The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

/pdf/new-directions-in-the-pursuit-of-majorana-fermions-in-solid-5cpnozn547.pdf

New directions in the pursuit of Majorana fermions in solid state systems.

Light-Emitting Diodes. (Monographs in Electrical and Electronic Engineering.) By A. A. Bergh and P. J. Dean. Pp. viii+591. (Clarendon: Oxford; Oxford University: London, 1976.) £22.

/pdf/light-emitting-diodes-ubzde6g9qc.pdf

Light-emitting diodes

The 1937 theoretical discovery of Majorana fermions--whose defining property is that they are their own anti-particles--has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review article highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic `topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to `engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals, and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects, and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions--the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

/pdf/new-directions-in-the-pursuit-of-majorana-fermions-in-solid-5afwb64kak.pdf

New directions in the pursuit of Majorana fermions in solid state systems

The synthesis of a quantum computer remains an ongoing challenge in modern physics. Whereas decoherence stymies most approaches, topological quantum computation schemes evade decoherence at the hardware level by storing quantum information non-locally. Here we establish that a key operation—braiding of non-Abelian anyons—can be implemented using one-dimensional semiconducting wires. Such wires can be driven into a topological phase supporting long-sought particles known as Majorana fermions that can encode topological qubits. We show that in wire networks, Majorana fermions can be meaningfully braided by simply adjusting gate voltages, and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental set-ups that enable probing of the Majorana fusion rules and the efficient exchange of arbitrary numbers of Majorana fermions. This work should open a new direction in topological quantum computation that benefits from physical transparency and experimental feasibility.

/pdf/non-abelian-statistics-and-topological-quantum-information-1uij8s14gt.pdf

Non-Abelian statistics and topological quantum information processing in 1D wire networks

Semiconductor InSb nanowires are expected to provide an excellent material platform for the study of Majorana fermions in solid state systems. Here, we report on the realization of a Nb-InSb nanowire-Nb hybrid quantum device and the observation of a zero-bias conductance peak structure in the device. An InSb nanowire quantum dot is formed in the device between the two Nb contacts. Due to the proximity effect, the InSb nanowire segments covered by the superconductor Nb contacts turn to superconductors with a superconducting energy gap Δ(InSb) ∼ 0.25 meV. A tunable critical supercurrent is observed in the device in high back gate voltage regions in which the Fermi level in the InSb nanowire is located above the tunneling barriers of the quantum dot and the device is open to conduction. When a perpendicular magnetic field is applied to the devices, the critical supercurrent is seen to decrease as the magnetic field increases. However, at sufficiently low back gate voltages, the device shows the quasi-particle Coulomb blockade characteristics and the supercurrent is strongly suppressed even at zero magnetic field. This transport characteristic changes when a perpendicular magnetic field stronger than a critical value, at which the Zeeman energy in the InSb nanowire is E(z) ∼ Δ(InSb), is applied to the device. In this case, the transport measurements show a conductance peak at the zero bias voltage and the entire InSb nanowire in the device behaves as in a topological superconductor phase. We also show that this zero-bias conductance peak structure can persist over a large range of applied magnetic fields and could be interpreted as a transport signature of Majorana fermions in the InSb nanowire.

Anomalous Zero-Bias Conductance Peak in a Nb-InSb Nanowire-Nb Hybrid Device.

Nanoscale superconductor/semiconductor hybrid devices are assembled from indium arsenide semiconductor nanowires individually contacted by aluminum-based superconductor electrodes. Below 1 kelvin, the high transparency of the contacts gives rise to proximity-induced superconductivity. The nanowires form superconducting weak links operating as mesoscopic Josephson junctions with electrically tunable coupling. The supercurrent can be switched on/off by a gate voltage acting on the electron density in the nanowire. A variation in gate voltage induces universal fluctuations in the normal-state conductance, which are clearly correlated to critical current fluctuations. The alternating-current Josephson effect gives rise to Shapiro steps in the voltage-current characteristic under microwave irradiation.

https://science.sciencemag.org/content/sci/309/5732/272.full.pdf

Tunable supercurrent through semiconductor nanowires

We report reproducible fabrication of InP−InAsP nanowire light-emitting diodes in which electron−hole recombination is restricted to a quantum-dot-sized InAsP section. The nanowire geometry naturally self-aligns the quantum dot with the n-InP and p-InP ends of the wire, making these devices promising candidates for electrically driven quantum optics experiments. We have investigated the operation of these nanoLEDs with a consistent series of experiments at room temperature and at 10 K, demonstrating the potential of this system for single photon applications.

Single quantum dot nanowire LEDs.

When two superconductors are electrically connected by a weak link--such as a tunnel barrier--a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of voltage steps in Josephson junctions under microwave irradiation, and in the magnetic flux periodicity of h/2e (where h is Planck's constant) in superconducting quantum interference devices. Here we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Owing to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, that is, in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions.

Supercurrent reversal in quantum dots

Electronic transport through nanostructures is greatly affected by the presence of superconducting leads1,2,3. If the interface between the nanostructure and the superconductors is sufficiently transparent, a dissipationless current (supercurrent) can flow through the device owing to the Josephson effect4,5. A Josephson coupling, as measured by the zero-resistance supercurrent, has been obtained using tunnel barriers, superconducting constrictions, normal metals and semiconductors. The coupling mechanisms vary from tunnelling to Andreev reflection5,6,7,8. The latter process has hitherto been observed only in normal-type systems with a continuous density of electronic states. Here we investigate a supercurrent flowing through a discrete density of states—that is, the quantized single particle energy states of a quantum dot9, or ‘artificial atom’, placed between superconducting electrodes. For this purpose, we exploit the quantum properties of finite-sized carbon nanotubes10. By means of a gate electrode, successive discrete energy states are tuned on- and off-resonance with the Fermi energy in the superconducting leads, resulting in a periodic modulation of the critical current and a non-trivial correlation between the conductance in the normal state and the supercurrent. We find, in good agreement with existing theory11, that the product of the critical current and the normal state resistance becomes an oscillating function, in contrast to being constant as in previously explored regimes.

Quantum supercurrent transistors in carbon nanotubes

The growth of III-V semiconductors on silicon would allow the integration of their superior (opto-)electronic properties with silicon technology. But fundamental issues such as lattice and thermal expansion mismatch and the formation of antiphase domains have prevented the epitaxial integration of III-V with group IV semiconductors. Here we demonstrate the principle of epitaxial growth of III-V nanowires on a group IV substrate. We have grown InP nanowires on germanium substrates by a vapour-liquid-solid method. Although the crystal lattice mismatch is large (3.7%), the as-grown wires are monocrystalline and virtually free of dislocations. X-ray diffraction unambiguously demonstrates the heteroepitaxial growth of the nanowires. In addition, we show that a low-resistance electrical contact can be obtained between the wires and the substrate.

Jorden A. van Dam

Papers

Tunable supercurrent through semiconductor nanowires

Single quantum dot nanowire LEDs.

Supercurrent reversal in quantum dots

Quantum supercurrent transistors in carbon nanotubes

Epitaxial growth of InP nanowires on germanium.