Influence of the boundary conditions on the fermi energy and density of states in a free-electron solid of sub-micron dimensions

Asymptotic expressions for the distribution of the eigenvalues of the Helmholtz-Schrödinger equation are used to anlyze the dependence of the Fermi energy, E_F, and the density of states, ρ(E), on sample size, shape, and electron density, in a free-electron model with Dirichlet boundary conditions. It is found that for very small samples E_F is increased relative to its asymptotic (i.e., bulk) value and ρ(E) is decreased relative to its bulk value. These effects are more pronounced for samples with low electron density and with a large surface-to-volume ratio. In general E_F and ρ(E_F) deviate significantly from their bulk values only for systems with fewer than 50,000 electrons and/or with linear dimensions of 100 Å or less. The use of smoothing functions to represent the density of states obtained from the exact eigenvalue distribution is also discussed. It is shown that an oscillating density of states leads to small cusps in the plot of E_F as a function of sample size. This is in qualitative agreement with the results of experiments on size-dependent oscillations in field emission from thin metallic films. Comparison is also made between photoemission experiments from thin films and other results obtained in this study.     

Electronic properties of TiC(100) and polar TiC(111) surfaces

The energy bands of films of TiC have been calculated using the linear-combination-of-atomic-orbitals method with parameters obtained by a fit to the bulk band structure. The Madelung potentials and charge redistribution have been determined self-consistently. For the neutral TiC(100) surface, the density of states (DOS) is similar to that of the bulk. For the non-neutral Ti-covered TiC(111) surface, Ti 3d-derived surface states appear around the Fermi energy E_F. The long-range electric field produced by the polar surfaces is screened by the charge redistribution, and the polar surfaces are stabilized. Characteristic features of TiC(111) compared to other surfaces of TiC are attributed to the high surface DOS at E_F.     

Spin-polarized metastable deexcitation spectroscopy study of iron films

A spin-polarized metastable deexcitation spectroscopy apparatus using a nozzle-skimmer pulsed discharge metastable atom source was developed. The oxygen adsorption dependence of the surface magnetism of thin iron films deposited on MgO(100) was investigated using this apparatus. The surface local density of states spilling towards the vacuum (SDOS) at around the Fermi energy, E_F, for the clean surface shows a negative polarization to the bulk. The oxygen derived SDOS for the lightly oxygen adsorbed surfaces (2–10 L) also shows a negative polarization while the SDOS at E_F changes its polarity to positive. The polarization of SDOS is not detected for the heavily oxidized surfaces (20–100 L).     

Some comments on the electronic properties of the surface space charge layer of copper phthalocyanine thin films

A simple analysis, using a theory of the surface space charge layer of semiconductors, of the published values of the work function φ and surface ionization energy Φ_s of copper phthalocyanine (CuPc) thin films was performed. Using a well known position of the Fermi level E_F within the band gap E_g the values of its absolute band bending eV_s and surface electron affinity X_s were determined. A small negative value of the absolute band bending eV_s = −0.17 ∓ 0.15 eV has been interpreted by the existence of the filled electronic surface states localized in the band gap below the Fermi level E_F. Such states were predicted theoretically for thin films and the crystalline surface of CuPc, and attributed to surface lattice defects of a high concentration.     

Abnormal electronic transport in disordered graphene nanoribbon

We investigate the conductivity σ of graphene nanoribbons with zigzag edges as a function of Fermi energy E_F in the presence of the impurities with different potential range. The dependence of σ(E_F) displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of σ(E_F) and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao et al. [Science 317 (2007) 1530 (SOM)].     

Charge-density-wave partial gap opening in quasi-2D KMo6O17 purple bronze studied by angle resolved photoemission spectroscopy

Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo₆O₁₇ purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ∼40 K well below the Peierls transition temperature for this material, with CDW transition temperature T_CDW ∼120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative k_F point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, E_F, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K_0.3MoO₃ blue bronze.     

