arXiv subjects

M. D. Johnson

Publications and source records attributed to M. D. Johnson.

75 records · Page 5Linked to original sources

arXiv1993

Haldane fractional statistics in the fractional quantum Hall effect

We have tested Haldane's ``fractional-Pauli-principle'' description of excitations around the $ν= 1/3$ state in the FQHE, using exact results for small systems of electrons. We find that Haldane's prediction $β= \pm 1/m$ for quasiholes and quasiparticles, respectively, describes our results well with the modification $β_{qp} = 2-1/3$ rather than $-1/3$. We also find that this approach enables us to better understand the {\it energetics\/} of the ``daughter'' states; in particular, we find good evidence, in terms of the effective interaction between quasiparticles, that the states $ν= 4/11$ and 4/13 should not be stable.

cond-mat↗

arXiv1993

Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet

In this article we discuss the ground state of a parabolically confined quantum dots in the limit of very strong magnetic fields where the electron system is completely spin-polarized and all electrons are in the lowest Landau level. Without electron-electron interactions the ground state is a single Slater determinant corresponding to a droplet centered on the minimum of the confinement potential and occupying the minimum area allowed by the Pauli exclusion principle. Electron-electron interactions favor droplets of larger area. We derive exact criteria for the stability of the maximum density droplet against edge excitations and against the introduction of holes in the interior of the droplet. The possibility of obtaining exact results in the strong magnetic field is related to important simplifications associated with broken time-reversal symmetry in a strong magnetic field.

cond-mat↗

arXiv1992

Magnetic Oscillations of a Fractional Hall Dot

We show that a quantum dot in the fractional Hall regime exhibits mesoscopic magnetic oscillations with a period which is a multiple of the period for free electrons. Our calculations are performed for parabolic quantum dots with hard-core electron-electron interactions and are exact in the strong field limit for $k_B T$ smaller than the fractional Hall gap. Explicit expressions are given for the temperature dependence of the amplitude of the oscillations.

cond-mat↗