Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero energy end states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

Nanowires can serve as one-dimensional templates for scalable qubit registers. Unique to nanowires is the possibility to easily vary the material even during wire growth. 5Such flexibility can be used to design wires with suppressed decoherence and push semiconductor qubit fidelities towards error-correction levels. Furthermore, electrical dots can be integrated with optical dots in p-n junction nanowires. 6 The coherence times achieved here are sufficient for the conversion of an electronic qubit into a photon, the flying qubit, for long-distance quantum communication. Figure 1a shows a scanning electron microscope image of our nanowire device. Two electrodes, source and drain, are used to apply a voltage bias of 6 mV across the InAs nanowire. Voltages applied to five closely spaced narrow gates underneath the nanowire

We propose an easy-to-build easy-to-detect scheme for realizing Majorana fermions at the ends of a chain of magnetic atoms on the surface of a superconductor. Model calculations show that such chains can be easily tuned between trivial and topological ground state. In the latter, spatial resolved spectroscopy can be used to probe the Majorana fermion end states. Decoupled Majorana bound states can form even in short magnetic chains consisting of only tens of atoms. We propose scanning tunneling microscopy as the ideal technique to fabricate such systems and probe their topological properties.

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Double quantum dot in the few-electron regime is achieved using local gating in an InSb nanowire. The spectrum of two-electron eigenstates is investigated using electric dipole spin resonance. Singlettriplet level repulsion caused by spin-orbit interaction is observed. The size and the anisotropy of singlet-triplet repulsion are used to determine the magnitude and the orientation of the spin-orbit effective field in an InSb nanowire double dot. The obtained results are confirmed using spin blockade leakage current anisotropy and transport spectroscopy of individual quantum dots.PACS numbers: 73.63. Kv, 85.35.Be The spin-orbit interaction (SOI) describes coupling between the motion of an electron and its spin. In one dimension, where electrons can move only to the left or to the right, the SOI couples this left or right motion to either spin-up or spin-down. An extreme situation occurs in what is called a helical liquid [1] where, in the presence of magnetic field, all spin-up electrons move to the left and all spin-down electrons to the right. As proposed recently [2,3], a helical liquid in proximity to a superconductor can generate Majorana fermions [4]. The search for Majorana fermions in 1D conductors is focused on finding the best material in terms of a strong spin-orbit interaction and large Landé g-factors. The latter is required for a helical liquid to exist at magnetic fields that do not suppress superconductivity. High g-factors of the order 50, strong SOI and the ability to induce superconductivity put forward InSb nanowires [5,6] as a natural platform for the realization of 1D topological states.The SOI can be expressed as an effective magnetic field B SO that depends on the electron momentum. An electron moving through the wire undergoes spin precession around B SO with a π rotation over a distance l SO called the spin-orbit length (see Fig. 1(a)). The length l SO is a direct measure of the SOI strength: a stronger SOI results in a shorter l SO . In this letter, we use spin spectra of single electrons in quantum dots [7] to extract l SO and the direction of B SO . In quantum dots, the SOI hybridizes states with different spin [5,8,9]. For a single electron, the SOI-hybridized spin-up and spin-down states form a spin-orbit qubit [10,11]. For two electrons SOI hybridization induces level repulsion between singlet and triplet states. The resulting level-repulsion gap between the well-defined qubit states can be used to measure the SOI: the gap size is determined by l SO [5,8,9] and the gap anisotropy indicates the direction of B SO [12][13][14]. Double quantum dots in InSb nanowires are defined by local gating (Figs. 1(b),1(c)). A finite voltage is applied across the source and drain electrodes; and the current through the nanowire is measured. Five gates underneath the wire create the confinement potential and control the electron number on the two dots [9,15]. We focus on the (1,1) charge configuration ( Fig. 1(d)), in which both the left and the right dot contain exactly one electron, each of them...

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system 1-5 . To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance 6-8 as well as edge-dominated current flow 9 . However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) 4 and there have been recent experimental indications of possible topological boundary states at their edges 10-13 . However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that

The Josephson e ect describes supercurrent flowing through a junction connecting two superconducting leads by a thin barrier 1 . This current is driven by a superconducting phase di erence ϕ between the leads. In the presence of chiral and time-reversal symmetry of the Cooper pair tunnelling process 2 , the current is strictly zero when ϕ vanishes. Only if these underlying symmetries are broken can the supercurrent for ϕ = 0 be finite [3][4][5] . This corresponds to a ground state of the junction being o set by a phase ϕ 0 , di erent from 0 or π. Here, we report such a Josephson ϕ 0 -junction based on a nanowire quantum dot. We use a quantum interferometer device to investigate phase o sets and demonstrate that ϕ 0 can be controlled by electrostatic gating. Our results may have far-reaching implications for superconducting flux-and phase-defined quantum bits as well as for exploring topological superconductivity in quantum dot systems.The process of Cooper pair tunnelling through a Josephson junction (JJ) is, in general, symmetric with respect to time inversion. This has a profound consequence for the JJ current-phase relation, I (ϕ). In particular it imposes the condition I (−ϕ) = −I (ϕ), which in turn results in I (ϕ = 0) being strictly zero. The I (ϕ = 0) = 0 condition is a consequence of the fact that for each process contributing to current flowing in one direction there is an opposite time-reversed process, in which spin-up and spin-down electrons are reversed, that exactly cancels this current. However, time inversion is not the only symmetry which can protect the I (ϕ = 0) = 0 condition. For example, in JJs based on single-domain ferromagnets, time inversion is broken, but the supercurrent is still zero for ϕ = 0 owing to chiral symmetry-that is, the symmetry between leftward and rightward tunnelling. This symmetry ensures that the tunnelling coefficient describing the electron tunnelling from the left lead to the right lead is exactly the same as the one describing the tunnelling in reverse, from the right lead to the left lead. The two tunnelling processes (leftward and rightward) cancel each other, which again results in I (ϕ = 0) being strictly zero. This is even the case for so-called π-junctions 6 , in which the current flow is reversed compared to usual JJs, but still the underlying symmetries guarantee zero current for ϕ = 0. To create conditions for a non-zero supercurrent to flow at ϕ = 0, both symmetries need to be broken 7 . Various ways have been proposed theoretically to break the underlying symmetries and create ϕ 0 -junctions, including ones based on non-centrosymmetric or multilayer ferromagnets 3,8 , quantum point contacts 4 , topological insulators 9,10 , diffusive systems 11,12 , nanowires 13,14 and quantum dots 5,15,16 . Alternatively, an effective built-in phase offset can be obtained by combining 0-and π-junctions in parallel 17,18 . However, no experimental demonstration of a ϕ 0 -junction has been reported until now.In quantum dots (QDs), breaking of both symmetries can be achiev...

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