First-principles study on the electronic structures of iron phthalocyanine monolayer

The electronic band structure and magnetic properties of iron phthalocyanine (FePc) monolayer were investigated by using the first-principles all-electron full-potential linearized augmented plane wave energy band method. It is found that the ferromagnetic FePc monolayer is energetically more stable than the paramagnetic one. The exchange interaction, which splits the majority and minority bands, influences strongly on the electronic structure near the Fermi level (E_F). Magnetic moment of the central Fe atom is calculated to 1.95 μ_B. The range of the positive polarization of Fe site is larger in the out-of-plane than in the in-plane direction. The FePc ligand remains paramagnetic. The presence of states at E_F indicates the metallic character of FePc monolayer both for the paramagnetic and ferromagnetic states. However, the large density of states at E_F of the majority spins in the ferromagnetic state is expected to cause a phase transition to insulating antiferromagnetic state from the metallic ferromagnetic one.     

Energy spectrum of charge carriers in Bi<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sb<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> alloys

Analysis of the quantum oscillations of magnetoresistance (the Shubnikov-de Haas effect) in Bi_{1 ? x} Sb _x alloys with an antimony content in the range 0.255 < x < 0.260 has revealed a Lifshitz electronic-topological transition, which quite possibly can be explained in terms of the existence of a saddle point in the energy spectrum of these compositions. Such a peculiarity comes into existence when the direct band gap at the L point of the Brillouin zone in the semiconductor region of the compounds with x > 0.04 becomes negative. This compel one to revise essentially all earlier calculations based on the previously obtained values of the band parameters. In order to check the agreement between the new values of the band parameters and the data on the density of states obtained from measurements of the thermopower in the classical limit of strong magnetic fields, theoretical calculations of the charge carrier concentration n and the density of states at the Fermi level ρ(E _F) have been performed for the case of negative values of the direct band gap at the L point E _gL. The calculations of the parameters n and ρ(E _F) have demonstrated that the change in E _gL and the corresponding correction of the band parameters ensure good agreement with the experimental data. According to these calculations, one electronic-topological transition occurs at an antimony content x ～ 0.165, when a saddle point appears in the energy spectrum. The second transition is associated with the transformation of the six ellipsoids of the Fermi surface into three dumbbell-like figures at antimony concentrations in the range 0.255 < x < 0.260.     

The magnetized electron gas in terms of Hurwitz zeta functions

We obtain explicit expressions for thermodynamic quantities of a relativistic degenerate free electron gas in a magnetic field in terms of Hurwitz zeta functions. The formulation allows for systematic expansion in all regimes. Three energy scales appear naturally in the degenerate relativistic gas: the Fermi energy E_F, the temperature T and an energy related to the magnetic field or Landau level spacing, eB/E_F. We study the cold and warm scenarios, T⪡eB/E_F and eB/E_F⪡T, respectively. We reproduce the oscillations of the magnetization as a function of the field in the cold regime and the dilution of them in the warm regime.     

Photoemission study of electronic structure evolution across the metal-insulator transition of heavily B-doped diamond

We studied the electronic structure evolution of heavily B-doped diamond films across the metal-insulator transition (MIT) using ultraviolet photoemission spectroscopy (UPS). From high-temperature UPS, through which electronic states near the Fermi level (E_F) up to ∼5k_BT can be observed (k_B is the Boltzmann constant and T the temperature), we observed the carrier concentration dependence of spectral shapes near E_F. Using another carrier concentration dependent UPS, we found that the change in energy position of sp-band of the diamond valence band, which corresponds to the shift of E_F, can be explained by the degenerate semiconductor model, indicating that the diamond valence band is responsible for the metallic states for samples with concentrations above MIT. We discuss a possible electronic structure evolution across MIT.     

