A possible sighting of Majorana states Nearly 80 years ago, the Italian physicist Ettore Majorana proposed the existence of an unusual type of particle that is its own antiparticle, the so-called Majorana fermion. The search for a free Majorana fermion has so far been unsuccessful, but bound Majorana-like collective excitations may exist in certain exotic superconductors. Nadj-Perge et al. created such a topological superconductor by depositing iron atoms onto the surface of superconducting lead, forming atomic chains (see the Perspective by Lee). They then used a scanning tunneling microscope to observe enhanced conductance at the ends of these chains at zero energy, where theory predicts Majorana states should appear. Science, this issue p. 602; see also p. 547 Scanning tunneling microscopy is used to observe signatures of Majorana states at the ends of iron atom chains. [Also see Perspective by Lee] 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.

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Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

Hybrid quantum materials allow for quantum phases that otherwise do not exist in nature1,2. For example, a one-dimensional topological superconductor with Majorana states bound to its ends can be realized by coupling a semiconductor nanowire to a superconductor in the presence of a strong magnetic field3–5. However, the applied magnetic fields are detrimental to superconductivity, and constrain device layout, components, materials, fabrication and operation6. Early on, an alternative source of Zeeman coupling that circumvents these constraints—using a ferromagnetic insulator instead of an applied field—was proposed theoretically7. Here, we report transport measurements in hybrid nanowires using epitaxial layers of superconducting Al and the ferromagnetic insulator EuS on semiconducting InAs nanowires. We infer a remanent effective Zeeman field exceeding 1 T and observe stable zero-bias conductance peaks in bias spectroscopy at zero applied field, consistent with topological superconductivity. Hysteretic spectral features in applied magnetic field support this picture. By incorporating a ferromagnetic layer in their superconductor–semiconductor nanowire hybrid device, Vaitiekėnas et al. show that zero-bias peaks—potential Majorana bound states—can be induced without an external magnetic field.

Zero-bias peaks at zero magnetic field in ferromagnetic hybrid nanowires

A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.

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A Josephson phase battery.

Among the major avenues that are being pursued for realizing quantum bits, the Majorana-based approach has been the most recent to be launched. It attempts to realize qubits that store quantum information in a topologically protected manner. The quantum information is protected by non-local storage in localized and well-separated Majorana zero modes, and manipulated by exploiting their non-abelian quantum statistics. Realizing these topological qubits is experimentally challenging, requiring superconductivity, helical electrons (created by spin–orbit coupling) and breaking of time-reversal symmetry to all cooperate in an uncomfortable alliance. Over the past decade, several candidate materials systems for realizing Majorana-based topological qubits have been explored, and there is accumulating, though still debated, evidence that zero modes are indeed being realized. This Review surveys the basic physical principles on which these approaches are based, the materials systems that are being developed and the current state of the field. We highlight both the progress that has been made and the challenges that still need to be overcome. Topological qubits are attractive because of the potential to store quantum information in a topologically protected manner; however, they are challenging to realize. This Review surveys the recent attempts to realize topological qubits out of materials systems that combine superconductivity, spin–orbit coupling and a magnetic field, and surveys both theoretical ideas and experimental results.

Engineered platforms for topological superconductivity and Majorana zero modes

We report transport measurements and tunneling spectroscopy in hybrid nanowires with epitaxial layers of superconducting Al and the ferromagnetic insulator EuS, grown on semiconducting InAs nanowires. In devices where the Al and EuS covered facets overlap, we infer a remanent effective Zeeman field of order 1 T, and observe stable zero-bias conductance peaks in tunneling spectroscopy into the end of the nanowire, consistent with topological superconductivity at zero applied field. Hysteretic features in critical current and tunneling spectra as a function of applied magnetic field support this picture. Nanowires with non-overlapping Al and EuS covered facets do not show comparable features. Topological superconductivity in zero applied field allows new device geometries and types of control.

Zero-field Topological Superconductivity in Ferromagnetic Hybrid Nanowires

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for the design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of freestanding vapor-liquid-solid grown and in-plane selective area grown semiconductor-ferromagnetic insulator-superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite and zinc-blende InAs/rock-salt EuS interfaces as well as rock-salt EuS/face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase is easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show that the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfill key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing.

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Semiconductor-Ferromagnetic Insulator-Superconductor Nanowires: Stray Field and Exchange Field.

Hybrid semiconductor–ferromagnetic insulator heterostructures are interesting due to their tunable electronic transport, self-sustained stray field, and local proximitized magnetic exchange. In thi...

Christian Koch

Papers

Semiconductor-Ferromagnetic Insulator-Superconductor Nanowires: Stray Field and Exchange Field.

Coherent Epitaxial Semiconductor-Ferromagnetic Insulator InAs/EuS Interfaces: Band Alignment and Magnetic Structure.