Erik P. A. M. Bakkers

Bio: Erik P. A. M. Bakkers is an academic researcher from Eindhoven University of Technology. The author has contributed to research in topics: Nanowire & Quantum dot. The author has an hindex of 61, co-authored 272 publications receiving 16144 citations. Previous affiliations of Erik P. A. M. Bakkers include Fundamental Research on Matter Institute for Atomic and Molecular Physics & Philips.

Majorana zero modes in superconductor–semiconductor heterostructures

Abstract: Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed-matter physics. In this Review, we survey the current status of this rapidly developing field, focusing on proposals for the realization of topological superconductivity in semiconductor–superconductor heterostructures. We examine materials science progress in growing InAs and InSb semiconductor nanowires and characterizing these systems. We then discuss the observation of robust signatures of Majorana zero modes in recent experiments, paying particular attention to zero-bias tunnelling conduction measurements and Coulomb blockade experiments. We also outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation.

Twinning superlattices in indium phosphide nanowires

Abstract: In most superconductors, the pairing-up of electrons responsible for resistance-free conductivity is driven by vibrations of the solid's crystal lattice. But there are other superconducting materials in which the 'glue' responsible for binding electrons is thought to have a very different origin: quantum fluctuations of spin or charge. An unusually 'violent' generalization of such a pairing mechanisms, in which spin and charge instabilities combine forces, has been identified in the unconventional superconductor CeRhIn5. These intimately coupled fluctuations significantly disrupt the flow of electrons in their normal unpaired state, yet also provide the quantum-mechanical glue necessary for generating superconducting pairs. In this paper, the crystal structure and stacking fault density of semiconducting nanowires composed of the same material are controlled by doping, leading to twinning superlattices. Periodic arrays of rotational dislocations lead to crystal heterostructures in indium phosphide and gallium phosphide nanowires. Semiconducting nanowires offer the possibility of nearly unlimited complex bottom-up design1,2, which allows for new device concepts3,4. However, essential parameters that determine the electronic quality of the wires, and which have not been controlled yet for the III–V compound semiconductors, are the wire crystal structure and the stacking fault density5. In addition, a significant feature would be to have a constant spacing between rotational twins in the wires such that a twinning superlattice is formed, as this is predicted to induce a direct bandgap in normally indirect bandgap semiconductors6,7, such as silicon and gallium phosphide. Optically active versions of these technologically relevant semiconductors could have a significant impact on the electronics8 and optics9 industry. Here we show first that we can control the crystal structure of indium phosphide (InP) nanowires by using impurity dopants. We have found that zinc decreases the activation barrier for two-dimensional nucleation growth of zinc-blende InP and therefore promotes crystallization of the InP nanowires in the zinc-blende, instead of the commonly found wurtzite, crystal structure10. More importantly, we then demonstrate that we can, once we have enforced the zinc-blende crystal structure, induce twinning superlattices with long-range order in InP nanowires. We can tune the spacing of the superlattices by changing the wire diameter and the zinc concentration, and we present a model based on the distortion of the catalyst droplet in response to the evolution of the cross-sectional shape of the nanowires to quantitatively explain the formation of the periodic twinning.

Quantized Majorana conductance.

Abstract: Majorana zero-modes - a type of localized quasiparticle - hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e 2 /h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e 2 /h, with a recent observation of a peak height close to 2e 2 /h. Here we report a quantized conductance plateau at 2e 2 /h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.

Realizing Majorana zero modes in superconductor-semiconductor heterostructures

Abstract: Realizing topological superconductivity and Majorana zero modes in the laboratory is one of the major goals in condensed matter physics. We review the current status of this rapidly-developing field, focusing on semiconductor-superconductor proposals for topological superconductivity. Material science progress and robust signatures of Majorana zero modes in recent experiments are discussed. After a brief introduction to the subject, we outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation in these systems.

