Multifractal wave functions and inelastic scattering in the integer quantum Hall effect

1994 ◽  
Vol 72 (22) ◽  
pp. 3582-3585 ◽  
Author(s):  
Tobias Brandes ◽  
Ludwig Schweitzer ◽  
Bernhard Kramer
Keyword(s):  
Inelastic Scattering ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Wave Functions ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum

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.

scholarly journals An all-epitaxial nitride heterostructure with concurrent quantum Hall effect and superconductivity

2021 ◽  
Vol 7 (8) ◽  
pp. eabf1388
Author(s):  
Phillip Dang ◽  
Guru Khalsa ◽  
Celesta S. Chang ◽  
D. Scott Katzer ◽  
Neeraj Nepal ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Electron Gas ◽  
Quantum Hall ◽  
High Electron Mobility Transistor ◽  
High Electron ◽  
2D Electron Gas ◽  
Integer Quantum Hall Effect ◽  
Topological Quantum ◽  
Integer Quantum

Creating seamless heterostructures that exhibit the quantum Hall effect and superconductivity is highly desirable for future electronics based on topological quantum computing. However, the two topologically robust electronic phases are typically incompatible owing to conflicting magnetic field requirements. Combined advances in the epitaxial growth of a nitride superconductor with a high critical temperature and a subsequent nitride semiconductor heterostructure of metal polarity enable the observation of clean integer quantum Hall effect in the polarization-induced two-dimensional (2D) electron gas of the high-electron mobility transistor. Through individual magnetotransport measurements of the spatially separated GaN 2D electron gas and superconducting NbN layers, we find a small window of magnetic fields and temperatures in which the epitaxial layers retain their respective quantum Hall and superconducting properties. Its analysis indicates that in epitaxial nitride superconductor/semiconductor heterostructures, this window can be significantly expanded, creating an industrially viable platform for robust quantum devices that exploit topologically protected transport.

Publisher’s Note: Charge Fractionalization in the Integer Quantum Hall Effect [Phys. Rev. Lett. 112, 166801 (2014)]

2014 ◽  
Vol 112 (18) ◽  
Author(s):  
Hiroyuki Inoue ◽  
Anna Grivnin ◽  
Nissim Ofek ◽  
Izhar Neder ◽  
Moty Heiblum ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Charge Fractionalization
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