Continuous Density Of States Research Articles

Role of spin-orbit coupling effects in rare-earth metallic tetra-borides: a first principle study

We have investigated the electronic structure of rare-earth tetraborides, $\textrm{RB}_{4}$, using first-principle electronic structure methods (DFT) implemented in Quantum Espresso (QE). In this article we have studied heather-to neglected strong spin-orbit coupling (SOC) effects present in these systems on the electronic structure of these system in the non-magnetic ground state. The calculations were done under GGA and GGA+SO approximations using ultrasoft pseudopotentials and fully relativistic ultrasoft pseudopotentials (for SOC case). Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) exchange-correlation functionals within the linearized plane-wave (LAPW) method as implemented in QE were used. The projected density of states consists of 3 distinct spectral peaks well below the Fermi energy and separated from the continuum density of states around the Fermi energy. The discrete peaks arises due to rare-earth $s$-orbital, rare-earth $p$ + B $p$ and B $p$-orbitals while the continuum arises due to hybridized B $p$, rare-earth $d$ orbitals. Upon inclusion of SOC the peak arising due to rare-earth $p$-orbitals gets split into two peaks corresponding to $j=0.5$ and $j=1.5$ configurations. In case of $\textrm{LaB}_{4}$, in the presence of SOC, spin-split $4f$ orbitals contributes to density of states at the Fermi level while the density of states at the Fermi level largely remains unaffected for all other materials under consideration.

Detecting the Universal Fractional Entropy of Majorana Zero Modes.

A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose entropy is log2. Upon strongly coupling one of the constituent MZMs to a reservoir with a continuous density of states, a universal entropy change of 1/2log2 is expected to be observed across an intermediate temperature plateau. We adapt the entropy-measurement scheme that was the basis of a recent experiment by Hartman etal. [Nat. Phys. 14, 1083 (2018)10.1038/s41567-018-0250-5] to the case of a proximitized topological system hosting MZMs and propose a method to measure this 1/2log2 entropy change-an unambiguous signature of the nonlocal nature of the topological state. This approach offers an experimental strategy to distinguish MZMs from non topological states.

Density Functional Theory Calculations Revealing Metal-like Band Structures for Ultrathin Germanium (111) and (211) Surface Layers.

To find out if germanium possesses facet-dependent electrical-conductivity properties, surface-state density functional theory (DFT) calculations were performed on one to six layers of germanium (100), (110), (111), and (211) planes. Tunable Ge(100) and Ge(110) planes always present the same semiconducting band structure with a band gap of 0.67 eV expected of bulk germanium. In contrast, one, two, four, and five layers of Ge(111) and Ge(211) plane models show metal-like band structures with continuous density of states (DOS) throughout the entire band. For three and six layers of Ge(111) and Ge(211) plane models, the normal semiconducting band structure was obtained. The plane layers with metal-like band structures also show Ge-Ge bond-length deviations and bond distortions, as well as significantly different 4s and 4p frontier-orbital electron counts and relative percentages integrated over the valence and conduction bands from those of the semiconducting state. These differences should contribute to strikingly dissimilar band structures. The calculation results suggest the observation of facet-dependent electrical-conductivity properties of germanium materials; when making transistors from germanium, the facet effects with shrinking dimensions approaching 3 nm may also need to be considered.

Generic Local Hamiltonians are Gapless

We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.

Metal-like Band Structures of Ultrathin Si {111} and {112} Surface Layers Revealed through Density Functional Theory Calculations.

Density functional theory calculations have been performed on Si (100), (110), (111), and (112) planes with tunable number of planes for evaluation of their band structures and density of states profiles. The purpose is to see whether silicon can exhibit facet-dependent properties derived from the presence of a thin surface layer having different band structures. No changes have been observed for single to multiple layers of Si (100) and (110) planes with a consistent band gap between the valence band and the conduction band. However, for 1, 2, 4, and 5 Si (111) and (112) planes, metal-like band structures were obtained with continuous density of states going from the valence band to the conduction band. For 3, 6, and more Si (111) planes, as well as 3 and 6 Si (112) planes, the same band structure as that seen for Si (100) and (110) planes has been obtained. Thus, beyond a layer thickness of five Si (111) planes at ≈1.6 nm, normal semiconductor behavior can be expected. The emergence of metal-like band structures for the Si (111) and (112) planes are related to variation in Si-Si bond length and bond distortion plus 3s and 3p orbital electron contributions in the band structure. This work predicts possession of facet-dependent electrical properties of silicon with consequences in FinFET transistor design.

