Trap-controlled fractal diffusion model of an atypical dielectric response

•New model of non-Debye dielectric relaxation, which leads to a new expression for an atypical two-power-law dielectric response, is developed.•A new expression for the complex dielectric permittivity in the frequency domain, which describes well the experimental dielectric spectra demonstrating atypical relaxation behavior, is obtained.•Relationships that relate microscopic parameters of the medium and parameters of atypical dielectric response, such as relaxation time and fractional-power exponents characterizing the shape of the dielectric loss peak are obtained. Within the framework of the multiple trapping and the fractal diffusion equation models a new expression for the complex dielectric permittivity in the frequency domain is found. The new expression allows us to describe an atypical two-power-law dielectric response. An analytical expression for the relaxation time, which is expressed through microscopic parameters of the structural and energy disorder of the system is obtained. Good agreement of the new expression for the complex dielectric permittivity with observed dielectric responses of porous glass composite ADP and nanoscale Si-layered system is demonstrated.