Energy spectrum, density of states, and optical transitions in strongly biased narrow-gap quantum wells

We study theoretically the effect of an electric field on the electron states and far-infrared optical properties in narrow-gap lead salt quantum wells. The electron states are described by a two-band Hamiltonian. An application of a strong electric field across the well allows the control of the energy gap between the two-dimensional (2D) states in a wide range. A sufficiently strong electric field transforms the narrow-gap quantum well to a nearly gapless 2D system, whose electron energy spectrum is described by linear dispersion relations ${\varepsilon }_{\sigma }\mathrm{}\left(k\right)\mathrm{}\sim \pm \left(k-k_{\sigma }\right),$ where $k_{\sigma }$ are the field-dependent 2D momenta corresponding to the minimum energy gaps for the states with spin numbers σ. Due to the field-induced shift of the 2D subband extrema away from $k=0\mathrm{}$ the density of states has inverse-square-root divergencies at the edges. This property may result in a considerable increase of the magnitude of the optical absorption and in the efficiency of the electro-optical effect.