Spin – Pseudospin Textures in Bilayer Quantum Hall Systems Bahman Roostaei
It is now well established that the two-dimensional electron gas (2DEG) in a double-quantum-well system (DQWS) at filling factor has a broken symmetry ground state that can be described as either an easy-plane pseudospin ferromagnet or as an excitonic superfluid. In most studies of the bilayer coherent states at or near filling factor , it is generally assumed that, due to the strong magnetic field, the ground state is fully spin polarized. The spin degrees of freedom could thus be left out of the analysis. Recent experiments, however, cast some doubts into the validity of this approximation. These experiments involve the measurement of the activation energy (Fig. 1) or the NMR time T1 near (Fig. 2). (Fig. 1) D. Terasawa, et. Al.,Physica E 22 (2004) 52-55 In this graph is the density imbalance between the layers		( Fig. 2) I.B Spielman,et.al.,PRL94,076803(2005)
The basic idea is as follows : A pseudospin excitation (meron) is a certain charge density profile formed in the double quantum well and is creating a charge imbalance between the two quantum wells. Sometimes (at low tunneling and high inter-well separation) the cost of this imbalance is more than the cost of tilting spins at the core of the merons even in presence of magnetic field. A CP(3) Skyrmion is a combined spin-pseudospin structure that has tilted spin at the core and reduced charge imbalance. --------------------------------------------------------------------- We have shown that crystal states with some amount of spin depolarization due either to the excitations of spin-Skyrmion or CP(3) Skyrmion exist around filling factor one that have lower energy than crystal states with full spin polarization. We show this by comparing the energy of several crystal states in the Hartree-Fock approximation. ---------------------------------------------------------------------- On the right column : (top) Energy difference between the CP(3) state and the Pseudospin texture lattice state for different values of the Zeeman coupling at . (bottom) Spin polarization per electron in the CP(3) state (dashed lines) for the different Zeeman couplings .
(Above) Spin textures in each well (bottom) and pseudospin textures in each spin component (top) of a CP(3) crystal at . The crystal has four merons per unit cell. In each unit cell, two merons with the same vorticities have opposite phases. The contours color indicated on the legends at the right side of each plot is for the z component of each field.

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