands of the lattice. A naturally filled band extension of the Pancharatnam-Zak phase is also constructed and studied.en_US
dc.language.isoenen_US
dc.publisherScientific Research Publishingen_US
dc.relation.urihttps://doi.org/10.4236/am.2023.141005en_US
dc.rights2023 The Author(s)en_US
dc.subjectgeometric phaseen_US
dc.subjectzak phaseen_US
dc.subjecttopological materialsen_US
dc.titleA Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Latticeen_US
dc.typeArticleen_US
Appears in Collections:Research Papers (TP)

Files in This Item:
File Description SizeFormat 
2023_Applied Mathematics_Vol.14_p82.pdfOpen Access1.22 MBAdobe PDFView/Open
Show simple item record


Items in RRI Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.