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 lattices lit at the corners
TL;DR: Higher-order topological states that are robust against certain classes of disorder and pinned to lattice corners are observed in photonics platforms as mentioned in this paper, where the topological state is obtained by applying a lattice lattice to the topology.
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Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
Yoon-Hyun Hwang,Yuting Qian,J. W. Yang,Jehyun Lee,Dong-Choon Ryu,Hong Chul Choi,Bohm-Jung Yang +6 more
TL;DR: In this article , the authors proposed a topological magnetic Dirac insulator (TMDI), whose two-dimensional surface hosts fourfold-degenerate Dirac fermions protected by either the $p'_c4mm$ or $p4'g'm$ magnetic wallpaper group.
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Topological optical Raman superlattices
TL;DR: In this article , an optical Raman superlattice system was proposed, which incorporates an optical super-layer and a Raman lattice, and it was shown that various topological features induced by the interplay between such two lattices remain largely unexplored.
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Quadrupole topological insulators in Ta2M3Te5 (M = Ni, Pd) monolayers
TL;DR: In this paper , the double-band inversion of the topology of transition-metal monolayers with two mirror reflections (M x and M y ) has been investigated.
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Orbital Shift‐Induced Boundary Obstructed Topological Materials with a Large Energy Gap
TL;DR: In this article , boundary obstructed topological phases caused by Wannier orbital shift between ordinary atomic sites are proposed, which cannot be indicated by symmetry eigenvalues at high symmetry momenta (symmetry indicators) in bulk.
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.
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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.
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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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