Weyl and Dirac semimetals in three-dimensional solids

Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices

Abstract: Majorana fermions are particles identical to their own antiparticles. They have been theoretically predicted to exist in topological superconductors. Here, we report electrical measurements on indium antimonide nanowires contacted with one normal (gold) and one superconducting (niobium titanium nitride) electrode. Gate voltages vary electron density and define a tunnel barrier between normal and superconducting contacts. In the presence of magnetic fields on the order of 100 millitesla, we observe bound, midgap states at zero bias voltage. These bound states remain fixed to zero bias, even when magnetic fields and gate voltages are changed over considerable ranges. Our observations support the hypothesis of Majorana fermions in nanowires coupled to superconductors.

Controlling the synthesis and assembly of silver nanostructures for plasmonic applications

Abstract: Coinage metals, such as Au, Ag, and Cu, have been important materials throughout history.1 While in ancient cultures they were admired primarily for their ability to reflect light, their applications have become far more sophisticated with our increased understanding and control of the atomic world. Today, these metals are widely used in electronics, catalysis, and as structural materials, but when they are fashioned into structures with nanometer-sized dimensions, they also become enablers for a completely different set of applications that involve light. These new applications go far beyond merely reflecting light, and have renewed our interest in maneuvering the interactions between metals and light in a field known as plasmonics.2–6 In plasmonics, the metal nanostructures can serve as antennas to convert light into localized electric fields (E-fields) or as waveguides to route light to desired locations with nanometer precision. These applications are made possible through a strong interaction between incident light and free electrons in the nanostructures. With a tight control over the nanostructures in terms of size and shape, light can be effectively manipulated and controlled with unprecedented accuracy.3,7 While many new technologies stand to be realized from plasmonics, with notable examples including superlenses,8 invisible cloaks,9 and quantum computing,10,11 conventional technologies like microprocessors and photovoltaic devices could also be made significantly faster and more efficient with the integration of plasmonic nanostructures.12–15 Of the metals, Ag has probably played the most important role in the development of plasmonics, and its unique properties make it well-suited for most of the next-generation plasmonic technologies.16–18 1.1. What is Plasmonics? Plasmonics is related to the localization, guiding, and manipulation of electromagnetic waves beyond the diffraction limit and down to the nanometer length scale.4,6 The key component of plasmonics is a metal, because it supports surface plasmon polariton modes (indicated as surface plasmons or SPs throughout this review), which are electromagnetic waves coupled to the collective oscillations of free electrons in the metal. While there are a rich variety of plasmonic metal nanostructures, they can be differentiated based on the plasmonic modes they support: localized surface plasmons (LSPs) or propagating surface plasmons (PSPs).5,19 In LSPs, the time-varying electric field associated with the light (Eo) exerts a force on the gas of negatively charged electrons in the conduction band of the metal and drives them to oscillate collectively. At a certain excitation frequency (w), this oscillation will be in resonance with the incident light, resulting in a strong oscillation of the surface electrons, commonly known as a localized surface plasmon resonance (LSPR) mode.20 This phenomenon is illustrated in Figure 1A. Structures that support LSPRs experience a uniform Eo when excited by light as their dimensions are much smaller than the wavelength of the light. Figure 1 Schematic illustration of the two types of plasmonic nanostructures discussed in this article as excited by the electric field (Eo) of incident light with wavevector (k). In (A) the nanostructure is smaller than the wavelength of light and the free electrons ... In contrast, PSPs are supported by structures that have at least one dimension that approaches the excitation wavelength, as shown in Figure 1B.4 In this case, the Eo is not uniform across the structure and other effects must be considered. In such a structure, like a nanowire for example, SPs propagate back and forth between the ends of the structure. This can be described as a Fabry-Perot resonator with resonance condition l=nλsp, where l is the length of the nanowire, n is an integer, and λsp is the wavelength of the PSP mode.21,22 Reflection from the ends of the structure must also be considered, which can change the phase and resonant length. Propagation lengths can be in the tens of micrometers (for nanowires) and the PSP waves can be manipulated by controlling the geometrical parameters of the structure.23