Quantum Effects on Melting Temperature of Two-Dimensional Wigner Solid

Quantum effects on the melting temperature triggered by the dislocation mechanism of Kosterlitz-Thouless-Halperin-Nelson-Young are estimated for two-dimensional Wigner solid. By use of the Wigner representation for the partition function we evaluated expansion coefficients of the shear modulus in terms of the Planck constant up to the order of \(⁴\). It is shown that there exist two different expansion parameters, \(²/m*r²₀T\) and \(e²²/ε₀m*r³₀T²\) where m * , ε 0 , r 0 and T are effective mass, dielectric constant, average distance and temperature respectively. The result indicates the existence of the maximum of the melting temperature, T M , at around n ( a * B / a B ) 2 ∼10 10 cm -2 with ε 2 0 ( m / m * ) T M ∼2 K where a B and m are the Bohr radius and the free electron mass and a * B = a B ε 0 m / m * is the effective Bohr radius. Effects of weak magnetic fields are also estimated.