Phase diagram and skyrmion energy for bilayer heterostructures at integer filling factors

Possible Jahn-Teller effect in Si inverse layers

“…Fig.4. Note that the prominent minimum of the skyrmion anisotropy energy gap coincide with the phase transition line C-F from the phase diagram Fig.3.This skyrmion anisotropic energy is similar to the bilayer case12 with t being the hopping constant between the two layers. In the experiment on GaAs bilayer 18 a profound reduction of the thermal activation gap has been found in some interval on the ν = 2 line.In the case ν = 1 we parameterize general rotations from the denominator sub-group by four angles:…”

“…This formula is valid in the limit E sk min ≪ E 1 . The resulting anisotropic part of a skyrmion gap is shown on the This skyrmion anisotropic energy is similar to the bilayer case 12 with t being the hopping constant between the two layers. In the experiment on GaAs bilayer 18 a profound reduction of the thermal activation gap has been found in some interval on the ν = 2 line.…”

“…Reference state is alternatively given by an electron occupation matrix: N ατ1,βτ2 = (1, 0, 0, 0), in the case ν = 1, and N ατ1,βτ2 = (1, 1, 0, 0), in the case ν = 2. Electron Green function on the lowest Landau level for the reference ground state of Hamiltonian (12) with Ω = 0 reads:…”

“…10 The layer degeneracy of electron states can be described by a four component spinor in combined spin-layer space. In the works 11,12 the total 2DEG Hamiltonian was subdivided into a symmetric part and a small anisotropic part which reduces the symmetry. Symmetric part is invariant under a hidden SU(4) group of transformations in the combined spin and valley Fock space which augment apparent group SU(2)⊗SU(2) of separate transformations in spin and valley spaces.…”