BIFURCATION OF CLIFFORD TORI IN BERGER 3-SPHERES

2014 ◽  
Vol 65 (4) ◽  
pp. 1345-1362 ◽  
Author(s):  
L. L. De Lima ◽  
J. H. De Lira ◽  
P. Piccione
Keyword(s):  
Clifford Tori

scholarly journals Four-band non-Abelian topological insulator and its experimental realization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Tianshu Jiang ◽  
Qinghua Guo ◽  
Ruo-Yang Zhang ◽  
Zhao-Qing Zhang ◽  
Biao Yang ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Edge State ◽  
Topological Classification ◽  
Symmetric System ◽  
Edge States ◽  
Experimental Realization ◽  
Topological Features ◽  
Significant Difference ◽  
Clifford Tori ◽  
Topological Charges

AbstractVery recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple entangled bulk bandgaps and support nontrivial edge states that manifest the non-Abelian topological features. Furthermore, a system with an even or odd number of bands will exhibit a significant difference in non-Abelian topological classification. To date, there has been scant research investigating even-band non-Abelian topological insulators. Here, we both theoretically explore and experimentally realize a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference in the four-dimensional (4D) rotation sense on the stereographically projected Clifford tori. We show the evolution of the bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way towards other even-band systems.

scholarly journals Four-band non-Abelian topological insulator and its experimental realization

2021 ◽  
Author(s):  
Tianshu Jiang ◽  
Qinghua Guo ◽  
Ruo-Yang Zhang ◽  
Zhao-Qing Zhang ◽  
Biao Yang ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Edge State ◽  
Symmetric System ◽  
Edge States ◽  
Experimental Realization ◽  
Topological Features ◽  
Significant Difference ◽  
Clifford Tori ◽  
Exhaustive Study ◽  
Topological Charges

Abstract Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.

Rigidity of the Clifford Tori inS 3

1988 ◽  
Vol 198 (4) ◽  
pp. 591-599 ◽  
Author(s):  
Yoshihisa Kitagawa
Keyword(s):  
Clifford Tori

New minimal surfaces in $${\mathbb {S}}^3$$ S 3 desingularizing the Clifford tori

2015 ◽  
Vol 364 (3-4) ◽  
pp. 763-776 ◽  
Author(s):  
Jaigyoung Choe ◽  
Marc Soret
Keyword(s):  
Minimal Surfaces ◽  
Clifford Tori

scholarly journals Clifford tori and unbiased vectors

2017 ◽  
Vol 79 (1) ◽  
pp. 33-51 ◽  
Author(s):  
Ole Andersson ◽  
Ingemar Bengtsson
Keyword(s):  
Clifford Tori
Sign in / Sign up

Export Citation Format

Share Document