SU(4)skyrmions and activation energy anomaly in bilayer quantum Hall systems

Abstract

The bilayer quantum Hall (QH) system has four energy levels in the lowest Landau level, corresponding to the layer and spin degrees of freedom. We investigate the system in the regime where all four levels are nearly degenerate and equally active. The underlying group structure is $\mathrm{SU}\left(4\right)$. At $\nu =1$ the QH state is a charge-transferable state between the two layers and the $\mathrm{SU}\left(4\right)$ isospin coherence develops spontaneously. Quasiparticles are isospin textures to be identified with $\mathrm{SU}\left(4\right)$ skyrmions. The skyrmion energy consists of the Coulomb energy, the Zeeman energy and the pseudo-Zeeman energy. The Coulomb energy consists of the self-energy, the capacitance energy and the exchange energy. At the balanced point only pseudospins are excited unless the tunneling gap is too large. Then, the $\mathrm{SU}\left(4\right)$ skyrmion evolves continuously from the pseudospin-skyrmion limit into the spin-skyrmion limit as the system is transformed from the balanced point to the monolayer point by controlling the bias voltage. Our theoretical result explains quite well the experimental data due to Murphyet al. [S. Q. Murphy, J. P. Eisenstein, G. S. Boebinger, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 72, 728 (1994)] and Sawada et al. [A. Sawada, D. Terasawa, N. Kumada, M. Morino, K. Tagashira, Z. F. Ezawa, K. Muraki, T. Saku, and Y. Hirayama, Physica E 18, 118 (2003); D. Terasawa, M. Morino, K. Nakada, S. Kozumi, A. Sawada, Z. F. Ezawa, N. Kumada, K. Muraki, T. Saku, and Y. Hirayama, Physica E 22, 52 (2004)] on the activation energy anomaly induced by applying parallel magnetic field.