Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators

2017/08/29 by Wladimir A. Benalcazar, B. Andrei Bernevig, Taylor L. Hughes · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Classical mechanics #Dipole #Ferroelectric and Piezoelectric Materials #Mathematics #Multipole expansion #Physics #Quadrupole #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.96.245115

published as Phys. Rev. B 96, 245115 (2017) · 72 pages, 52 figures

arxiv created 2017/08/29 · openalex created_date 2017/08/31 · openalex publication_date 2017/12/11 · arxiv updated 2017/12/20 · openalex updated_date 2026/08/06

Abstract

The Berry phase provides a modern formulation of electric polarization in crystals. Recently, this formulation was extended by the authors to higher electric multipole moments. In quantum mechanical crystalline insulators, such higher multipole moments manifest themselves by the presence of boundary-localized moments of lower dimension. In the presence of certain symmetries, these moments are quantized, and their boundary signatures are fractionalized. Here, the authors elaborate in detail on the theory of higher multipole moments and discuss associated topological pumping phenomena, as well as higher-order topological insulators derived from them.

Citations

• Topological field theory of time-reversal invariant insulators
• Periodic table for topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Inversion-symmetric topological insulators
• Berry’s phase for energy bands in solids
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Insulators with Inversion Symmetry
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Topological Crystalline Insulators
• Quantal phase factors accompanying adiabatic changes
• Maximally localized Wannier functions for entangled energy bands
• Maximally-localized generalized Wannier functions for composite energy bands
• Reflection-Symmetric Second-Order Topological Insulators and Superconductors

Cited by

• Reflection-Symmetric Second-Order Topological Insulators and Superconductors
• Polarization Engineering of the Orbital Hall Conductivity in Two-dimensional Ferroelectric Higher-Order Topological Insulator Tl₂S and SnS
• Lattice models with exactly solvable topological hinge and corner states

Related

• Quantized Electric Multipole Insulators
• Quantized crystalline-electromagnetic responses in insulators
• Many-body multipole indices revealed by the real-space dynamical mean-field theory
• Orbital magnetic quadrupole moment in higher order topological phases
• Acoustic Higher-Order Topological Insulators Protected by Multipole Chiral Numbers