scholarly journals Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Jun Mei ◽  
Zeguo Chen ◽  
Ying Wu
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Two Dimensional ◽  
Edge States

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 Superconducting edge states in a topological insulator

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
I. V. Yurkevich ◽  
V. Kagalovsky
Keyword(s):  
Topological Insulator ◽  
Time Reversal ◽  
Collective Motion ◽  
Effective Theory ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Edge States ◽  
Translation Invariant ◽  
Clean System ◽  
The Stability

AbstractWe study the stability of multiple conducting edge states in a topological insulator against perturbations allowed by the time-reversal symmetry. A system is modeled as a multi-channel Luttinger liquid, with the number of channels equal to the number of Kramers doublets at the edge. Assuming strong interactions and weak disorder, we first formulate a low-energy effective theory for a clean translation invariant system and then include the disorder terms allowed by the time-reversal symmetry. In a clean system with N Kramers doublets, N − 1 edge states are gapped by Josephson couplings and the single remaining gapless mode describes collective motion of Cooper pairs synchronous across the channels. Disorder perturbation in this regime, allowed by the time reversal symmetry is a simultaneous backscattering of particles in all N channels. Its relevance depends strongly on the parity if the number of channel N is not very large. Our main result is that disorder becomes irrelevant with the increase of the number of edge modes leading to the stability of the edge states superconducting regime even for repulsive interactions.

TOPOLOGICAL PHOTONIC STATES

2013 ◽  
Vol 28 (02) ◽  
pp. 1441001 ◽  
Author(s):  
CHENG HE ◽  
LIANG LIN ◽  
XIAO-CHEN SUN ◽  
XIAO-PING LIU ◽  
MING-HUI LU ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Group Velocity ◽  
Time Reversal ◽  
Edge State ◽  
Time Reversal Symmetry ◽  
Edge States ◽  
Energy Bands ◽  
Integer Quantum Hall Effect ◽  
Topological States ◽  
Photonic States

As exotic phenomena in optics, topological states in photonic crystals have drawn much attention due to their fundamental significance and great potential applications. Because of the broken time-reversal symmetry under the influence of an external magnetic field, the photonic crystals composed of magneto-optical materials will lead to the degeneracy lifting and show particular topological characters of energy bands. The upper and lower bulk bands have nonzero integer topological numbers. The gapless edge states can be realized to connect two bulk states. This topological photonic states originated from the topological property can be analogous to the integer quantum Hall effect in an electronic system. The gapless edge state only possesses a single sign of gradient in the whole Brillouin zone, and thus the group velocity is only in one direction leading to the one-way energy flow, which is robust to disorder and impurity due to the nontrivial topological nature of the corresponding electromagnetic states. Furthermore, this one-way edge state would cross the Brillouin center with nonzero group velocity, where the negative-zero-positive phase velocity can be used to realize some interesting phenomena such as tunneling and backward phase propagation. On the other hand, under the protection of time-reversal symmetry, a pair of gapless edge states can also be constructed by using magnetic–electric coupling meta-materials, exhibiting Fermion-like spin helix topological edge states, which can be regarded as an optical counterpart of topological insulator originating from the spin–orbit coupling. The aim of this article is to have a comprehensive review of recent research literatures published in this emerging field of photonic topological phenomena. Photonic topological states and their related phenomena are presented and analyzed, including the chiral edge states, polarization dependent transportation, unidirectional waveguide and nonreciprocal optical transmission, all of which might lead to novel applications such as one-way splitter, optical isolator and delay line. In addition, the possible prospect and development of related topics are also discussed.

scholarly journals Real and imaginary edge states in stacked Floquet honeycomb lattices

2020 ◽  
Vol 93 (8) ◽  
Author(s):  
Alexander Fritzsche ◽  
Bastian Höckendorf ◽  
Andreas Alvermann ◽  
Holger Fehske
Keyword(s):  
Time Reversal ◽  
Edge State ◽  
Band Gaps ◽  
Time Reversal Symmetry ◽  
Edge States ◽  
Single Edge ◽  
Different Types ◽  
Stark Contrast

Abstract We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap. The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter. In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remains spatially localized while its amplitude continuously increases. Our model is well-suited for realizing these edge states in photonic waveguide lattices. Graphical abstract

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