Tartarus: A relativistic Green’s function quantum average atom code

A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparison to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. We also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.

Extraordinary near-band-edge photoluminescence in the highly epitaxial ZnO films deposited by PLD

Highly epitaxial ZnO films deposited on c-plane sapphire substrate by pulsed laser deposition exhibited enhanced extraordinary spectral features in the near-band-edge region, which were studied in comparison with the annealed sample and the bulk ZnO crystal. Based on the characterization in structure and photoluminescence, the near-band-edge emission was assigned to the tail-state luminescence due to the exciton localization, which is different from the bound excitons, instead has the continuous density of states at the deeper levels, probably created by the defects, chemical disorders, and the lattice strains.

Continuous Multi-exponential Method for Analyzing Transient Photoconductivity in Amorphous Oxide Semiconductors

ABSTRACTAmorphous oxide semiconductors (AOS) are promising candidate materials for thin film transistors in display devices, but one major challenge for mass application is their instability under illumination. In this work, a theoretical method for analyzing transient photoconductivity response in such AOS thin films is reviewed, namely the continuous multi-exponential model. This model can deduce a continuous distribution of decay time constants representing activation energy levels in an AOS, and is shown to reliably reproduce a model of density of states (DOS) of mid-gap traps assumed to be responsible for the transient photoconductivity. Provided the data collection time is sufficiently long, the continuous multi-exponential model was verified to reconstruct the modeled continuous DOS spectrum, thus providing a powerful tool to analyze photoresponse in AOS. This method has the advantage that no prior assumptions about the form of the density of states are needed, but the drawback that long data collection times are required for the transient to be fully relaxed.

Carrier transfer from InAs quantum dots to ErAs metal nanoparticles

Erbium arsenide (ErAs) is a semi-metallic material that self-assembles into nanoparticles when grown in GaAs via molecular beam epitaxy. We use steady-state and time-resolved photoluminescence to examine the mechanism of carrier transfer between indium arsenide (InAs) quantum dots and ErAs nanoparticles in a GaAs host. We probe the electronic structure of the ErAs metal nanoparticles (MNPs) and the optoelectronic properties of the nanocomposite and show that the carrier transfer rates are independent of pump intensity. This result suggests that the ErAs MNPs have a continuous density of states and effectively act as traps. The absence of a temperature dependence tells us that carrier transfer from the InAs quantum dots to ErAs MNPs is not phonon assisted. We show that the measured photoluminescence decay rates are consistent with a carrier tunneling model.

Weak magnetic field solution of Schrödinger equation in two dimensions and continuous density of states

Green function method is applied to the solution of Schrödinger equation in two-dimensions where there is a constant and nearly uniform magnetic field Bo applied perpendicularly and there are infinitesimally weak scatterers within the system. Electronic density of states n(E) obtained from the average Green function go is a continuous function of energy E and not in the form of discrete Landau spikes even in the pure system with no disorder. Self consistent calculation of self-energy gives two possible scattering time values, one leading to resistance increase with Bo while the other causing decrease in resistance.

Generating Long Supramolecular Pathways with a Continuous Density of States by Physically Linking Conjugated Molecules via Their End Groups

Self-assembly of conjugated 2,5-dialkoxy-phenylene-thienylene-based oligomers on epitaxial monolayer graphene was studied in ultrahigh vacuum by low-temperature scanning tunneling microscopy (STM). The formation of long one-dimensional (1D) supramolecular chain-like structures has been observed, associated to a physical linking of their ends which involved the rotation of the end thiophene rings in order to allow π-π stacking of these end-groups. dI/dV maps taken at an energy corresponding to the excited states showed a continuous electronic density of states, which tentatively suggests that within such molecular chains conjugation of electrons is preserved even across physically linked molecules. Thus, in a self-organization process conjugation may be extended by appropriately adapting conformations of neighboring molecules. Our STM results on such self-organized end-linked molecules potentially represent a direct visualization of J-aggregates.

