Negative refractive index in doped semiconductors

Based on methods of Quantum Optics, the possibility of achieving the negative index of refraction in a semiconductor with donor-like impurity is discussed. The quantum states of hydrogen-like donor atom and states of an electron in the conduction band constitute a discrete-level atomic medium within the optical range. The coherent coupling of an electric dipole transition with a magnetic dipole transition leads to permeability and permittivity responses and, within some frequency band, ensures the negative refractive index. The magnetic moment between two quasi-atomic states separated by optical frequencies is induced by the low-frequency e.m. field. The implementation of this scheme is carried out in tin-doped indium oxide (ITO) and calculations show feasibility of this effect within a broad bandwidth with a high figure of merit $\sim$10.