scholarly journals Classification of crystalline insulators without symmetry indicators: Atomic and fragile topological phases in twofold rotation symmetric systems

2019 ◽  
Vol 100 (11) ◽  
Author(s):  
Sander H. Kooi ◽  
Guido van Miert ◽  
Carmine Ortix
Keyword(s):  
Topological Phases ◽  
Rotation Symmetric ◽  
Symmetric Systems

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 Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Max Geier ◽  
Ion Cosma Fulga ◽  
Alexander Lau
Keyword(s):  
Topological Insulators ◽  
Three Dimensions ◽  
Topological Phases ◽  
Rotation Symmetry ◽  
First Order ◽  
Zero Modes ◽  
Symmetry Classes ◽  
Topological Lattice ◽  
Rotation Symmetric ◽  
Translation Symmetry

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d-2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

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