Topological insulators in silicene: Quantum hall, quantum spin hall and quantum anomalous hall effects

2013 ◽  
Author(s):  
Motohiko Ezawa
Keyword(s):  
Topological Insulators ◽  
Quantum Hall ◽  
Quantum Spin ◽  
Hall Effects ◽  
Quantum Spin Hall

scholarly journals Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator

2020 ◽  
Vol 6 (26) ◽  
pp. eaba4625
Author(s):  
Saquib Shamim ◽  
Wouter Beugeling ◽  
Jan Böttcher ◽  
Pragya Shekhar ◽  
Andreas Budewitz ◽  
...  
Keyword(s):  
Quantum Wells ◽  
Quantum Hall ◽  
Quantum Spin ◽  
Majorana Fermions ◽  
Quantum Spin Hall Effect ◽  
Topological Materials ◽  
Quantum Hall Effects ◽  
Hall Effects ◽  
Low Magnetic Field ◽  
Quantum Spin Hall

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.

scholarly journals Hinged quantum spin Hall effect in antiferromagnetic topological insulators

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Yue-Ran Ding ◽  
Dong-Hui Xu ◽  
Chui-Zhen Chen ◽  
X. C. Xie
Keyword(s):  
Hall Effect ◽  
Topological Insulators ◽  
Quantum Spin ◽  
Spin Hall Effect ◽  
Quantum Spin Hall Effect ◽  
Quantum Spin Hall

scholarly journals Designing photonic topological insulators with quantum-spin-Hall edge states using topology optimization

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1363-1369 ◽  
Author(s):  
Rasmus E. Christiansen ◽  
Fengwen Wang ◽  
Ole Sigmund ◽  
Søren Stobbe
Keyword(s):  
Topology Optimization ◽  
Band Gap ◽  
Design Problem ◽  
Topological Insulators ◽  
Quantum Spin ◽  
Edge States ◽  
Unit Cells ◽  
Improved Performance ◽  
Inverse Design Problem ◽  
Quantum Spin Hall

AbstractDesigning photonic topological insulators (PTIs) is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C6ν-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink-and-grow approach to quantum-spin-Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50% larger than in previous designs. Furthermore, we find a directional β-factor exceeding 99% and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto-unexplored symmetry constraints.

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