Local density-of-states

Thus, if we knew the second moment of the local density of states we should be able to determine the atomic binding energy via the square root relationship. However, as quantum... 

The presence of a defect in the lattice (impurity, surface, vacancy...) breaks the symmetry and induces perturbations of the electronic structure in its vicinity. Thus it is convenient to introduce the concept of local density of states (LDOS) at site i ... 

We have seen that the cooperative region, which represents a nominal dynamical unit of liquid, is of rather modest size, resulting in observable fluctuation effects. Xia and Wolynes [45] computed the relaxation barrier distribution. The configurational entropy must fluctuate, with the variance given by the usual expression [77] 5Sc) ) = Cp barrier height for a particular region is directly related to the local density of states, and hence to... 

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

The scanning tunneling microscope uses an atomically sharp probe tip to map contours of the local density of electronic states on the surface. This is accomplished by monitoring quantum transmission of electrons between the tip and substrate while piezoelectric devices raster the tip relative to the substrate, as shown schematically in Fig. 1 [38]. The remarkable vertical resolution of the device arises from the exponential dependence of the electron tunneling process on the tip-substrate separation, d. In the simplest approximation, the tunneling current, 1, can be simply written in terms of the local density of states (LDOS), ps(z,E), at the Fermi level (E = Ep) of the sample, where V is the bias voltage between the tip and substrate... 

The study of adsorbates on metal surfaces is a particularly fruitful area, which has received much attention. Experimentally, atomic adsorbates are known to yield very different images ranging from bumps [S on Pt(l 11)] to depression [O on Ni(lOO)] depending on the nature of the interaction with the LDOS of the metal surface [58,70,71]. The phenomenon has been analyzed in terms of the impact of the adsorbate on the local density of states at the substrate Fermi level [57,71-75]. Importantly, even... 

To give an example of a wide band gap material, Fig. 8.5 shows the calculated DOS of bulk quartz (Si02). The band gap from the calculation shown in this figure is 5.9 eV. Even remembering that DFT typically underestimates the band gap, it is clear that quartz is an insulator. Unlike Si, the valence band of quartz includes several separate energy bands with distinct energy gaps between them. We will return to these bands when we discuss the local density of states in Section 8.2. 

To interpret the electronic structure of a material, it is often useful to understand what states are important in the vicinity of specific atoms. One standard way to do this is to use the local density of states (LDOS), defined as the number of electronic states at a specified energy weighted by the fraction of the total electron density for those states that appears in a specified volume around a nuclei. Typically, this volume is simply taken to be spherical so to calculate the LDOS we must specify the effective radii of each atom of interest. This definition cannot be made unambiguously. If a radius that is too small is used, information on electronic states that are genuinely associated with the nuclei will be missed. If the radius is too large, on the other hand, the LDOS will include contributions from other atoms. 

Figure 6. Local density of states in units of states per eV per atom for surface layer (top panel) and in the bulk (solid line) over the entire run.

If V is small enough that the density of electronic states does not vary significantly within it, the sum in Eq. (1.10) can be conveniently written in terms of the local density of states (LDOS) at the Fermi level. At a location z and energy E, the LDOS ps(z, E) of the sample is defined as... 

In STM experiments, we are only interested in the electrons near the Fermi level. An important quantity is the number of electrons per unit volume per unit energy near the Fermi level, or the Fermi-level local density of states (LDOS). Inside a Sommerfeld metal, it is a constant... 

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