Disorder driven peculiarities of metal-insulator transition in the interacting fermions ensemble

We demonstrate that introducing disorder to a system of interacting fermions can lead to a metal-dielectric transition (MDT) in it. Additionally, depending on the relationship between the degree of disorder and the real physical dimensionality, d, the phase transition can change from a second to a first order. To model the disorder, we replace the ordinary single-particle kinetic energy operator with a fractional Laplacian with a Lévy index of 0 < α < 2. In this case, the parameter α serves as a phenomenological descriptor of the degree of disorder. Our analysis of the system conductivity has allowed us to obtain criteria for the stability of the metallic phase against MDT, depending on the spatial dimension d. We have compared our results with many experimental features of real physical systems like graphene. Furthermore, our findings, which involve varying the degree of disorder using the parameter α, have allowed us to show how to improve the controllability of the optimal thickness and electron mobility in transition metal dichalcogenide channel transistors and other microelectronic devices.