Two-dimensional metal-insulator transition as a strong localization induced crossover phenomenon

Low-disorder and high-mobility two-dimensional (2D) electron (or hole) systems confined in semiconductor heterostructures undergo an apparent metal-insulator transition (MIT) at low temperatures as the carrier density (n) is varied. In some situations, the 2D MIT can be caused at a fixed low carrier density by changing an externally applied in-plane magnetic field parallel to the 2D layer. The goal of the current work is to obtain the critical density (n₂) for the 2D MIT with the system being an effective metal (Anderson insulator) for density n above (below) n₂. We study the 2D MIT phenomenon theoretically as a possible strong localization induced crossover process controlled by the Ioffe-Regel criterion, k₅l=1, where k₅ (n) is the 2D Fermi wave vector and l (n) is the disorder-limited quantum mean free path on the metallic side. Calculating the quantum mean free path in the effective metallic phase from a realistic Boltzmann transport theory including disorder scattering effects, we solve the integral equation (with l depending on n through multidimensional integrals) defined by the Ioffe-Regel criterion to obtain the nonuniversal critical density n₂ as a function of the applicable physical experimental parameters including disorder strength, in-plane magnetic field, spin and valley degeneracy, background dielectric constant and carrier effective mass, and temperature. The key physics underlying the nonuniversal parameter dependence of the critical density is the density dependence of the screened Coulomb disorder. Our calculated results for the crossover critical density n₂ appear to be in qualitative and semiquantitative agreement with the available experimental data in different 2D semiconductor systems lending credence to the possibility that the apparent 2D MIT signals the onset of the strong localization crossover in disordered 2D systems. We also compare the calculated critical density obtained from the Ioffe-Regel criterion with that obtained from a classical percolation theory, concluding that experiments support the Ioffe-Regel criterion for the 2D MIT crossover phenomena.