The valence electronic structure of conducting pyrrole polymers: Evidence against a linear metallic chain picture

A UPS study of various conducting polypyrrole films is presented. Most of the valence band features can be explained by states derived from the orbitals of the pyrrole monomer and the associated anion molecules. In close vicinity of the Fermi energy, a density of states is observed which decreases linearly towards E_F. The corresponding states are introduced by oligomer formation. The π-electronic density at E_F is reduced by at least two orders of magnitude compared to ordinary sp-metals. The UPS spectra are consistent with short conjugation lengths and large amounts of disorder, but the corresponding defect states can not directly be observed.     

Electronic structure of the conduction band of the interface region of ultrathin films of substituted perylenedicarboximides and the germanium oxide surface

The results of the investigation of the electronic structure of the conduction band and the interfacial potential barrier during the formation of interfaces of dioctyl-substituted perylenedicarboximide (PTCDI-C₈) and diphenyl-substituted perylenedicarboximide (PTCDI-Ph) ultrathin films with the oxidized germanium surface have been presented. The experimental results have been obtained using the very low energy electron diffraction (VLEED) technique in the total current spectroscopy (TCS) mode at energies in the range from 5 to 20 eV above the Fermi level E_F. The positions of the maxima of the fine structure of total current spectra (FSTCS) of the PTCDI-C₈ and PTCDI-Ph films differ significantly in the energy range from 9 to 20 eV above the Fermi level E_F, which can be associated with the difference between the substituents of the chosen molecules, dioctyl- and diphenyl-, respectively. At the same time, the positions of the lowenergy maxima in the FSTCS spectra at an energy 6–7 eV above the Fermi level E_F for the PTCDI-C₈ and PTCDI-Ph films almost coincide with each other. It has been suggested that these maxima are attributed to the electronic states of the perylene core of the molecules under investigation. The process of the formation of interfacial potential barriers of the PTCDI-C₈ and PTCDI-Ph films with the oxidized germanium surface has been analyzed. It has been found that the work functions of the surface, E_vac–E_F, differ little from 4.6 ± 0.1 eV over the entire range of organic coating thicknesses from 0 to 6 nm.     

Comparative photoemission study of the electronic properties of L-CVD SnO2 thin films

In this work we present the results of comparative XPS and PYS studies of electronic properties of the space charge layer of the L-CVD SnO₂ thin films after air exposure and subsequent UHV annealing at 400 °C, with a special emphasis on the interface Fermi level position.From the centre of gravity of binding energy of the main XPS Sn 3d_5/2 line the interface Fermi level position E_F − E_v in the band gap has been determined. It was in a good correlation with the value estimated from the offset of valence band region of the XPS spectrum, as well as from the photoemission yield spectroscopy (PYS) measurements. Moreover, from the valence band region of the XPS spectrum and PYS spectrum two different types of filled electronic band gap states of the L-CVD SnO₂ thin films have been derived, located at 6 and 3 eV with respect to the Fermi level.     

Surface states of charge carriers in epitaxial films of the topological insulator Bi2Te3

The galvanomagnetic properties of p-type bismuth telluride heteroepitaxial films grown by the hot wall epitaxy method on oriented muscovite mica substrates have been investigated. Quantum oscillations of the magnetoresistance associated with surface electronic states in three-dimensional topological insulators have been studied in strong magnetic fields ranging from 6 to 14 T at low temperatures. The cyclotron effective mass, charge carrier mobility, and parameters of the Fermi surface have been determined based on the results of analyzing the magnetoresistance oscillations. The dependences of the cross-sectional area of the Fermi surface S(k _F), the wave vector k _F, and the surface concentration of charge carriers n _s on the frequency of magnetoresistance oscillations in p-type Bi₂Te₃ heteroepitaxial films have been obtained. The experimentally observed shift of the Landau level index is consistent with the value of the Berry phase, which is characteristic of topological surface states of Dirac fermions in the films. The properties of topological surface states of charge carriers in p-type Bi₂Te₃ films obtained by analyzing the magnetoresistance oscillations significantly expand fields of practical application and stimulate the investigation of transport properties of chalcogenide films.     

