Two-dimensional electron crystal in magnetic field. Topological phase transitions and stability region.

The phase diagram of a 2-dim. electron system in the magnetic field $\text{H}$ is analyzed. We obtain ab initio the free energy F{U_iκ} of a deformed electron crystal when the long-range Coulomb forces and $\text{H}$ are taken into account. Using F{u_iκ} we find H-dependent interaction between the dislocations and the curve of the topological melting due to the dissociation of dislocation pairs. The topological melting curve for H → ∞ asimptotically approaches to the melting curve of a classical crystal. This result is obtained using Feynman variational technique as well. We examine also the electron liquid crystal phase and the stability region of a 2-dim. crystal at $\text{H}$ ≠ 0. The first-order phase transitions from the crystal and liquid crystal to the isotropic liquid are predicted to take place in a definite region of the phase diagram. We find the increase of the crystal and liquid crystal region on the T-n phase diagram with H increase. The various phenomenological stability criteria are ånaylzed.