scholarly journals Two-dimensional symmetry-protected topological phases withPSU(N)and time-reversal symmetry

2013 ◽  
Vol 88 (1) ◽  
Author(s):  
Jeremy Oon ◽  
Gil Young Cho ◽  
Cenke Xu
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Topological Phases ◽  
Two Dimensional ◽  
Symmetry Protected

scholarly journals Fragility of time-reversal symmetry protected topological phases

2020 ◽  
Vol 16 (12) ◽  
pp. 1181-1183 ◽  
Author(s):  
Max McGinley ◽  
Nigel R. Cooper
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Topological Phases ◽  
Symmetry Protected

scholarly journals Stability of Time-Reversal Symmetry Protected Topological Phases

2021 ◽  
Vol 127 (8) ◽  
Author(s):  
Tian-Shu Deng ◽  
Lei Pan ◽  
Yu Chen ◽  
Hui Zhai
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Topological Phases ◽  
Symmetry Protected

scholarly journals Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vadim Grinenko ◽  
Debarchan Das ◽  
Ritu Gupta ◽  
Bastian Zinkl ◽  
Naoki Kikugawa ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Symmetry Breaking ◽  
Time Reversal ◽  
Order Parameter ◽  
Muon Spin Rotation ◽  
Horizontal Line ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Symmetry Protected ◽  
Line Node

AbstractThere is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz order.

scholarly journals Edge theories of two-dimensional fermionic symmetry protected topological phases protected by unitary Abelian symmetries

2021 ◽  
Vol 104 (7) ◽  
Author(s):  
Shang-Qiang Ning ◽  
Chenjie Wang ◽  
Qing-Rui Wang ◽  
Zheng-Cheng Gu
Keyword(s):  
Topological Phases ◽  
Two Dimensional ◽  
Symmetry Protected

Time-reversal symmetry protected chiral interface states between quantum spin and quantum anomalous Hall insulators

2015 ◽  
Vol 92 (7) ◽  
Author(s):  
Huaqing Huang ◽  
Zhaoyou Wang ◽  
Nannan Luo ◽  
Zhirong Liu ◽  
Rong Lü ◽  
...  
Keyword(s):  
Time Reversal ◽  
Interface States ◽  
Quantum Spin ◽  
Time Reversal Symmetry ◽  
Symmetry Protected

scholarly journals Photonic topological insulator with broken time-reversal symmetry

2016 ◽  
Vol 113 (18) ◽  
pp. 4924-4928 ◽  
Author(s):  
Cheng He ◽  
Xiao-Chen Sun ◽  
Xiao-Ping Liu ◽  
Ming-Hui Lu ◽  
Yulin Chen ◽  
...  
Keyword(s):  
Topological Insulator ◽  
Time Reversal ◽  
Magnetoelectric Coupling ◽  
Electronic Systems ◽  
Time Reversal Symmetry ◽  
Edge States ◽  
Protection Mechanism ◽  
Fundamental Particles ◽  
Left And Right ◽  
Symmetry Protected

A topological insulator is a material with an insulating interior but time-reversal symmetry-protected conducting edge states. Since its prediction and discovery almost a decade ago, such a symmetry-protected topological phase has been explored beyond electronic systems in the realm of photonics. Electrons are spin-1/2 particles, whereas photons are spin-1 particles. The distinct spin difference between these two kinds of particles means that their corresponding symmetry is fundamentally different. It is well understood that an electronic topological insulator is protected by the electron’s spin-1/2 (fermionic) time-reversal symmetry Tf2=−1. However, the same protection does not exist under normal circumstances for a photonic topological insulator, due to photon’s spin-1 (bosonic) time-reversal symmetry Tb2=1. In this work, we report a design of photonic topological insulator using the Tellegen magnetoelectric coupling as the photonic pseudospin orbit interaction for left and right circularly polarized helical spin states. The Tellegen magnetoelectric coupling breaks bosonic time-reversal symmetry but instead gives rise to a conserved artificial fermionic-like-pseudo time-reversal symmetry, Tp (Tp2=−1), due to the electromagnetic duality. Surprisingly, we find that, in this system, the helical edge states are, in fact, protected by this fermionic-like pseudo time-reversal symmetry Tp rather than by the bosonic time-reversal symmetry Tb. This remarkable finding is expected to pave a new path to understanding the symmetry protection mechanism for topological phases of other fundamental particles and to searching for novel implementations for topological insulators.

scholarly journals Cubic 3D Chern photonic insulators with orientable large Chern vectors

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Chiara Devescovi ◽  
Mikel García-Díez ◽  
Iñigo Robredo ◽  
María Blanco de Paz ◽  
Jon Lasa-Alonso ◽  
...  
Keyword(s):  
Time Reversal ◽  
Degrees Of Freedom ◽  
Surface States ◽  
Magnetic Response ◽  
Time Reversal Symmetry ◽  
General Strategy ◽  
Topological Phases ◽  
Magnetization Axis ◽  
Opening Up ◽  
Internal Symmetries

AbstractTime Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite the numerous demonstrations of 2D topological phases, few examples of 3D topological systems with TRS breaking exist. In this article, we devise a general strategy to design 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRS broken environment with orientable and arbitrarily large Chern vectors. The designs display topologically protected chiral and unidirectional surface states with disjoint equifrequency loops. The resulting crystals present the following characteristics: First, by increasing the Chern number, multiple surface states channels can be supported. Second, the Chern vector can be oriented along any direction simply changing the magnetization axis, opening up larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, by lowering the TRS breaking requirements, the system is ideal for realistic photonic applications where the magnetic response is weak.

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