We use first principles calculations to study the electronic properties of rock salt rare earth monopnictides La$X$ ($X=$N, P, As, Sb, Bi). A new type of topological band crossing termed `linked nodal rings is found in LaN when the small spin-orbital
coupling (SOC) on nitrogen orbitals is neglected. Turning on SOC gaps the nodal rings at all but two points, which remain gapless due to $C_4$-symmetry and leads to a 3D Dirac semimetal. Interestingly, unlike LaN, compounds with other elements in the pnictogen group are found to be topological insulators (TIs), as a result of band reordering due to the increased lattice constant as well as the enhanced SOC on the pnictogen atom. These TI compounds exhibit multi-valley surface Dirac cones at three $bar{M}$-points on the $(111)$-surface.
A major challenge of spintronics is in generating, controlling and detecting spin-polarized current. Manipulation of spin-polarized current, in particular, is difficult. We demonstrate here, based on calculated transport properties of graphene nanori
bbons, that nearly +-100% spin-polarized current can be generated in zigzag graphene nanoribbons (ZGNRs) and tuned by a source-drain voltage in the bipolar spin diode, in addition to magnetic configurations of the electrodes. This unusual transport property is attributed to the intrinsic transmission selection rule of the spin subbands near the Fermi level in ZGNRs. The simultaneous control of spin current by the bias voltage and the magnetic configurations of the electrodes provides an opportunity to implement a whole range of spintronics devices. We propose theoretical designs for a complete set of basic spintronic devices, including bipolar spin diode, transistor and logic gates, based on ZGNRs.
