Activation Energy in a Quantum Hall Ferromagnet and Non-Hartree-Fock Skyrmions

Abstract

The energy of Skyrmions is calculated with the help of a technique based on the excitonic representation: the basic set of one-exciton states is used for the perturbation-theory formalism instead of the basic set of one-particle states. We use the approach, at which a skyrmion-type excitation (at zero Lande factor) is considered as a smooth non-uniform rotation in the 3D spin space. The result within the framework of an excitonically diagonalized part of the Coulomb Hamiltonian can be obtained by any ratio $r_C=(e^2/\epsilon l_B)/\hslash {\omega }_c$ [where $e^2/\epsilon l_B$ is the typical Coulomb energy ($l_B$ being the magnetic length); ${\omega }_c$ is the cyclotron frequency], and the Landau-level mixing is thereby taken into account. In parallel with this, the result is also found exactly, to second order in terms of the $r_C$ (if supposing $r_C$ to be small) with use of the total Hamiltonian. When extrapolated to the region $r_C\sim 1$, our calculations show that the skyrmion gap becomes substantially reduced in comparison with the Hartree-Fock calculations. This fact brings the theory essentially closer to the available experimental data.

14 pages, 1 figure. to appear in Phys. Rev. B, Vol. 65 (Numbers ~ 19-22), 2002

References in corpus (1)

• Auger-like Relaxation of Inter-Landau-Level Magneto-Plasmon Excitations in the Quantised Hall Regime

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