scholarly journals Edge states of integral quantum Hall states versus edge states of antiferromagnetic quantum spin chains

1996 ◽  
Vol 53 (24) ◽  
pp. 16420-16424 ◽  
Author(s):  
Yong Baek Kim
Keyword(s):  
Quantum Hall ◽  
Quantum Spin ◽  
Spin Chains ◽  
Edge States ◽  
Quantum Spin Chains ◽  
Quantum Hall States ◽  
Integral Quantum ◽  
Hall States

scholarly journals Photonic topological semimetals in bianisotropic metamaterials

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
You-Zhong Yu ◽  
Chih-Yu Kuo ◽  
Ruey-Lin Chern ◽  
C. T. Chan
Keyword(s):  
Quantum Hall ◽  
Quantum Spin ◽  
Topological Invariants ◽  
Edge States ◽  
Irregular Boundary ◽  
Topological Features ◽  
Quantum Hall States ◽  
Fermi Arcs ◽  
Topological Semimetals ◽  
Hall States

AbstractWe analyze the photonic topological phases in bianisotropic metamaterials characterized by a chirality tensor with zero trace. We found that the strength of chirality component determines the topological character of the metamaterial. The underlying medium can be considered as a topological semimetal with the nontrivial band gap in the momentum space. The topological properties are described by the spin-orbit Hamiltonians with spin 1 and characterized by the nonzero topological invariants. In particular, photonic quantum Hall states exist when the longitudinal chirality component exceeds the permittivity, whereas photonic quantum spin Hall states are present when the chiral nihility occurs. Considering the dispersion in the frequency domain, the bianisotropic metamaterial is regarded as a photonic Weyl system that supports the Weyl points and Fermi arcs. The topological features are further illustrated with the robust transport of edge states at an irregular boundary of the metamaterial.

EDGE EXCITATIONS IN THE FRACTIONAL QUANTUM HALL STATES AT GENERAL FILLING FRACTIONS

1991 ◽  
Vol 05 (01) ◽  
pp. 39-46 ◽  
Author(s):  
X.G. WEN
Keyword(s):  
Quantum Hall ◽  
Low Energy ◽  
Effective Theory ◽  
Edge States ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Hall States

We propose a scheme to construct the edge states for the Fractional Quantum Hall (FQH) states obtained by the Jain’s scheme. The low energy effective theory of the edge excitations is obtained. We calculate the number of the branches and the electron propagators of the edge states for various FQH states. We demonstrate that two FQH states with the same filling fraction may have different topological orders and may support different edge excitations.

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