Topological superconductors which support Majorana fermions are thought to be realized in one-dimensional semiconducting wires coupled to a superconductor [1][2][3]. Such excitations are expected to exhibit non-Abelian statistics and can be used to realize quantum gates that are topologically protected from local sources of decoherence [4,5]. Here we report the observation of the fractional a.c. Josephson effect in a hybrid semiconductor/superconductor InSb/Nb nanowire junction, a hallmark of topological matter. When the junction is irradiated with a radio-frequency f 0 in the absence of an external magnetic field, quantized voltage steps (Shapiro steps) with a height ∆V = hf 0 /2e are observed, as is expected for conventional superconductor junctions, where the supercurrent is carried by charge-2e Cooper pairs. At high magnetic fields the height of the first Shapiro step is doubled to hf 0 /e, suggesting that the supercurrent is carried by charge-e quasiparticles. This is a unique signature of Majorana fermions, elusive particles predicted ca. 80 years ago [6].In 1928 Dirac reconciled quantum mechanics and special relativity in a set of coupled equations, which became the cornerstone of quantum mechanics [7]. Its main prediction that every elementary particle has a complex conjugate counterpart -an antiparticle -has been confirmed by numerous experiments. A decade later Majorana showed that Dirac's equation for spin-1/2 particles can be modified to permit real wavefunctions [6,8]. The complex conjugate of a real number is the number itself, which means that such particles are their own antiparticles. While the search for Majorana fermions among elementary particles is ongoing [9], excitations with similar properties may emerge in electronic systems [4], and are predicted to be present in some unconventional states of matter [10][11][12][13][14][15].Ordinary spin-1/2 particles or excitations carry a charge, and thus cannot be their own antiparticles. In a superconductor, however, free charges are screened, and charge-less spin-1/2 excitations become possible. The BCS theory allows fermionic excitations which are a mixture of electron and hole creation operators, γ i = c † i + c i . This creation operator is invariant with respect to charge conjugation, c † i ↔ c i . If the energy of an excitation created in this way is zero, the excitation will be a Majorana particle. However, such zero-energy modes are not permitted in ordinary s-wave superconductors.The current work is inspired by the paper of Sau et al.[15] who predicted that Majorana fermions can be formed in a coupled semiconductor/superconductor system. Superconductivity can be induced in a semiconductor material by the proximity effect. At zero magnetic field electronic states are doubly-degenerate and Majorana modes are not supported. In semiconductors with strong spin-orbit (SO) interactions the two spin branches are separated in momentum space, but SO interactions do not lift the Kramer's degeneracy. However, in * To whom correspondence should be addre...

Conventional computer electronics creates a dichotomy between how information is processed and how it is stored. Silicon chips process information by controlling the flow of charge through a network of logic gates. This information is then stored, most commonly, by encoding it in the orientation of magnetic domains of a computer hard disk. The key obstacle to a more intimate integration of magnetic materials into devices and circuit processing information is a lack of efficient means to control their magnetization. This is usually achieved with an external magnetic field or by the injection of spin-polarized currents [1,2,3]. The latter can be significantly enhanced in materials whose ferromagnetic properties are mediated by charge carriers [4]. Among these materials, conductors lacking spatial inversion symmetry couple charge currents to spin by intrinsic spin-orbit (SO) interactions, inducing nonequilibrium spin polarization [5,6,7,8,9,10,11] tunable by local electric fields. Here we show that magnetization of a ferromagnet can be reversibly manipulated by the SO-induced polarization of carrier spins generated by unpolarized currents. Specifically, we demonstrate domain rotation and hysteretic switching of magnetization between two orthogonal easy axes in a model ferromagnetic semiconductor.In crystalline materials with inversion asymmetry, intrinsic spin-orbit interactions (SO) couple the electron spin with its momentumhk. The coupling is given by the Hamiltonian H so =h 2σ · Ω(k), whereh is the Planck's constant andσ is the electron spin operator (for holesσ should be replaced by the total angular momentum J). Electron states with different sign of the spin projection on Ω(k) are split in energy, analogous to the Zeeman splitting in an external magnetic field. In zinc-blende crystals such as GaAs there is a cubic Dresselhaus term[12] Ω D ∝ k 3 , while strain introduces a term Ω ε = C∆ε(k x , −k y , 0) that is linear in k, where ∆ε is the difference between strain in theẑ andx,ŷ directions [13]. In wurzite crystals or in multilayered materials with structural inversion asymmetry there also exists the Rashba term[14] Ω R which has a different symmetry with respect to the direction of k,, whereẑ is along the axis of reduced symmetry. In the presence of an electric field the electrons acquire an average momentumh∆k(E), which leads to the generation of an electric current j =ρ −1 E in the conductor, whereρ is the resistivity tensor. This current defines the preferential axis for spin precession Ω(j) . As a result, a nonequilibrium current-induced spin polarization J E Ω(j) is generated, whose magnitude J E depends on the strength of various mechanisms of momentum scattering and spin relaxation [5,15]. This spin polarization has been measured in non-magnetic semiconductors using optical [7,8,9,11,16] and electron spin resonance [17] techniques. It is convenient to parameterize J E in terms of an effective magnetic field H so . Different contributions to H so have different current dependencies (∝ j or j 3 ), as we...

Charged carriers with different spin states are spatially separated in a two-dimensional hole gas. Because of strong spin-orbit interaction, holes at the Fermi energy in GaAs have different momenta for two possible spin states traveling in the same direction, and, correspondingly, different cyclotron orbits in a weak magnetic field. Two point contacts, acting as a monochromatic source of ballistic holes and a narrow detector arranged in the magnetic focusing geometry are demonstrated to work as a tunable spin filter.

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We demonstrate the local oxidation nanopatterning of graphene films by an atomic force microscope. The technique provides a method to form insulating trenches in graphene flakes and to fabricate nanodevices with sub-nanometer precision. We demonstrate fabrication of a 25-nm-wide nanoribbon and submicron size nanoring from a graphene flake. We also found that we can write either trenches or bumps on the graphene surface depending on the lithography conditions. We attribute the bumps to partial oxidation of the surface and incorporation of oxygen into the graphene lattice.