Energy gap | EPFL Graph Search

In solid-state physics, an energy gap or band gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is often known more abstractly as a spectral gap, a term which need not be specific to electrons or solids. Band gap If an energy gap exists in the band structure of a material, it is called band gap. The physical properties of semiconductors are to a large extent determined by their band gaps, but also for insulators and metals the band structure—and thus any possible band gaps—govern their electronic properties. Superconductors Superconducting gap For superconductors the energy gap is a region of suppressed density of states around the Fermi energy, with the size of the energy gap much smaller than the energy scale of the band structure. The superconducting energy gap is a key aspect in the theoretical description of superconductivity and

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

Experimental observation of thermal fluctuations in single superconducting Pb nanoparticles through tunneling measurements

Klaus Kern

An important question in the physics of superconducting nanostructures is the role of thermal fluctuations (TFs) on superconductivity in the zero-dimensional limit. Here, we probe the evolution of superconductivity as a function of temperature and particle size in single, isolated Pb nanoparticles. Accurate determination of the size and shape of each nanoparticle makes our system a good model to quantitatively compare the experimental findings with theoretical predictions. In particular we study the role of TFs on the tunneling density of states (DOS) and the superconducting energy gap (Delta) in these nanoparticles. For the smallest particles h

2011

Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)

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

The energy gap Delta of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Delta was found to decrease from its bulk value as a function of inverse island thickness. Corresponding T-c values, estimated using bulk gap-to-T-c 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 freestanding Pb films show that the electron-phonon coupling constant, determining T-c, decreases with diminishing film thickness.

2009

Quantum size effects in ultrathin metallic islands

I-Po Hong

EPFL2009