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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Transparent Josephson junctions in higher-order topological insulator WTe2 via Pd diffusion
Martin Endres,Artem Kononov,Michael Stiefel,M. Wyss,H. Suriya Arachchige,Jiaqiang Yan,David Mandrus,Kenji Watanabe,Takashi Taniguchi,Christian Schönenberger +9 more
TL;DR: In this article , the authors reported the formation of superconducting PdTe x as the origin of observed superconductivity, and found an atomically sharp interface in vertical direction to the van der Waals layers between the diffusion crystal and its host crystal, forming state-of-the-art contacts to a TI.
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Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries.
TL;DR: In this article, the Lanczos transformation was applied to a quantized hexadecapole higher-order topological insulator (HOTI) and a deterministic aperiodic 1D array (DAA) was constructed to emulate 4D HOTI in 1D.
Posted Content
Homotopic topological phases of matter in two dimensions: theory and application to Sr$_2$RuO$_4$
TL;DR: In this paper, the authors introduce topological phases of matter defined by skyrmions in the ground state spin expectation value textures in the Brillouin zone, the chiral and helical topological topological SKRMs of matter.
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Transport induced dimer state from topological corner states
TL;DR: In this paper, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice.
Journal ArticleDOI
Wannier band transitions in disordered π-flux ladders
Jahan Claes,Taylor L. Hughes +1 more
TL;DR: In this paper, a mirror-symmetric $ensuremath{pi}$-flux ladder in one dimension has been studied in the presence of disorder, and a real-space renormalization group procedure has been derived to understand a different type of disorder-induced transition between nontrivial and trivial Wannier topological phases.
References
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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.
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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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