scholarly journals Classification of topological phases of parafermionic chains with symmetries

2017 ◽  
Vol 95 (20) ◽  
Author(s):  
D. Meidan ◽  
E. Berg ◽  
Ady Stern
Keyword(s):  
Topological Phases

scholarly journals Why are fractional charges of orientifolds compatible with Dirac quantization?

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Yuji Tachikawa ◽  
Kazuya Yonekura
Keyword(s):  
String Theory ◽  
Double Cover ◽  
Topological Phases ◽  
Duality Group ◽  
Dirac Quantization ◽  
Type Iib String Theory ◽  
Symmetry Protected

Orientifold pp-planes with p\le 4p≤4 have fractional Dpp-charges, and therefore appear inconsistent with Dirac quantization with respect to D(6{-}p)(6−p)-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the \etaη invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the  pin^++ version of the double cover of GL(2,Z).

scholarly journals Quantized electric multipole insulators

Science ◽  
2017 ◽  
Vol 357 (6346) ◽  
pp. 61-66 ◽  
Author(s):  
Wladimir A. Benalcazar ◽  
B. Andrei Bernevig ◽  
Taylor L. Hughes
Keyword(s):  
Necessary Conditions ◽  
Berry Phase ◽  
Electric Polarization ◽  
Topological Invariants ◽  
Topological Phases ◽  
Minimal Models ◽  
Fractional Charge ◽  
Electric Multipole Moments ◽  
Topological Phases Of Matter

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.

Theoretical construction of weak topological crystalline insulators

2017 ◽  
Vol 31 (20) ◽  
pp. 1750136
Author(s):  
Qing-Li Zhu ◽  
Liang Hua ◽  
Ji-Mei Shen
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Discrete Symmetry ◽  
Topological Phases ◽  
Symmetry Classes ◽  
New Type ◽  
Theoretical Construction ◽  
Topological Crystalline Insulators ◽  
Group Symmetries

Inspired by the discovery of topological crystalline insulators (TCIs) in three-dimensional materials such as Pb[Formula: see text]Sn[Formula: see text]Se(Te), the classification of topological insulators has been extended to other discrete symmetry classes such as crystal point group symmetries. In this paper, we construct and study a simple model of weak TCIs, which will serve as a more viable project in the experimental probe for such new type of topological phases.

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