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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Interaction-induced lattices for bound states: Designing flat bands, quantized pumps, and higher-order topological insulators for doublons
TL;DR: In this paper, the authors show that the center of mass of bound systems with interactions defines a distinct lattice with respect to the one experienced by noninteracting particles, and explore several scenarios including localization, Berry phases and topological bands.
Posted Content
Corner states in second-order mechanical topological insulator
Abstract: We numerically and experimentally study corner states in a continuous elastic plate with em-bedded bolts in a hexagonal pattern. While preserving C6 crystalline symmetry, the system can transition from a topologically trivial to a non-trivial configuration. We create interfacial corners of 60° and 120° by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states with and without topological origin. Notably, some of the corner states are highly localized and tunable. By taking advantage of this property, we experimentally demonstrate one-way corner localization in a Z-shaped domain wall.
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Higher-order topological insulator in a dodecagonal quasicrystal
TL;DR: In this article, a quasicrystalline higher-order topological insulator (HOTI) was discovered in a dodecagonal topological lattice, which is protected by a combination of the twelvefold rotational symmetry and mirror symmetry, as well as particlehole symmetry.
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Microwave Signature of Topological Andreev level Crossings in a Bismuth-based Josephson Junction.
Anil Murani,Anil Murani,B. Dassonneville,A. Kasumov,Julien Basset,Meydi Ferrier,R. Deblock,S. Guéron,Hélène Bouchiat +8 more
TL;DR: A microwave probing of a phase-biased Josephson junction built around a bismuth nanowire, a predicted second order topological insulator, and which was previously shown to host one-dimensional ballistic edge states finds absorption peaks at the Andreev level crossings, whose temperature and frequency dependencies point to protected topological crossings.
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Unhinging the Surfaces of Higher-Order Topological Insulators and Superconductors.
Apoorv Tiwari,Apoorv Tiwari,Ming Hao Li,Bogdan Andrei Bernevig,Titus Neupert,Siddharth Parameswaran +5 more
TL;DR: This work shows that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators and superconductors can be gapped while preserving the protecting C_{2n}T symmetry upon the introduction of non-Abelian surface topological order.
References
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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.
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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.
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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.
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.
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