Electronic structure of the conduction band upon the formation of ultrathin fullerene films on the germanium oxide surface

The results of the investigation of the electronic structure of the conduction band in the energy range 5–25 eV above the Fermi level E_F and the interfacial potential barrier upon deposition of aziridinylphenylpyrrolofullerene (APP-C₆₀) and fullerene (C₆₀) films on the surface of the real germanium oxide ((GeO₂)Ge) have been presented. The content of the oxide on the (GeO₂)Ge surface has been determined using X-ray photoelectron spectroscopy. The electronic properties have been measured using the very low energy electron diffraction (VLEED) technique in the total current spectroscopy (TCS) mode. The regularities of the change in the fine structure of total current spectra (FSTCS) with an increase in the thickness of the APP-C₆₀ and C₆₀ coatings to 7 nm have been investigated. A comparison of the structures of the FSTCS maxima for the C₆₀ and APP-C₆₀ films has made it possible to reveal the energy range (6–10 eV above the Fermi level E_F) in which the energy states are determined by both the π* and σ* states and the FSTCS spectra have different structures of the maxima for the APP-C₆₀ and unsubstituted C₆₀ films. The formation of the interfacial potential barrier upon deposition of APP-C₆₀ and C₆₀ on the (GeO₂)Ge surface is accompanied by an increase in the work function of the surface E_vac–E_F by the value of 0.2–0.3 eV, which corresponds to the transfer of the electron density from the substrate to the organic films under investigation. The largest changes occur with an increase in the coating thickness to 3 nm, and with further deposition of APP-C₆₀ and C₆₀, the work function of the surface changes only slightly.     

Camel's back induced stabilization of electron-hole liquids : GaP

A camel's back-like nonparabolicity of the longitudinal electron mass enhances the density of states and strongly stabilized an electron-hole-liquid. In GaP therefore the EHL density is doubled to 8.6 × 18¹⁸cm^?3 and the Fermi energy ratio E_F^h/E_F^e changes from 1.9 to 4.9. The theoretical binding energy agrees with the experimental E_B=17.5±3meV interpreting the luminescence at 2.30 eV as a superposition of liquid and plasma recombination radiation.     

Selfconsistent model calculations of electronic states at narrow-band-metal surfaces

For a nondegenerate narrow energy band spanned by a semiinfinite chain of three-dimensional atoms, the electronic potential and the electron density of states are calculated selfconsistently in the vicinity of the chain end. The electron-electron interaction is treated in the Hartree-Fock approximation, using the Green function method. The results for the potential and the density of states are discussed in terms of the parameters which determine the bulk electronic structure, such as the Fermi energy E_F and the intra- and interatomic Coulomb repulsion k₀ and K₁. Futhermore, the self consistent method is extended to an impurity atom at the chain end. The existence of bonding and antibonding surface states is found to depend on both the bulk and impurity parameters, such as the intraatomic Coulomb repulsion U_α and the nearest neighbour hopping element T.     

Crystal structure, electronic and elastic properties for novel Hf3AlN and Zr3AlN ceramics explored by first principles studies

Investigations into crystal structure, electronic and elastic properties of M₃AlN (M=Hf, Zr) had been conducted by plane-wave pseudopotential calculations. The absence of band gap at the Fermi level and the finite value of the density of states at the Fermi energy reveal the metallic behavior of these two compounds. The charge density distributions and density of states indicate that there exist relatively soft Al-M and strong N-M covalent bonds, which might be contributed to layered chemical bonding character of M₃AlN. By analyzing Cauchy pressure and the bulk modulus to C₄₄ ratio, Hf₃AlN was predicted to be more ductile than Zr₃AlN.     

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk “poor conductors” in which Fermi energy E_F is located in the region of localized states not so far from the Anderson mobility edge E_c. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: ‘critical’ superconductive state formed at E_F = E_c, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E_F still deeper inside a localized band. The ‘critical’ superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap Δ, that is due to many-body correlations and a new “pseudo-gap” energy scale Δ_P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T_c. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to the presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T) ∼ 1/T.Based on these results we propose a new “pseudo-spin” scenario of superconductor-insulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.