Chirality-dependent properties of carbon nanotubes: electronic structure, optical dispersion properties, Hamaker coefficients and van der Waals–London dispersion interactions

Optical dispersion spectra at energies up to 30 eV play a vital role in understanding the chirality-dependent van der Waals–London dispersion interactions of single wall carbon nanotubes (SWCNTs). We use one-electron theory based calculations to obtain the band structures and the frequency dependent dielectric response function from 0–30 eV for 64 SWCNTs differing in radius, electronic structure classification, and geometry. The resulting optical dispersion properties can be categorized over three distinct energy intervals (M, π, and σ, respectively representing 0–0.1, 0.1–5, and 5–30 eV regions) and over radii above or below the zone-folding limit of 0.7 nm. While π peaks vary systematically with radius for a given electronic structure type, σ peaks are independent of tube radius above the zone folding limit and depend entirely on SWCNT geometry. We also observe the so-called metal paradox, where a SWCNT has a metallic band structure and continuous density of states through the Fermi level but still behaves optically like a material with a large optical band gap between M and π regions. This paradox appears to be unique to armchair and large diameter zigzag nanotubes. Based on these calculated one-electron dielectric response functions we compute and review van der Waals–London dispersion spectra, full spectral Hamaker coefficients, and van der Waals–London dispersion interaction energies for all calculated frequency dependent dielectric response functions. Our results are categorized using a new optical dielectric function classification scheme that groups the nanotubes according to observable trends and notable features (e.g. the metal paradox) in the 0–30 eV part of the optical dispersion spectra. While the trends in these spectra begin to break down at the zone folding diameter limit, the trends in the related van der Waals–London dispersion spectra tend to remain stable all the way down to the smallest single wall carbon nanotubes in a given class.

Open-boundary cluster model for calculation of adsorbate-surface electronic states

We have developed a simple embedded-cluster model approach to investigate adsorbate-surface systems. In our approach, the physically relevant subsystem is described as an open-quantum system by considering a model cluster subject to an outgoing-wave boundary condition at the edge. This open-boundary cluster model (OCM) is free from artificial waves reflected at the cluster edge, and thus the adsorbate properties computed with the OCM are almost independent of the model cluster size. The exact continuous density of states (DOS) of a one-dimensional periodic potential model is shown to be precisely reproduced with the OCM. The accurate DOS leads to an appropriate description of adsorbate-surface chemical bonding. Moreover, the open-boundary treatment of the OCM allows us to evaluate the electron-transfer rate from the adsorbate to the surface, whereas the conventional cluster model does not give any information about such a dynamical process.

Highly Fluorescent Noble-Metal Quantum Dots

Highly fluorescent, water-soluble, few-atom noble-metal quantum dots have been created that behave as multielectron artificial atoms with discrete, size-tunable electronic transitions throughout the visible and near infrared. These molecular metals exhibit highly polarizable transitions and scale in size according to the simple relation E(Fermi)/N(1/3), predicted by the free-electron model of metallic behavior. This simple scaling indicates that fluorescence arises from intraband transitions of free electrons, and these conduction-electron transitions are the low-number limit of the plasmon-the collective dipole oscillations occurring when a continuous density of states is reached. Providing the missing link between atomic and nanoparticle behavior in noble metals, these emissive, water-soluble Au nanoclusters open new opportunities for biological labels, energy-transfer pairs, and light-emitting sources in nanoscale optoelectronics.

Quantum supercurrent transistors in carbon nanotubes

Electronic transport through nanostructures is greatly affected by the presence of superconducting leads. If the interface between the nanostructure and the superconductors is sufficiently transparent, a dissipationless current (supercurrent) can flow through the device owing to the Josephson effect. A Josephson coupling, as measured by the zero-resistance supercurrent, has been obtained using tunnel barriers, superconducting constrictions, normal metals and semiconductors. The coupling mechanisms vary from tunnelling to Andreev reflection. The latter process has hitherto been observed only in normal-type systems with a continuous density of electronic states. Here we investigate a supercurrent flowing through a discrete density of states-that is, the quantized single particle energy states of a quantum dot, or 'artificial atom', placed between superconducting electrodes. For this purpose, we exploit the quantum properties of finite-sized carbon nanotubes. By means of a gate electrode, successive discrete energy states are tuned on- and off-resonance with the Fermi energy in the superconducting leads, resulting in a periodic modulation of the critical current and a non-trivial correlation between the conductance in the normal state and the supercurrent. We find, in good agreement with existing theory, that the product of the critical current and the normal state resistance becomes an oscillating function, in contrast to being constant as in previously explored regimes.

