We review some of the recent surprising theoretical and experimental results obtained on the transport properties of small disordered metal samples. Even in the presence of disorder, the quantum mechanical interference of electron wavefunctions can still be observed. The Aharonov-Bohm effect is a particularly clear demonstration of this. In doubly connected structures (such as loops of wire) threaded by a magnetic flux, the electrical conductance oscillates because of the Aharonov-Bohm effect. In fact, because the electron trajectories are diffusive (i.e. random walks), even a lone wire (a singly connected structure) will exhibit a random pattern of conductance fluctuations as a function of the magnetic field because of the same interference effects. All that is required for the observation of these interferences is that the electrons retain ‘phase memory’ duing the period of transit through the sample. The length over which memory is maintained (the phase coherence length) can be much larger tha...

Aharonov-Bohm effect in normal metal quantum coherence and transport

Classical field theory

The development of a coherent field-emission electron beam has facilitated practical applications of electron holography. This paper reviews this field of growing importance, making special reference to the application of electron holography to current technological problems. It is seen that the phase distribution of an electron wave function transmitted through a specimen can be observed as an interference micrograph, thus providing considerable information about the microscopic distribution of electromagnetic potentials. For example, a magnetic sample's contour fringes directly indicate its magnetic lines of force. These fringes can also show the equipotential lines of an electric sample and thickness contours of a homogeneous specimen. Holographic techniques can be effectively employed to improve the accuracy of phase measurements up to an order of $\frac{2\ensuremath{\pi}}{100}$. This opens the way for use of electron holography as a high-precision measurement method that can cast light on wide regions of the microscopic world pertinent to both basic science and practical industry.

Applications of electron holography

Common industrial lubricants include natural and synthetic hydrocarbons and perfluoropolyethers (PFPEs), where the latter is widely used in commercial applications requiring extreme operating conditions due to their high temperature stability and extremely low vapor pressure. However, PFPEs exhibit low electrical conductivity, making them undesirable in some nanotechnology applications. Ionic liquids (ILs) have been explored as lubricants for various device applications due to their excellent electrical conductivity as well as good thermal conductivity, where the latter allows frictional heating dissipation. Since they do not emit volatile organic compounds, they are regarded as “green” lubricants. In this article, we review the different types of ILs and their physical properties responsible for lubrication. We also discuss their suitability as lubricants, since the long-term performance of ILs as lubricants may be affected by issues such as corrosion, oxidation, tribochemical reactions, and toxicity. We present nanotribological, electrical, and spectroscopic studies of IL films along with conventional tribological investigations, recognizing that understanding the tribological performance at various length scales is a crucial step in selecting and designing effective lubricants.

A Review of Ionic Liquids for Green Molecular Lubrication in Nanotechnology

Despite the huge progress achieved recently by means of the corrector for aberrations, allowing now a true atomic resolution of 0.1 nm, hence making it an unrivalled tool for nanoscience, transmission electron microscopy (TEM) suffers from a severe drawback: in a conventional electron micrograph only a poor phase contrast can be achieved, i.e. phase structures are virtually invisible. Therefore, conventional TEM is nearly blind for electric and magnetic fields, which are pure phase objects. Since such fields provoked by the atomic structure, e.g. of semiconductors and ferroelectrics, largely determine the solid state properties, hence the importance for high technology applications, substantial object information is missing.Electron holography in TEM offers the solution: by superposition with a coherent reference wave, a hologram is recorded, from which the image wave can be completely reconstructed by amplitude and phase. Now the object is displayed quantitatively in two separate images: one representing the amplitude, the other the phase. From the phase image, electric and magnetic fields can be determined quantitatively in the range from micrometre down to atomic dimensions by all wave optical methods that one can think of, both in real space and in Fourier space.Electron holography is pure wave optics. Therefore, we discuss the basics of coherence and interference, the implementation into a TEM, the path of rays for recording holograms as well as the limits in lateral and signal resolution. We outline the methods of reconstructing the wave by numerical image processing and procedures for extracting the object properties of interest. Furthermore, we present a broad spectrum of applications both at mesoscopic and atomic dimensions.This paper gives an overview of the state of the art pointing at the needs for further development. It is also meant as encouragement for those who refrain from holography, thinking that it can only be performed by specialists in highly specialized laboratories. In fact, a modern TEM built for atomic resolution and equipped with a field emitter or a Schottky emitter, well aligned by a skilled operator, can deliver good holograms. Running commercially available image processing software and mathematics programs on a laptop-computer is sufficient for reconstruction of the amplitude and phase images and extracting desirable object information.

https://iopscience.iop.org/article/10.1088/0034-4885/71/1/016102/pdf

Electron holography?basics and applications

/pdf/shift-of-an-electron-interference-pattern-by-enclosed-46azsz0j30.pdf

Shift of an electron interference pattern by enclosed magnetic flux

1 The free-electron model.- 1.1 The classical Drude theory.- 1.2 Fermi-Dirac statistics.- 1.3 The Sommerfeld model.- 1.4 The density of states.- 2 Properties of free-electron solids.- 2.1 The electronic heat capacity.- 2.2 The magnetic susceptibility.- 2.3 Transport properties.- 2.4 Hall effect and magnetoresistance.- 2.5 Relaxation effects: high-frequency conductivity.- 2.6 Metals and semiconductors.- 3 Crystal structures and the reciprocal lattice.- 3.1 Crystal structures.- 3.2 The reciprocal lattice.- 4 Electrons in a periodic potential.- 4.1 Bloch's theorem.- 4.2 The Brillouin zone.- 4.3 Nearly free electrons.- 5 Electronic band structures.- 5.1 The band structure of real metals.- 5.2 Metals, semiconductors and insulators.- 5.3 Density of states and heat capacity.- 6 The potential V(r) many-body effects.- 6.1 The one-electron approximation and the choice of V(r).- 6.2 Many-body effects.- 7 The dynamics of Bloch electrons.- 7.1 The velocity and the Lorentz force.- 7.2 Orbits in a magnetic field.- 7.3 Orbit quantization.- 7.4 The de Haas-van Alphen effect.- 8 Collisions.- 8.1 Scattering by static defects.- 8.2 Phonon scattering.- 8.3 Relaxation times and mean free paths.- 9 Electrical conductivity of metals.- 9.1 The basic expression for ?.- 9.2 Temperature dependence of ?.- 9.3 Matthiessen's rule.- 9.4 The Kondo effect.- 10 Metals in a temperature gradient.- 10.1 Thermal conductivity.- 10.2 Thermoelectric effects.- 11 Magnetoresistance and Hall effect.- 11.1 Basic ideas: the free-electron model.- 11.2 Real metals.- 12 Radio-frequency, optical and other properties.- 12.1 Radio-frequency properties.- 12.2 Optical and other properties.- 13 Carriers in semiconductors.- 13.1 The number of carriers.- 13.2 Donors and acceptors.- 13.3 Carrier mobilities and positive holes.- 14 Transport properties of semiconductors.- 14.1 Scattering.- 14.2 Simple transport properties.- 14.3 Cyclotron resonance and optical properties.- 14.4 Orbit quantization and the quantum Hall effect.- 15 Other topics.- 15.1 Charge density waves.- 15.2 Disordered alloys.- 15.3 Localization.- Problems.- Answers to problems.- Further reading.

R. G. Chambers

Papers

Shift of an electron interference pattern by enclosed magnetic flux

Electrons in Metals and Semiconductors