Quantum scaling for the metal-insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase's resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.