Concept

E

Summary
E, or e, is the fifth letter and the second vowel letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is e (pronounced 'iː); plural es, Es or E's. It is the most commonly used letter in many languages, including Czech, Danish, Dutch, English, French, German, Hungarian, Latin, Latvian, Norwegian, Spanish, and Swedish. History The Latin letter 'E' differs little from its source, the Greek letter epsilon, 'Ε'. This in turn comes from the Semitic letter hê, which has been suggested to have started as a praying or calling human figure (hillul 'jubilation'), and was most likely based on a similar Egyptian hieroglyph that indicated a different pronunciation. In Semitic, the letter represented /h/ (and /e/ in foreign words); in Greek, hê became the letter epsilon, used to represent /e/. The various forms of the Old Italic script and the Latin alphabet followed this usage.
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Related publications (7)

Quantum size effects in ultrathin metallic islands

I-Po Hong

This thesis reports measurements concerning quantum size effects of single crystalline metallic islands by using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Different sample systems are presented in the following chapters. In chapter 2, several aspects of quantum well states (QWS) of Pb ultrathin islands grown on Si(111) substrate are reported. The differential conductance spectra of QWS can be understood by discrete energy levels with linewidth broadening because of finite quasiparticle lifetime. Using low temperature scanning tunneling spectroscopy, we studied the linewidth of unoccupied quantum-well states (QWS) in Pb islands, grown on Si(111) on two different Pb/Si interfaces, of thicknesses between 7 and 22 monolayers. A quantitative analysis of the differential conductance spectra allowed us to determine the QWS lifetime broadening as a function of energy, showing agreement with 3D Fermi-liquid theory, as well as the electron-phonon (e-ph) contribution between 5 and 50 K. Layer-dependent ab initio calculations of the e-ph linewidth contributions are in excellent agreement with the data. Importantly, the sum of the calculated e-e and e-ph lifetime broadening follows the experimentally observed quadratic energy dependence. In chapter 3, studies investigating reduction of the superconducting gap of ultrathin Pb islands are presented. The energy gap Δ of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Δ was found to decrease from its bulk value as a function of inverse island thickness. Corresponding Tc values, estimated using bulk gap-to-Tc ratio, are in quantitative agreement with ex situ magnetic susceptibility measurements, however, in strong contrast to previous scanning probe results. Layer-dependent ab initio density functional calculations for free-standing Pb films show that the electron-phonon coupling constant, determining Tc, decreases with diminishing film thickness. In chapter 4, we present preliminary results on single electron tunneling and Coulomb blockade phenomena of metallic islands decoupled from a Ag(111) substrate by dielectric NaCl layers. Using low temperature STM/STS, the geometry of the metallic island can be determined unambiguously and the single electron tunneling properties are characterized. Using orthodox theory of single electron tunneling, the tunneling spectra can be reproduced qualitatively. Despite minor quantitative disagreement between data and simulations, the parameters of the double barrier tunneling junction, including the capacitances and the resistances of both junctions, as well as the residual charge, can be determined.
EPFL2009

Decay mechanisms of excited electrons in quantum-well states of ultrathin Pb islands grown on Si(111): Scanning tunneling spectroscopy and theory

I-Po Hong, François Patthey, Wolf-Dieter Schneider

Using low-temperature scanning tunneling spectroscopy at 5 and 50 K, we studied the linewidth of unoccupied quantum-well states in ultrathin Pb islands, grown on Si(111) on two different Pb/Si interfaces. A quantitative analysis of the differential conductance spectra allowed us to determine the electron-electron (e-e), electron-phonon (e-ph) and the interface and defect contributions to the lifetime. Layer-dependent ab initio calculations of the e-ph linewidth contribution are in excellent agreement with the data. Importantly, the sum of the calculated e-e and e-ph lifetime broadening follows the experimentally observed quadratic energy dependence.
2009

Thermal origin of quasilocalized excitations in glasses

Elisabeth Agoritsas, Thomas Willem Jan de Geus, Wencheng Ji, Marko Popovic, Matthieu Wyart

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasilocalized modes of the Hessian that grows upon cooling, while others predict a pseudogap D-L (omega) similar to omega(alpha). To unify these views and observations, we generate glassy configurations of controlled gap magnitude w e at temperature T = 0, using so-called breathing particles, and study how such gapped states respond to thermal fluctuations. We find that (i) the gap always fills up at finite T with D-L (omega) approximate to A(4)(T) omega(4) and A(4) similar to exp(-E-a/T) at low T, (ii) E-a rapidly grows with omega(c), in reasonable agreement with a simple scaling prediction E-a similar to omega(4)(c) and (iii) at larger omega(c) excitations involve fewer particles, as we rationalize, and eventually become stringlike. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudogap distribution is populated with its magnitude rapidly decreasing at lower T. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a stringlike relaxation occurring near the glass transition.
AMER PHYSICAL SOC2020
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