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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Book ChapterDOI
Topological Crystalline Insulators
Titus Neupert,Frank Schindler +1 more
TL;DR: Topological crystalline insulators as discussed by the authors are gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations.
Journal ArticleDOI
Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
TL;DR: In this article, the authors demonstrate the possibility of realizing a two-dimensional \emph{Floquet} second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment $Q^{\rm Flq}_{xy}=0.5$, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold and time-reversal Dirac mass perturbation.
Journal ArticleDOI
Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians
TL;DR: Benalcazar et al. as discussed by the authors established a bulk-boundary correspondence linking the presence of such Majorana bound states to bulk topological invariants, and showed that topological crystalline superconductor protected by rotational symmetry displays second-order topological superconductivity.
Journal ArticleDOI
Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
Koichi Asaga,Takahiro Fukui +1 more
TL;DR: In this article, an effective theory of the boundary-obstructed topological phases (BOTP) transition of two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a uniform magnetic field is presented.
Journal ArticleDOI
Dual-Polarization Second-Order Photonic Topological Insulators
TL;DR: In this paper, a dual-polarization topological photonic crystal structure for both transverse magnetic and transverse electric modes through topology optimization is proposed, and the robustness of these corner states against defects is explicitly demonstrated.
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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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.
Journal ArticleDOI
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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