scholarly journals Andreev reflection in edge states of time-reversal-invariant Landau levels

2015 ◽  
Vol 91 (24) ◽  
Author(s):  
K. G. S. H. Gunawardana ◽  
Bruno Uchoa
Keyword(s):  
Time Reversal ◽  
Andreev Reflection ◽  
Landau Levels ◽  
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.

scholarly journals Quantitative robustness analysis of topological edge modes in C6 and valley-Hall metamaterial waveguides

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1433-1441 ◽  
Author(s):  
Bakhtiyar Orazbayev ◽  
Romain Fleury
Keyword(s):  
Time Reversal ◽  
Topological Insulators ◽  
Statistical Study ◽  
Robustness Analysis ◽  
Ensemble Average ◽  
Edge States ◽  
Edge Mode ◽  
Metamaterial Waveguide ◽  
Recent Advances ◽  
First Time

AbstractRecent advances in designing time-reversal-invariant photonic topological insulators have been extended down to the deep subwavelength scale, by employing synthetic photonic matter made of dense periodic arrangements of subwavelength resonant scatterers. Interestingly, such topological metamaterial crystals support edge states that are localized in subwavelength volumes at topological boundaries, providing a unique way to design subwavelength waveguides based on engineering the topology of bulk metamaterial insulators. While the existence of these edge modes is guaranteed by topology, their robustness to backscattering is often incomplete, as time-reversed photonic modes can always be coupled to each other by virtue of reciprocity. Unlike electronic spins which are protected by Kramers theorem, photonic spins are mostly protected by weaker symmetries like crystal symmetries or valley conservation. In this paper, we quantitatively studied the robustness of subwavelength edge modes originating from two frequently used topological designs, namely metamaterial spin-Hall (SP) effect based on C6 symmetry, and metamaterial valley-Hall (VH) insulators based on valley preservation. For the first time, robustness is evaluated for position and frequency disorder and for all possible interface types, by performing ensemble average of the edge mode transmission through many random realizations of disorder. In contrast to our results in the previous study on the chiral metamaterial waveguide, the statistical study presented here demonstrates the importance of the specific interface on the robustness of these edge modes and the superior robustness of the VH edge stated in both position and frequency disorder, provided one works with a zigzag interface.

scholarly journals Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Omar Jamadi ◽  
Elena Rozas ◽  
Grazia Salerno ◽  
Marijana Milićević ◽  
Tomoki Ozawa ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Symmetry Breaking ◽  
Distinctive Feature ◽  
Direct Evidence ◽  
Landau Levels ◽  
Honeycomb Lattice ◽  
Edge States ◽  
Photonic Lattices ◽  
Synthetic Magnetic Field

Abstract We report the realization of a synthetic magnetic field for photons and polaritons in a honeycomb lattice of coupled semiconductor micropillars. A strong synthetic field is induced in both the s and p orbital bands by engineering a uniaxial hopping gradient in the lattice, giving rise to the formation of Landau levels at the Dirac points. We provide direct evidence of the sublattice symmetry breaking of the lowest-order Landau level wavefunction, a distinctive feature of synthetic magnetic fields. Our realization implements helical edge states in the gap between n = 0 and n = ±1 Landau levels, experimentally demonstrating a novel way of engineering propagating edge states in photonic lattices. In light of recent advances in the enhancement of polariton–polariton nonlinearities, the Landau levels reported here are promising for the study of the interplay between pseudomagnetism and interactions in a photonic system.

Sign in / Sign up

Export Citation Format

Share Document