IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

Annual review of condensed matter physics

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

Inhomogeneous superconductors can host electronic excitations, known as Andreev bound states (ABSs), below the superconducting energy gap. With the advent of topological superconductivity, a new kind of zero-energy ABS with exotic qualities, known as a Majorana bound state (MBS), has been discovered. A special property of MBS wavefunctions is their non-locality, which, together with non-Abelian braiding, is the key to their promise in topological quantum computation. We focus on hybrid superconductor–semiconductor nanowires as a flexible and promising experimental platform to realize one-dimensional topological superconductivity and MBSs. We review the main properties of ABSs and MBSs, state-of-the-art techniques for their detection and theoretical progress beyond minimal models, including different types of robust zero modes that may emerge without a band-topological transition. Topological Majorana bound states have potential for encoding, manipulating and protecting quantum information in condensed-matter systems. This Review discusses emergence and characterization of Majorana bound states in realistic devices based on hybrid semiconducting nanowires and their connection to more conventional Andreev bound states.

From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires

Owing to its excellent electrical, mechanical, thermal and optical properties, graphene has attracted great interests since it was successfully exfoliated in 2004. Its two dimensional nature and superior properties meet the need of surface plasmons and greatly enrich the field of plasmonics. Recent progress and applications of graphene plasmonics will be reviewed, including the theoretical mechanisms, experimental observations, and meaningful applications. With relatively low loss, high confinement, flexible feature, and good tunability, graphene can be a promising plasmonic material alternative to the noble metals. Optics transformation, plasmonic metamaterials, light harvesting etc. are realized in graphene based devices, which are useful for applications in electronics, optics, energy storage, THz technology and so on. Moreover, the fine biocompatibility of graphene makes it a very well candidate for applications in biotechnology and medical science.

Plasmons in graphene: Recent progress and applications

The model of interacting fermion systems in one dimension known as a Tomonaga–Luttinger liquid (TLL)1,2 provides a simple and exactly solvable theoretical framework that predicts various intriguing physical properties. Evidence of a TLL has been observed as power-law behaviour in electronic transport on various types of one-dimensional conductor3,4,5. However, these measurements, which rely on d.c. transport involving electron tunneling processes, cannot identify the long-awaited hallmark of charge fractionalization, in which an injection of elementary charge e from a non-interacting lead is divided into the non-trivial effective charge e* and the remainder, e−e* (refs 6, 7, 8). Here, we report time-resolved transport measurements9 on an artificial TLL composed of coupled integer quantum Hall edge channels10, in which we successfully identify single charge fractionalization processes. A wave packet of charge q incident from a non-interacting region breaks up into several fractionalized charge wave packets at the edges of the artificial TLL, from which transport eigenmodes can be evaluated directly. These results are informative for elucidating the nature of TLLs and low-energy excitations in the edge channels11. Charge fractionalization can be observed in artificial Tomonaga–Luttinger liquids by using a time-resolved electron transport experiment.

Fractionalized wave packets from an artificial Tomonaga-Luttinger liquid

Edge magnetoplasmon (EMP) transport in gated and ungated quantum Hall systems is investigated by time-of-flight measurements. We measured the velocity, the amplitude, and the broadening of the EMP pulse injected by applying a voltage pulse to an Ohmic contact. We show that the transverse width of EMPs in the ungated sample is determined by the potential profile in the edge region, independent of the filling factor. In the gated sample, on the other hand, EMPs are confined by the innermost incompressible strip and their transverse width depends on the filling factor and the bulk electron density. We also find that scattering of EMPs by the bulk electrons is modified by the presence of the gate.

Edge magnetoplasmon transport in gated and ungated quantum Hall systems

We investigate the group velocity of edge magnetoplasmons (EMPs) in the quantum Hall regime by means of time-of-flight measurement. The EMPs are injected from an Ohmic contact by applying a voltage pulse, and detected at a quantum point contact by applying another voltage pulse to its gate. We find that the group velocity of the EMPs traveling along the edge channel defined by a metallic gate electrode strongly depends on the voltage applied to the gate. The observed variation of the velocity can be understood to reflect the degree of screening caused by the metallic gate, which damps the in-plane electric field and, hence, reduces the velocity. The degree of screening can be controlled by changing the distance between the gate and the edge channel with the gate voltage.

Voltage-controlled group velocity of edge magnetoplasmon in the quantum Hall regime

Preparation and properties of high transition temperature aromatic polyphosphonates by phase‐transfer‐catalyzed polycondensation of phenylphosphonic dichloride with bisphenols

Plasmons, which are collective charge oscillations, could provide a means of confining electromagnetic field to nanoscale structures. Recently, plasmonics using graphene have attracted interest, particularly because of the tunable plasmon dispersion, which will be useful for tunable frequency in cavity applications. However, the carrier density dependence of the dispersion is weak (proportional to n(1/4)) and it is difficult to tune the frequency over orders of magnitude. Here, by exploiting electronic excitation and detection, we carry out time-resolved measurements of a charge pulse travelling in a plasmon mode in graphene corresponding to the gigahertz range. We demonstrate that the plasmon velocity can be changed over two orders of magnitude by applying a magnetic field B and by screening the plasmon electric field with a gate metal; at high B, edge magnetoplasmons, which are plasmons localized at the sample edge, are formed and their velocity depends on B, n and the gate screening effect.

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Hiroshi Kamata

Papers

Fractionalized wave packets from an artificial Tomonaga-Luttinger liquid

Edge magnetoplasmon transport in gated and ungated quantum Hall systems

Voltage-controlled group velocity of edge magnetoplasmon in the quantum Hall regime

Preparation and properties of high transition temperature aromatic polyphosphonates by phase‐transfer‐catalyzed polycondensation of phenylphosphonic dichloride with bisphenols

Plasmon transport in graphene investigated by time-resolved electrical measurements