Quantum Transport Effects in Copper(II) Phthalocyanine Sandwiched between Gold Nanoelectrodes

The electrical transmission of copper(II) phthalocyanine (CuPc) sandwiched between gold nanoelectrodes is studied on the basis of the Green function formalism coupled with the Gaussian-broadening technique. In the Au-CuPc-Au junction, broadened density of states (DOS) of the Au chains is defined as continuous DOS of electrodes to calculate the Green function of the electrodes. Two peaks of the transmission function found in the vicinity of the Fermi level are analyzed in terms of molecular orbitals (MOs). A convenient procedure to analyze MO contribution to a transmission peak is proposed. It is found that (I) symmetry-matched interactions between CuPc and the gold nanoelectrodes are important to the enhancement of the transmission function and (II) the nanoelectrodes have almost no effect on the electronic states of CuPc.

Energy spectrum and optical properties of polymer–nanocrystal composites

AbstractComposite systems containing semiconductor nanocrystals (NCs) embedded into a conducting polymer matrix have a number of key distinctions from semiconductor quantum dot heterostructures. Low electron affinity of conducting polymers results in a type‐II heterojunction at the NC‐polymer interface with electrons localized inside NC and delocalized holes with a continuous density of states. Optical properties of nanocomposites were considered accounting for the above‐mentioned features of energy spectrum. The results explain a series of experimentally observed peculiarities including various and sometimes featureless absorption spectra, large Stokes shift and activationless photoconductivity. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Green's function formalism coupled with Gaussian broadening of discrete states for quantum transport: application to atomic and molecular wires.

A Green's function formalism incorporating broadened density of states (DOS) is proposed for the calculation of electrical conductance. In cluster-molecule-cluster systems, broadened DOS of the clusters are defined as continuous DOS of electrodes and used to calculate Green's function of electrodes. This approach combined with density functional theory is applied to the electrical transmission of gold atomic wires and molecular wires consisting of benzene-1,4-dithiolate, benzene-1,4-dimethanethiolate, 4,4(')-bipyridine, hexane dithiolate, and octane dithiolate. The B3LYP, B3PW91, MPW1PW91, SVWN, and BPW91 functionals with the LANL2DZ, CEP, and SDD basis sets are employed in the calculation of conductance. The width parameter was successfully determined to reproduce the quantum unit of conductance 2e(2)/h in gold atomic wires. The combination of the B3LYP hybrid functional and the CEP-31G basis set is excellent in reproducing measured conductances of molecular wires by Tao et al. [Science 301, 1221 (2003); J. Am. Chem. Soc. 125, 16164 (2003); Nano Lett. 4, 267 (2004)].

Multi-ionization of helium and lithium using the independent electron and independent event models with intrinsic CDW

Cross sections for the multi-ionization of He and Li are presented for impact energies in the range of 50 to 1000 keV/amu. These are calculated using the eikonal initial state approximation to represent the input and exit channels of the active electrons. The ionization process is simulated in a variety of ways, most notably an attempt to account for the effects of electron correlation via the inclusion of a continuum density of states (CDS) term. Inadequacies, of the CDW formulation at small impact parameters, and of the models themselves, are discussed and conclusions are drawn on what repercussions this has for the cross sections calculated.

Density of States in a-Si:H from SCLC and Its Application in Modeling a Vertical TFT

ABSTRACTSteady-state space-charge limited current (SCLC) measurements are used to investigate the density of states (DOS) in the mobility gap of hydrogenated amorphous silicon (a-Si:H). The density of states is calculated by different methods based on both continuous DOS and discrete traps assumptions. The density of states found by the SCLC measurements is used to set the trap densities and trap energy levels to model a vertical a-Si:H thin-film transistor (TFT) using the Medici device simulation package. The effect of different sets of traps in the bulk of a-Si:H and variation of the physical dimensions of the device on the characteristics of the vertical TFT is studied. The simulation on the space-charge limited current is performed to verify the validity and accuracy of the SCLC method.