Topological Aspects of Quantum Hall Fluid and Berry Phase

1998 ◽  
Vol 12 (26) ◽  
pp. 2649-2707 ◽  
Author(s):  
Banasri Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Characteristic Features

We have analyzed here the recent development towards our understanding of the Integral and Fractional Quantum Hall effect. It has been pointed out that the chiral anomaly and Berry phase approach embraces in a unified way the whole spectrum of quantum Hall systems with their various characteristic features. This formalism also helps us to understand the edge states observed in Hall fluids. It is argued that Hall fluids with even denominator filling factor leads to the non-Abelian Berry phase.

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.

scholarly journals Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

2016 ◽  
Vol 12 (2) ◽  
pp. 118-122 ◽  
Author(s):  
Javier D. Sanchez-Yamagishi ◽  
Jason Y. Luo ◽  
Andrea F. Young ◽  
Benjamin M. Hunt ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Edge States ◽  
Electron Hole ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Graphene Electron

QUANTUM HALL EFFECT AND BERRY PHASE

1994 ◽  
Vol 08 (26) ◽  
pp. 1643-1653 ◽  
Author(s):  
DIPTI BANERJEE ◽  
PRATUL BANDYOPADHYAY
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Intense Magnetic Field ◽  
Topological Features

It is shown here that a particle in an intense magnetic field may acquire the Berry phase and the topological features associated with this phase may be taken to be responsible for both the integrally and fractionally quantized Hall effect. The two different manifestations of quantum Hall effect have been realized in a unified scheme where the electrons associated with the fractional quantum Hall effect are found to be in an excited state having higher angular momentum.

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