Relation between the Chiral Anomaly and the Quantized Hall Effect

1985 ◽  
Vol 54 (18) ◽  
pp. 1973-1975 ◽  
Author(s):  
Ahmed Abouelsaood
Keyword(s):  
Hall Effect ◽  
Chiral Anomaly

scholarly journals Chiral Anomaly as the Origin of the Planar Hall Effect in Weyl Semimetals

2017 ◽  
Vol 119 (17) ◽  
Author(s):  
S. Nandy ◽  
Girish Sharma ◽  
A. Taraphder ◽  
Sumanta Tewari
Keyword(s):  
Hall Effect ◽  
Chiral Anomaly ◽  
Planar Hall Effect ◽  
Weyl Semimetals

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

scholarly journals Progress Review on Topological Properties of Heusler Materials

2020 ◽  
Vol 213 ◽  
pp. 02016
Author(s):  
Zhi Lin
Keyword(s):  
Hall Effect ◽  
Surface States ◽  
Anomalous Hall Effect ◽  
Edge State ◽  
Chiral Anomaly ◽  
Dirac Fermion ◽  
High Symmetry ◽  
Heusler Compounds ◽  
Topological Properties ◽  
Topological State

Starting from crystal, electronic and magnetic structures of Heusler compounds, this paper studies the new topological materials related to Heusler compounds and their topological properties, such as anomalous Hall effect, skyrmions, chiral anomaly, Dirac fermion, Weyl fermion, transverse Nernst thermoelectric effect, thermal spintronics and topological surface states. It can be discovered that the topological state of Heusler compound can be well protected due to its high symmetry, thus producing rich topological properties. Heusler materials belonged to Weyl semimetals usually have strong anomalous Hall effect, and the Heusler materials with doping or Anomalous Nernst Effect (ANE) usually have higher thermoelectric figure of merit. These anomalous effects are closely related to the strong spin–orbit interaction. In application, people can use the non-dissipative edge state of quantum anomalous Hall effect to develop a new generation of low-energy transistors and electronic devices. The conversion efficiency of thermoelectric materials can be improved by ANE, and topological superconductivity can be used to promote the progress of quantum computation.

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.

scholarly journals Superconductivity in doped Weyl semimetal Mo0.9IR0.1Te2 with broken inversion symmetry

2021 ◽  
Author(s):  
Manasi Mandal ◽  
Chandan Patra ◽  
Anshu Kataria ◽  
Suvodeep Paul ◽  
Surajit Saha ◽  
...  
Keyword(s):  
Hall Effect ◽  
Chiral Anomaly ◽  
Inversion Symmetry ◽  
Type Ii ◽  
Promising Candidate ◽  
Planar Hall Effect ◽  
Topological Superconductor ◽  
Weyl Semimetal ◽  
Type Ii Superconductivity ◽  
Magneto Resistance

Abstract This work presents the emergence of superconductivity in Ir - doped Weyl semimetal T$_d$ - MoTe$_{2}$ with broken inversion symmetry. Chiral anomaly induced planar Hall effect and anisotropic magneto-resistance confirm the topological semimetallic nature of Mo$_{1-x}$Ir$_{x}$Te$_{2}$. Observation of weak anisotropic, moderately coupled type-II superconductivity in T$_d$ -Mo$_{1-x}$Ir$_{x}$Te$_{2}$ makes it a promising candidate for topological superconductor.

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 Nonlinear Hall effect in Weyl semimetals induced by chiral anomaly

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Rui-Hao Li ◽  
Olle G. Heinonen ◽  
Anton A. Burkov ◽  
Steven S.-L. Zhang
Keyword(s):  
Hall Effect ◽  
Chiral Anomaly ◽  
Weyl Semimetals

scholarly journals Probing the chiral anomaly by planar Hall effect in Dirac semimetal Cd3As2 nanoplates

2018 ◽  
Vol 98 (16) ◽  
Author(s):  
Min Wu ◽  
Guolin Zheng ◽  
Weiwei Chu ◽  
Yequn Liu ◽  
Wenshuai Gao ◽  
...  
Keyword(s):  
Hall Effect ◽  
Chiral Anomaly ◽  
Planar Hall Effect ◽  
Dirac Semimetal

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 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.

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