Quantum Effects on Melting Temperature of Two-Dimensional Wigner Solid in Strong Magnetic Fields

Abstract

Melting temperature due to dislocation mechanism of two-dimensional Wigner solid in strong magnetic fields, H, is estimated as a function of inverse of the field strength. In the limit of strong fields the melting temperature, T_M, is shown to satisfy the classical relation e²(πn)^1⁄2⁄ε₀T_M=Γ₀ for any electron density, n. Here ε₀ is the dielectric constant. As the field decreases, T_M gets lower and this field dependence is estimated to the order of H⁻². The result indicates that the region of densities and temperatures is very limited for the existence of the Wigner solid even in strong fields. Combining the present result with the former Hartree-Fock calculations on the critical temperature of the charge density wave instability, we propose a phase diagram of the Si-inversion layer in strong magnetic fields.