scholarly journals Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal

Crystals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 137 ◽  
Author(s):  
Xiao-Chen Sun ◽  
Cheng He ◽  
Xiao-Ping Liu ◽  
Yi Zou ◽  
Ming-Hui Lu ◽  
...  

Time-reversal symmetry (TRS) of electrons is associated with an anti-unitary operator with T 2 = − 1 , which induces Kramers degeneracy and plays an important role in realizing the quantum spin Hall effect (QSHE). By contrast, TRS of photons is described by T b 2 = 1 . We point out that due to this difference, TRS is not the necessary condition for the construction of the photonic analogue of the QSHE. Instead, by constructing an artificial pseudo TRS T p with T p 2 = − 1 in a photonic system, one can realize the photonic Kramers degeneracy and a pair of topological protected edge states, a photonic analogue of the QSHE. Specifically, by retrieving the optical parameters of materials with the pseudo TRS, we propose a photonic topological insulator (PTI) utilizing a pair of double-degenerate transverse electric (TE) and transverse magnetic (TM) polarizations to mimic the spin up and down states of the electron. We demonstrate that the unidirectional polarization-dependent transportation of TE and TM edge states can be realized in this system based on computer simulations. For all possible symmetry types, we check the robustness of these topological states by using a complete set of impurities, including three Pauli matrices and one complex conjugate operator. The results show that the PTI is protected by the pseudo TRS T p . In general, an arbitrary pair of optical polarizations on the Bloch sphere can be utilized to construct photonic pseudospin states and the PTI. Our findings confirm the physical meaning of the pseudo TRS and may provide guidance for future PTI designs.

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiujuan Zhang ◽  
Zhi-Kang Lin ◽  
Hai-Xiao Wang ◽  
Zhan Xiong ◽  
Yuan Tian ◽  
...  

AbstractSymmetry and topology are two fundamental aspects of many quantum states of matter. Recently new topological materials, higher-order topological insulators, were discovered, featuring bulk–edge–corner correspondence that goes beyond the conventional topological paradigms. Here we discover experimentally that the nonsymmorphic p4g acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, whereas the second band gap exhibits quadrupole topology with anomalous Wannier bands. Such a topological hierarchy allows us to observe experimentally distinct, multiplexed topological phenomena and to reveal a topological transition triggered by the geometry transition from the p4g group to the C4v group, which demonstrates elegantly the fundamental interplay between symmetry and topology. Our study demonstrates that classical systems with controllable geometry can serve as powerful simulators for the discovery of novel topological states of matter and their phase transitions.


Nanoscale ◽  
2020 ◽  
Vol 12 (40) ◽  
pp. 20890-20897
Author(s):  
Yongqing Cai ◽  
Gang Zhang ◽  
Yong-Wei Zhang

As one of the most intriguing elemental 2D materials beyond graphene, stanene is a unique material possessing a strong quantum spin Hall effect and is promising for spintronics applications.


2020 ◽  
Vol 117 (28) ◽  
pp. 16214-16218 ◽  
Author(s):  
Berthold Jäck ◽  
Yonglong Xie ◽  
B. Andrei Bernevig ◽  
Ali Yazdani

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer’s pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.


Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3289
Author(s):  
Tomasz Kwapiński ◽  
Marcin Kurzyna

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Peng Zhang ◽  
Ryo Noguchi ◽  
Kenta Kuroda ◽  
Chun Lin ◽  
Kaishu Kawaguchi ◽  
...  

AbstractA quantum spin Hall (QSH) insulator hosts topological states at the one-dimensional (1D) edge, along which backscattering by nonmagnetic impurities is strictly prohibited. Its 3D analogue, a weak topological insulator (WTI), possesses similar quasi-1D topological states confined at side surfaces. The enhanced confinement could provide a route for dissipationless current and better advantages for applications relative to strong topological insulators (STIs). However, the topological side surface is usually not cleavable and is thus hard to observe. Here, we visualize the topological states of the WTI candidate ZrTe5 by spin and angle-resolved photoemission spectroscopy (ARPES): a quasi-1D band with spin-momentum locking was revealed on the side surface. We further demonstrate that the bulk band gap is controlled by external strain, realizing a more stable WTI state or an ideal Dirac semimetal (DS) state. The highly directional spin-current and the tunable band gap in ZrTe5 will provide an excellent platform for applications.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jae-Hyuck Choi ◽  
William E. Hayenga ◽  
Yuzhou G. N. Liu ◽  
Midya Parto ◽  
Babak Bahari ◽  
...  

AbstractTopological insulator lasers (TILs) are a recently introduced family of lasing arrays in which phase locking is achieved through synthetic gauge fields. These single frequency light source arrays operate in the spatially extended edge modes of topologically non-trivial optical lattices. Because of the inherent robustness of topological modes against perturbations and defects, such topological insulator lasers tend to demonstrate higher slope efficiencies as compared to their topologically trivial counterparts. So far, magnetic and non-magnetic optically pumped topological laser arrays as well as electrically pumped TILs that are operating at cryogenic temperatures have been demonstrated. Here we present the first room temperature and electrically pumped topological insulator laser. This laser array, using a structure that mimics the quantum spin Hall effect for photons, generates light at telecom wavelengths and exhibits single frequency emission. Our work is expected to lead to further developments in laser science and technology, while opening up new possibilities in topological photonics.


2020 ◽  
Vol 6 (26) ◽  
pp. eaba4625
Author(s):  
Saquib Shamim ◽  
Wouter Beugeling ◽  
Jan Böttcher ◽  
Pragya Shekhar ◽  
Andreas Budewitz ◽  
...  

The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.


2016 ◽  
Vol 49 (5) ◽  
pp. 055305 ◽  
Author(s):  
Ya-ping Wang ◽  
Chang-wen Zhang ◽  
Wei-xiao Ji ◽  
Run-wu Zhang ◽  
Ping Li ◽  
...  

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