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 invariants and corner states for Hamiltonians on a three-dimensional lattice
Shin Hayashi,Shin Hayashi +1 more
TL;DR: In this paper, K-theory applied for the quarterplane Toeplitz extension is used to define topological invariants for periodic Hamiltonians with a spectral gap on the bulk and edges.
Journal ArticleDOI
Higher-order bosonic topological phases in spin models
Oleg Dubinkin,Taylor L. Hughes +1 more
TL;DR: In this article, two spin models for a second-order topological phase protected by a global symmetry were presented, one from layers of an exactly solvable cluster model for a one-dimensional and the other from more conventional spin couplings (XY or Heisenberg).
Journal ArticleDOI
Majorana corner flat bands in two-dimensional second-order topological superconductors
TL;DR: In this paper, it was shown that confining a second-order topological superconductor with a harmonic potential leads to a proliferation of Majorana corner modes, which have a fundamentally different origin from that of the conventional mechanism.
Journal ArticleDOI
Higher-order topological phases in tunable C 3 symmetric photonic crystals
TL;DR: In this paper, the authors demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods.
Journal ArticleDOI
Floquet second order topological superconductor based on unconventional pairing
TL;DR: In this paper, the authors theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase in the high-temperature platform both in two dimension (2D) and three dimension (3D).
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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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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