NUMERICAL STUDY OF JASTROW-SLATER TRIAL STATES FOR THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (07) ◽  
pp. 503-510 ◽  
Author(s):  
NANDINI TRIVEDI ◽  
J.K. JAIN
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Numerical Study ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Correlation Factors

We study the recently proposed trial states for the fractional quantum Hall effect, which are constructed by multiplying the wavefunction for filled Landau levels with Jastrow correlation factors. In spite of the essential use of higher Landau levels, we demonstrate the validity of the variational states using Monte Carlo methods by showing that the Jastrow factors ensure (i) these states lie predominantly in the lowest Landau level and (ii) they have very low interaction energies.

scholarly journals Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene

Science ◽  
2014 ◽  
Vol 345 (6192) ◽  
pp. 55-57 ◽  
Author(s):  
A. Kou ◽  
B. E. Feldman ◽  
A. J. Levin ◽  
B. I. Halperin ◽  
K. Watanabe ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Bilayer Graphene ◽  
Fractional Quantum Hall Effect ◽  
Many Body ◽  
Electron Hole ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The distinct combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH states. Here, we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors ν = 2p + 2/3, with hints of additional states appearing at ν = 2p + 3/5, where p = –2, –1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

NON-1/m FRACTIONAL QUANTUM HALL EFFECT IS A MANIFESTATION OF ANYON SUPERCONDUCTIVITY

1991 ◽  
Vol 05 (10) ◽  
pp. 1739-1749 ◽  
Author(s):  
Chia-Ren Hu
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Statistical Correlation ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
The Mean

Regarding electrons as anyons of index αs pierced with -(m+αs) flux quanta per particle, and letting the mean field of these fluxes cancel the external magnetic field B, we obtain the filling factor ν=1/(m+αs), where m must be odd. Demanding the resulting system of anyons to exhibit "anyon supercanductivity", we obtain αs=±(1-q/n) where q is odd, and n>q is relatively prime to q. For q=1 we recover a formula due to Jain, and resolve the mystery why, for a state with ν=n/(2pn±1)<1 he requires use of the statistical correlation of n filled Landau levels. For q=3,5,⋯, we obtain the fractions 4/11, 4/13, 5/13, etc., which are missing from Jain's list. Thus this non-heirarchical approach to the non-1/m fractional quantum Hall effect has the strengths of Jain's composite-fermion approach, but not its (potential) weaknesses.

Fractional quantum Hall effect in hole Landau levels

1990 ◽  
Vol 41 (2) ◽  
pp. 1290-1293 ◽  
Author(s):  
S.-R. Eric Yang ◽  
A. H. MacDonald ◽  
D. Yoshioka
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Fractional Quantum ◽  
Fractional Quantum Hall
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