scholarly journals Topological Photonic Media and the Possibility of Toroidal Electromagnetic Wavepackets

2019 ◽  
Vol 9 (7) ◽  
pp. 1468 ◽  
Author(s):  
Masaru Onoda
Keyword(s):  
Topological Insulators ◽  
Periodic Structures ◽  
Quantum Hall ◽  
Surface States ◽  
Simple Algorithm ◽  
Helical Surface ◽  
Surface Modes ◽  
Quantum Hall Systems ◽  
Angular Momenta ◽  
The Stability

This study aims to present a theoretical investigation of a feasible electromagnetic wavepacket with toroidal-type dual vortices. The paper begins with a discussion on geometric phases and angular momenta of electromagnetic vortices in free space and periodic structures, and introduces topological photonic media with a review on topological phenomena of electron systems in solids, such as quantum Hall systems and topological insulators. Representative simulations demonstrate both the characteristics of electromagnetic vortices in a periodic structure and of exotic boundary modes of a topological photonic crystal, on a Y-shaped waveguide configuration. Those boundary modes stem from photonic helical surface modes, i.e., a photonic analog of electronic helical surface states of topological insulators. Then, we discuss the possibility of toroidal electromagnetic wavepackets via topological photonic media, based on the dynamics of an electronic wavepacket around the boundary of a topological insulator and a correspondence relation between electronic helical surface states and photonic helical surface modes. Finally, after introducing a simple algorithm for the construction of wavepacket solutions to Maxwell’s equations with multiple types of vortices, we examine the stability of a toroidal electromagnetic wavepacket against reflection and refraction, and further discuss the transformation laws of its topological properties in the corresponding processes.

scholarly journals Electron–hole asymmetry of the topological surface states in strained HgTe

2017 ◽  
Vol 114 (13) ◽  
pp. 3381-3386 ◽  
Author(s):  
Andreas Jost ◽  
Michel Bendias ◽  
Jan Böttcher ◽  
Ewelina Hankiewicz ◽  
Christoph Brüne ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Quantum Hall ◽  
Surface States ◽  
Metallic Surface ◽  
Electron Hole ◽  
Linear Dispersion ◽  
Strong Electron ◽  
Quantum Oscillations ◽  
Strong Deviation ◽  
Topological Surface

Topological insulators are a new class of materials with an insulating bulk and topologically protected metallic surface states. Although it is widely assumed that these surface states display a Dirac-type dispersion that is symmetric above and below the Dirac point, this exact equivalence across the Fermi level has yet to be established experimentally. Here, we present a detailed transport study of the 3D topological insulator-strained HgTe that strongly challenges this prevailing viewpoint. First, we establish the existence of exclusively surface-dominated transport via the observation of an ambipolar surface quantum Hall effect and quantum oscillations in the Seebeck and Nernst effect. Second, we show that, whereas the thermopower is diffusion driven for surface electrons, both diffusion and phonon drag contributions are essential for the hole surface carriers. This distinct behavior in the thermoelectric response is explained by a strong deviation from the linear dispersion relation for the surface states, with a much flatter dispersion for holes compared with electrons. These findings show that the metallic surface states in topological insulators can exhibit both strong electron–hole asymmetry and a strong deviation from a linear dispersion but remain topologically protected.

SKYRMIONS IN QUANTUM HALL FERROMAGNETS

1999 ◽  
Vol 13 (05n06) ◽  
pp. 461-468 ◽  
Author(s):  
H. A. FERTIG
Keyword(s):  
Close Agreement ◽  
Filling Factor ◽  
Quantum Hall ◽  
Time Dependent ◽  
Square Lattice ◽  
Hartree Fock ◽  
Quantum Hall Systems ◽  
Spin Ordering ◽  
Lattice State ◽  
The Stability

Properties of skyrmions in quantum Hall systems are reviewed. It is shown that, using a Hartree-Fock technique, the size of skyrmions near filling factor ν=1 may be computed, yielding a result in close agreement with experiment. Finite densities of skyrmions are shown to lead to a crystal state with square symmetry due to the spin-dependent nature of their mutual interactions. The square lattice state has an unusual spin ordering which leads to a new gapless mode, analogous to spin waves in a two-dimensional XY antiferromagnet. The stability of the ordered spin state is assessed using a time-dependent Hartree-Fock approach, and a phase diagram is derived which shows the parameter range for which long-range spin ordering is destroyed by quantum fluctuations.

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