Quantized electric multipole insulators
TLDR
This work introduces a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked and opens a venue for the expansion of the classification of topological phases of matter.Abstract:
The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.read more
Citations
More filters
Journal ArticleDOI
Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator $\text{Bi}_{2-x}\text{Sm}_x\text{Se}_3$
TL;DR: In this article, a universal mechanism to generate chiral hinge states in the ferromagnetic axion insulator phase is proposed, which leads to an exotic transport phenomena, the quantum anomalous Hall effect (QAHE) on some particular surfaces determined by both the crystalline symmetry and the magnetization direction.
Journal ArticleDOI
Higher-order symmetry-protected topological states for interacting bosons and fermions
TL;DR: In this article, a topological field theory for symmetry-protected topological phases in strongly interacting many-body systems with a generalized bulk-boundary correspondence is proposed, which leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations.
Journal ArticleDOI
Active topological photonics
Yasutomo Ota,Kenta Takata,Tomoki Ozawa,Alberto Amo,Zhetao Jia,Boubacar Kante,Masaya Notomi,Masaya Notomi,Yasuhiko Arakawa,Satoshi Iwamoto +9 more
TL;DR: In this article, the authors review the cutting-edge research on active topological photonics, in which optical gain plays a pivotal role, and discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topologically edge modes.
Journal ArticleDOI
Second-order topological non-Hermitian skin effects
TL;DR: In this article, the second-order topological skin effects of chiral-symmetric Hermitian systems were investigated and it was found that the skin modes are localized at the corners.
Journal ArticleDOI
Higher-Order Weyl Semimetals
TL;DR: Higher-order Weyl semimetals manifest themselves uniquely by exhibiting concurrent chiral Fermi-arc surface states, topological hinge states, and the momentum-dependent fractional hinge charge, revealing a novel class of higher-order topological phases.
References
More filters
Journal ArticleDOI
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
TL;DR: In this article, the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field effect transistor, was measured and it was shown that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device.
Journal ArticleDOI
Quantized Hall conductance in a two-dimensional periodic potential
TL;DR: In this article, the Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential, where the Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap.
Journal ArticleDOI
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the 'Parity Anomaly'
TL;DR: A two-dimensional condensed-matter lattice model is presented which exhibits a nonzero quantization of the Hall conductance in the absence of an external magnetic field, and exhibits the so-called "parity anomaly" of (2+1)-dimensional field theories.
Journal ArticleDOI
Maximally localized generalized Wannier functions for composite energy bands
Nicola Marzari,David Vanderbilt +1 more
TL;DR: In this paper, a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid is presented, which is suitable for use in connection with conventional electronic-structure codes.
Journal ArticleDOI
Theory of polarization of crystalline solids
TL;DR: It is shown that physically $\ensuremath{\Delta}P can be interpreted as a displacement of the center of charge of the Wannier functions.
Related Papers (5)
Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
(d-2)-Dimensional Edge States of Rotation Symmetry Protected Topological States.
Zhida Song,Zhong Fang,Chen Fang +2 more