scholarly journals Elastic gauge fields and zero-field three-dimensional quantum Hall effect in hyperhoneycomb lattices

2019 ◽  
Vol 99 (20) ◽  
Author(s):  
Sang Wook Kim ◽  
Bruno Uchoa
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Gauge Fields ◽  
Zero Field

Three-dimensional quantum Hall effect in Weyl and double-Weyl semimetals

2018 ◽  
Vol 382 (44) ◽  
pp. 3205-3210
Author(s):  
Zhi-Peng Gao ◽  
Zhi Li ◽  
Dan-Wei Zhang
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Weyl Semimetals

scholarly journals INTERACTING QUANTUM TOPOLOGIES AND THE QUANTUM HALL EFFECT

2008 ◽  
Vol 23 (09) ◽  
pp. 1327-1336 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
KUMAR S. GUPTA ◽  
SEÇKIN KÜRKÇÜOǦLU
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Wave Functions ◽  
Gauge Fields ◽  
Representation Space ◽  
Covariant Formulation ◽  
Integer Quantum Hall Effect ◽  
Background Magnetic Field ◽  
Integer Quantum

The algebra of observables of planar electrons subject to a constant background magnetic field B is given by [Formula: see text], the product of two mutually commuting Moyal algebras. It describes the free Hamiltonian and the guiding center coordinates. We argue that [Formula: see text] itself furnishes a representation space for the actions of these two Moyal algebras, and suggest physical arguments for this choice of the representation space. We give the proper setup to couple the matter fields based on [Formula: see text] to electromagnetic fields which are described by the Abelian commutative gauge group [Formula: see text], i.e. gauge fields based on [Formula: see text]. This enables us to give a manifestly gauge covariant formulation of integer quantum Hall effect (IQHE). Thus, we can view IQHE as an elementary example of interacting quantum topologies, where matter and gauge fields based on algebras [Formula: see text] with different θ′ appear. Two-particle wave functions in this approach are based on [Formula: see text]. We find that the full symmetry group in IQHE, which is the semidirect product [Formula: see text] acts on this tensor product using the twisted coproduct Δθ. Consequently, as we show, many particle sectors of each Landau level have twisted statistics. As an example, we find the twisted two particle Laughlin wave functions.

Butterfly spectrum and quantum Hall effect in three-dimensional FISDW

2003 ◽  
Vol 133-134 ◽  
pp. 79-81
Author(s):  
M. Koshino ◽  
H. Aoki ◽  
T. Osada
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Three Dimensional

scholarly journals Six-dimensional quantum Hall effect and three-dimensional topological pumps

2018 ◽  
Vol 98 (12) ◽  
Author(s):  
Ioannis Petrides ◽  
Hannah M. Price ◽  
Oded Zilberberg
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Three Dimensional
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