Showing papers by "John B. Pendry published in 1990"

Low-Energy Electron Diffraction

Abstract: The essential elements are an ultrahigh vacuum (UHV) chamber to preserve surface cleanliness, an electron gun to produce a collimated beam of electrons in the energy range 0 to 500 eV, a crystal holder and manipulator, and some means of observing the diffracted electrons, typically a fluorescent screen. Further details may be found elsewhere.(1–3) The major difficulty is common to all surface experiments, namely, to keep the surface clean. The UHV chamber will normally contain an array of techniques for cleaning the surface (provision for heating the sample, ion bombardment) as well as some means of detecting impurities at the surface, usually by detection of Auger signals from adsorbed atoms. LEED is very sensitive to cleanliness of the surface and small amounts of contaminant can produce quite spurious results. Experiments conducted on clean, perfect, surfaces can produce a large amount of structural information of high precision. Obviously it is only possible to produce precise data for surfaces which are well defined in the first place.

Maximal fluctuations — A new phenomenon in disordered systems

Abstract: Rigorous results for 1D systems combined with more intuitive results for higher dimensions indicate that there is a universal theorem on fluctuations in the transmission coefficient of disordered systems. Recognising that the transmission coefficient for waves traversing a disordered system can be no greater than unity, and no less than zero, the theorem states that in each channel either | t | 2 ≈1 or | t | 2 ≈0, with the probability set by the conductance. This is the most extreme excursion of the distribution possible, hence the name “maximal fluctuations”. The effect is distinct from the universal fluctuations which refer to the sensitivity of t to changes in the medium.

Transfer matrices and conductivity in two- and three-dimensional systems. I. Formalism

Abstract: The electronic states responsible for transport constitute a wildly fluctuating minority of the total number of states in a disordered system. These fluctuations are the essence of the problem and demand a rich and powerful formulation if they are to be described accurately. In this paper the author introduces a new formalism for treating transport in three-dimensional systems based on the transfer matrix. The method gains its power from the interplay of theory of the symmetric group, which enables irrelevant parts of the mathematics to be thrown out, leaving the essentials intact but simplified. Analogies with replica theory are drawn, and replica symmetry breaking discussed.

Direct low-energy electron-diffraction analysis of c(2 x 2)O/Ni(100) including substrate reconstruction.

Abstract: Cette analyse des structures d'absorption complexes est decrite comme une inversion du tenseur de diffraction des electrons lents, est appliquee au systeme d'absorption c(2×2)o/Ni(100)

Statistics and scaling in one-dimensional disordered systems

Abstract: The authors present a new calculation of the statistical cumulants of -ln mod t mod 2 and Theta where t= mod t mod exp(i Theta ) is the transmission of a one-dimensional (1D) disordered system. They find that both variables are normally distributed in the long-length limit, and that in general the distributions obey a two-parameter scaling. However, it does not follow that the distributions of mod t mod 2 or 1/ mod t mod 2 are log-normal. They find that mod t mod 2 is never log-normal while 1/ mod t mod 2 is so only for weak disorder. For the 1D Anderson model they show that there is a crossover to a single-parameter scaling in the weak-disorder limit.

Transfer matrices and conductivity in two- and three-dimensional systems. II. Application to localised and delocalised systems

Abstract: For pt.I see ibid., vol.2, p.3273 (1990). In the previous paper a formalism was established for the calculation of intensities reflected from a disordered system, and hence for the transmitted intensities via the unitarity relationship. Here the author shows how the method can be applied to calculation of the conductivity of a three-dimensional (3D) system in the limiting case of weak disorder. First the one-dimensional (1D) situation is discussed and canonical models developed for the classical diffusive case and for the quantum localised case. The author's 3D theory can then be mapped onto the classical 1D case in the limit of weak disorder, and onto the quantum 1D case in the limit that all lateral hopping is eliminated and the author has a collection of independent 1D systems. Thus the theory has the power and flexibility to describe both localised and delocalised systems, a unique advantage in discussing more complex effects.

Log-normal distribution as a description of fluctuations in one-dimensional disordered systems.

Abstract: Electrons and other waves show strong and complex fluctuations in the transmission coefficient, \ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$. A theory must accurately describe the distribution for both small \ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$, and for large \ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$ which dominate the average. We present a new method for calculating the statistical cumulants of the logarithm of the transmission, -ln\ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$, of a one-dimensional disordered system. In the long-wavelength limit both ln\ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$, and the phase of ${\mathit{t}}_{\mathit{L}}$ approach a normal distribution. This does not imply that \ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$ or 1/\ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$ obey a log-normal distribution. In fact the conductance \ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$ is never log normal, and the resistance 1/\ensuremath{\Vert}${\mathit{t}}_{\mathit{L}}$${\mathrm{\ensuremath{\Vert}}}^{2}$ only sometimes so.