Implications of the chiral anomaly for quantum Hall-effect devices

1985 ◽  
Vol 31 (10) ◽  
pp. 6588-6591 ◽  
Author(s):  
A. Widom ◽  
M. H. Friedman ◽  
Y. N. Srivastava
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Chiral Anomaly

scholarly journals Chiral Anomaly, Topological Field Theory, and Novel States of Matter

2018 ◽  
Vol 30 (06) ◽  
pp. 1840007 ◽  
Author(s):  
Jürg Fröhlich
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Time Reversal ◽  
Topological Insulators ◽  
Large Scale ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Open Problems ◽  
Spin Currents ◽  
Spin Orbit Interactions

Starting with a description of the motivation underlying the analysis presented in this paper and a brief survey of the chiral anomaly, I proceed to review some basic elements of the theory of the quantum Hall effect in 2D incompressible electron gases in an external magnetic field, (“Hall insulators”). I discuss the origin and role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly or spontaneously broken time reversal, i.e. in Hall insulators and “Chern insulators”. The topological Chern–Simons action yielding the large-scale response equations for the 2D bulk of such states of matter is displayed. A classification of Hall insulators featuring quasi-particles with abelian braid statistics is sketched. Subsequently, the chiral edge spin currents encountered in some time-reversal invariant 2D topological insulators with spin-orbit interactions and the bulk response equations of such materials are described. A short digression into the theory of 3D topological insulators, including “axionic insulators”, follows next. To conclude, some open problems are described and a problem in cosmology related to axionic insulators is mentioned. As far as the quantum Hall effect and the spin currents in time-reversal invariant 2D topological insulators are concerned, this review is based on extensive work my collaborators and I carried out in the early 1990’s. Dedicated to the memory of Ludvig Dmitrievich Faddeev — a great scientist who will be remembered

CHIRAL ANOMALY IN EUCLIDEAN (2+1)-DIMENSIONAL SPACE AND AN APPLICATION TO THE QUANTUM HALL EFFECT

2008 ◽  
Vol 22 (17) ◽  
pp. 2675-2689 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Magnetic Field ◽  
Dirac Equation ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Zero Mode ◽  
Dimensional Space ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Regularization Procedure ◽  
Chiral Transformation

The chiral anomaly in (2+1)-dimensions and its relationship to the zero mode of the Dirac equation in the massless case is studied. Solutions are obtained for the Dirac equation under a vector potential which generates a constant magnetic field. It is shown that there is an anomaly term associated with the corresponding chiral transformation. It can be calculated by using the regularization procedure of Fujikawa. The results are applied to the quantum Hall effect.

Engineering the chiral anomaly: the quantum Hall effect

1985 ◽  
Vol 42 (3) ◽  
pp. 137-140 ◽  
Author(s):  
Y. N. Srivastava ◽  
A. Widom ◽  
M. H. Friedman
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Chiral Anomaly

scholarly journals TOPOLOGICAL ASPECTS OF HIGH-Tc SUPERCONDUCTIVITY, FRACTIONAL QUANTUM HALL EFFECT AND BERRY PHASE

1999 ◽  
Vol 13 (28) ◽  
pp. 3393-3404 ◽  
Author(s):  
B. BASU ◽  
D. PAL ◽  
P. BANDYOPADHYAY
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Fractional Quantum ◽  
High Tc ◽  
Fractional Quantum Hall

We have analysed here the equivalence of RVB states with ν=1/2 FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the three-dimensional spinons and holons are chracterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with ν=1/2.

The Hierarchy of Fractional Quantum Hall States and Berry Phase

1998 ◽  
Vol 12 (01) ◽  
pp. 49-62 ◽  
Author(s):  
B. Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Berry Phase ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Dynamical Phase ◽  
Integer Quantum Hall Effect

The Hierarchy of Fractional Quantum Hall (FQH) states have been studied here in the framework of chiral anomaly and Berry Phase. It is shown that the unambiguously observed FQH states with filling factor ν=p/q with p even or odd and q an odd integer can be considered from the viewpoint that the Berry phase associated with even number of vortices can be removed to the dynamical phase and the corresponding fermionic state attains a higher Landau level. This also leads to the fact that FQH states with even denominator filling factor can arise when we have pairs of degenerate electrons giving rise to the non-Abelian Berry phase which suggests that these FQH states correspond to non-Abelian Hall fluid. In this framework Integer Quantum Hall Effect (IQHE) as well as Fractional Quantum Hall Effect (FQHE) with filling factor ν=p/q with q odd or even can be studied in a unified way.

Localization and many-body interactions in the quantum Hall effect determined by polarized optical emission

1991 ◽  
Vol 44 (8) ◽  
pp. 4006-4009 ◽  
Author(s):  
B. B. Goldberg ◽  
D. Heiman ◽  
M. Dahl ◽  
A. Pinczuk ◽  
L. Pfeiffer ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Optical Emission ◽  
Many Body ◽  
Many Body Interactions

Quantum Hall effect in a saddle-point system

1998 ◽  
Vol 2 (1-4) ◽  
pp. 523-526
Author(s):  
M.V Budantsev ◽  
Z.D Kvon ◽  
A.G Pogosov ◽  
E.B Olshanetskii ◽  
D.K Maude ◽  
...  
Keyword(s):  
Saddle Point ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point System ◽  
Saddle Point System
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