# Bulletin of the American Physical Society

# APS March Meeting 2011

## Volume 56, Number 1

## Monday–Friday, March 21–25, 2011; Dallas, Texas

### Abstract: C1.00122 : The complete interpretation of the fractions in quantum Hall effect

#### Author:

We propose that the modified cyclotron energy is given by
(h/2$\pi )\omega _{c}$(1/2)g(n+1/2) so that the fractional charge
is given by the angular momentum with both signs of spin, j = $l
\pm $ s. In addition to the (i) principal fractions given by
(1/2)g our theory with effective charge e*=(1/2)ge, has (ii)
resonances at $\nu _{1}-\nu _{2}$ and (iii) two-particle states
at $\nu _{1}+\nu _{2}$ and there are (iv) clusters with spin
$>$1/2, where $\nu $ is a filling factor. This theory explains
all of the 101 fractions and full graphene series. The fractional
charges of graphene [2] are also explained. The series also
explains the even denominators for S=0,1,2, {\ldots}, as in
electron clusters. The S=0, L=0, corresponds to half filled
Landau level. S=1/2, L=0 with negative sign before s in j gives
the zero-energy state. All of the predicted fractions agree with
the data.
\\[4pt]
[1] K. N. Shrivastava, AIP Conf. Proc. 1150, 59-67 (2009).
\\[0pt]
[2] K. I. Bolotin, et al, Nature 462, 196(2009).

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.C1.122

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