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

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

2001-07-12

arxiv.org/abs/cond-mat/0107272v7

Phys. Rev. B 65, 195310 (2002)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevB.65.195310

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_{\tiny C}=(e^2/\epsilon {}l_B)/\hbar \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 $r_{\tiny C}$ (if supposing $r_{\tiny C}$ to be small) with use of the total Hamiltonian. When extrapolated to the region $r_{\tiny C}\sim 1$, 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.

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