We present the effective low-energy theory for interacting one-dimensional (1D) quantum wires subject to Rashba spin-orbit coupling. Under a one-loop renormalization-group scheme including all allowed interaction processes for not too weak Rashba coupling, we show that electron-electron backscattering is an irrelevant perturbation. Therefore no gap arises and electronic transport is described by a modified Luttinger liquid theory. As an application of the theory, we discuss the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities. Interactions are shown to induce a slower power-law decay of the RKKY range function than the usual 1D noninteracting $\text{cos}\left(2k_{F}x\right)/\left|x\right|$ law. Moreover, in the noninteracting Rashba wire, the spin-orbit coupling causes a twisted (anisotropic) range function with several different spatial oscillation periods. In the interacting case we show that one special oscillation period leads to the slowest decay and therefore dominates the Ruderman-Kittel-Kasuya-Yosida interaction for large separation.

A transfer matrix model of a luminescent down-shifter (LDS) layer, consisting of silicon nanocrystals (Si-NCs) embedded in a silicon oxide matrix, on a silicon solar cells is presented. To enhance the efficiency of the silicon solar cell, we propose using a SiO₂/Si-NCs double layer stack, as an anti-reflection-coating (ARC) and as a LDS material. The optical characteristics of this stack have been simulated and optimized as a front surface coating. The cell performances have been simulated by means of a two-dimensional device simulator and compared with the performances of a reference silicon solar cell. We found a 6% relative enhancement of the energy conversion efficiency with respect to the reference cell. We demonstrate that this enhancement results from the lower reflectance and from the down-shifter effect of the Si-NCs activated coating stack.

We have calculated the optical conductivity of a disorder-free single graphene sheet in the presence of spin-orbit coupling, using the Kubo formalism. Both intrinsic and structural-inversion-asymmetry induced types of spin splitting are considered within a low-energy continuum theory. Analytical results are obtained that allow us to identify distinct features arising from spin-orbit couplings. We point out how optical-conductivity measurements could offer a way to determine the strengths of spin splitting due to various origins in graphene.