scholarly journals First Principles Calculation of the Topological Phases of the Photonic Haldane Model

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2229
Author(s):  
Filipa R. Prudêncio ◽  
Mário G. Silveirinha
Keyword(s):  
Photonic Crystal ◽  
Time Reversal ◽  
First Principles ◽  
First Principles Calculation ◽  
Time Reversal Symmetry ◽  
Topological Phases ◽  
Edge States ◽  
Haldane Model ◽  
Type Boundary ◽  
Spatially Varying

Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed-matter systems, as it unveiled that a broken time-reversal symmetry is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo-Tellegen coupling. Here, we use Green’s function method to determine from “first principles” the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo-Tellegen parameter.

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 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.

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 properties of Sb(111) surface: A first-principles study

2021 ◽  
Author(s):  
Wang Shuangxi ◽  
Zhang Ping
Keyword(s):  
Time Reversal ◽  
First Principles ◽  
Density Functional ◽  
Bilayer Film ◽  
Time Reversal Symmetry ◽  
First Principles Calculations ◽  
Topological Properties ◽  
Functional Theory ◽  
Topological States ◽  
Reduced Surface

Abstract First-principles calculations based on density functional theory were performed to systematically study the electronic properties of the thin film of antimony in (111) orientation. Considering the spinorbit interaction, for stoichiometric surface, the topological states keep robust for six-bilayer case, and can be recovered in the three-bilayer film, which are guaranteed by time-reversal symmetry and inverse symmetry. For reduced surface doped by non-magnetic Bi or magnetic Mn atom, localized three-fold symmetric features can be identified. Moreover, band structures show that the non-trivial topological states stand for non-magnetic substitutional Bi atom, while can be eliminated by adsorbed or substitutional magnetic Mn atom.

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