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
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Topological Corner Modes Induced by Dirac Vortices in Arbitrary Geometry.
TL;DR: In this article, a general scheme of inducing topological corner modes (TCMs) in arbitrary geometry based on Dirac vortices from aperiodic Kekul\'e modulations is presented.
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Acoustic Realization of a Four-Dimensional Higher-Order Chern Insulator and Boundary-Modes Engineering
TL;DR: In this article, a new type of 4D higher-order topological system demonstrated in an acoustic crystal offers a powerful and novel approach to wave-steering applications, which can be used in a variety of applications.
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Majorana bound states in semiconducting nanostructures
TL;DR: In this paper, the authors give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures, where the Majorana wave functions can be obtained explicitly by standard methods.
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Pseudospin induced topological corner state at intersecting sonic lattices
TL;DR: In this article, the authors demonstrate a domain wall induced topological corner state that is bound at the crossing point among finite acoustic graphenel-like crystals based on designing multipolar pseudospin resonances, which give rise to topologically trivial and nontrivial transitions across the domain walls that flank this unusual corner excitation toward the crossing points.
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Type-II quadrupole topological insulators
TL;DR: In this paper, a new type of quadrupole topological insulator (dubbed type-II) was discovered, which violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously.
References
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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.
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Theory of polarization of crystalline solids
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