Calculation of the few-electron states in semiconductor carbon nanotube quantum dots by exact diagonalisation

The 3 and 4-electron states of a gated semiconducting carbon nanotube quantum dot are calculated by exact diagonalisation of a modified effective mass Hamiltonian. A typical nanotube quantum dot is examined and the few-electron states are Wigner molecule-like. The exact diagonalisation method and the rate of convergence of the calculation are discussed

Amplitude Reduction in EXAFS.

In real systems, inelastic processes remove photoelectrons from the elastic scattering channel. This reduces the amplitude of the EXAFS causing disagreement between the experimental and theoretically predicted amplitudes. Traditionally these discrepancies were treated by including two semi empirical reduction factors in the data analysis; a mean free path term, which models the so called extrinsic loss processes, and a constant amplitude reduction factor which accounts for many electron excitations at the absorbing atom. The extrinsic inelastic effects may, however, be modelled more rigorously using a complex exchange and correlation potential. For example the Hedin-Lundqvist (H-L) potential used in most EXAFS data analysis programs. We present a method by which the losses caused by such a potential may be evaluated quickly and easily in the first Born approximation. The losses produced by the H-L potential significantly overestimate those produced by the mean free path alone. Instead the losses appear to agree well with the total reduction given by the semi-empirical reduction factors. These losses do not exhibit the correct low or high energy behaviour but do show excellent agreement with experiment over the range of a typical EXAFS spectrum. We therefore conclude, that the semi-empirical reduction parameters should not be included when data fitting using the H-L potential

Interacting electrons in a semiconducting carbon nanotube dot: A 2-band approach

A new 2-band effective mass theory for the interacting electron states in a carbon nanotube quantum dot is outlined. The states of two interacting electrons are calculated by exact diagonalisation of the 2-band Hamiltonian. A range of different nanotube and dot parameters are investigated and, interestingly, the 2-electron ground states are found to be ferromagnetic

Multiple-electron excitation in X-ray absorption: a screened model of the core-hole-photoelectron potential

The probability of secondary electron shake-off in X-ray absorption is calculated using a model form for the time- and energy-dependent core-hole-photoelectron potential, screened by the single plasmon pole dielectric function of the surrounding material. The resultant excitation probabilities are related to the energy-dependent intrinsic loss function in EXAFS data analysis and compared with experiment. Reasonable agreement is obtained close to the absorption edge although the calculation is less accurate at higher photon energies. The theory described allows the losses to be calculated with little computational effort, making the method suitable for routine EXAFS data analysis

Generalised effective mass theory of sub-surface scanning tunnelling microscopy : application to weakly bound impurity states

We apply our generalised effective mass theory of sub-surface scanning tunnelling microscopy (STM) (Phys. Rev. B 19, 195304 (2010)) to simulate STM images of electronic states localised around sub-surface Si dopant atoms in GaAs. In the case of these shallow impurity-states, we demonstrate that electrostatic effects from image-charges and from the STM tip have a strong influence on the sub-surface state and hence the simulated image

Efficient method for calculating electronic states in self-assembled quantum dots

It is demonstrated that the bound electronic states of a self-assembled quantum dot may be calculated more efficiently with a harmonic-oscillator (HO) basis than with the commonly used plane-wave basis. First, the bound electron states of a physically realistic self-assembled quantum dot model are calculated within the single-band, position-dependent effective mass approximation including the full details of the strain within the self-assembled dot. A comparison is then made between the number of states needed to diagonalize the Hamiltonian with either a HO or a plane-wave basis. With the harmonic-oscillator basis, significantly fewer basis functions are needed to converge the bound-state energies to within a fraction of a meV of the exact energies. As the time needed to diagonalize the matrix varies as the cube of the matrix size this leads to a dramatic decrease in the computing time required. With this basis the effects of a magnetic field may also be easily included. This is demonstrated, and the field dependence of the bound electron energies is shown

Semiconducting carbon nanotube quantum dots: Calculation of the interacting electron states by exact diagonalisation

In semiconducting carbon nanotube quantum dots that contain a few interacting electrons the electron-electron correlation is always important. The states of up to six interacting electrons in such a dot are calculated by exact diagonalisation of a 2-band, effective mass Hamiltonian. The addition energy and the few-electron density are investigated for a wide range of dots with different physical properties and, in a large proportion of these dots, the electrons are found to form Wigner molecules

An investigation of the use of the Hedin-Lundqvist exchange and correlation potential in EXAFS data analysis

In real systems, inelastic processes remove photoelectrons from the elastic scattering channel. This reduces the amplitude of the EXAFS. Traditionally the discrepancies between experimental and theoretical amplitudes were treated by including two semi-empirical reduction factors in the data analysis. Some inelastic effects may, however, be modelled more rigorously using a complex exchange and correlation potential, for example the Hedin-Lundqvist (HL) potential used in most EXAFS data-analysis programs. In this paper a systematic study of the effects of the HL potential on the calculated EXAFS amplitudes is presented. Expressions are derived whereby the EXAFS amplitudes may be examined in the presence of an arbitrary complex potential independently to the rest of the EXAFS signal. These results are used to study the effects of the HL potential on EXAFS data analysis in detail

Efficient Calculation of Electron States in Self-Assembled Quantum Dots: Application to Auger Relaxation

An efficient method for calculation of self-assembled dot states within the effective mass approximation is described and its application to the calculation of Auger relaxation rates is detailed. The method is based on expansion of the dot states in a harmonic oscillator basis whose parameters are optimised to improve the convergence rate. This results in at least an order of magnitude reduction in the number of basis states required to represent electron states accurately compared to the conventional plane wave approach. Auger relaxation rates are calculated for harmonic oscillator model states and exact states for various pyramidal models. The dipole approximation, previously used to calculate Auger rates, is found to be inaccurate by a factor of around 2–3. The harmonic oscillator states do not reproduce the rates for the more realistic pyramidal models very well and even within the set of pyramidal models variations in the dot shape and size can change the rates by up to an order of magnitude. Typical Auger relaxation rates are on a picosecond timescale but the actual value is strongly dependent on the density of electrons outside the dot

Undergraduate e-Journals

Most undergraduate science programmes provide students with a project through which they can obtain some experience of the research process, but few students get to know the mechanism by which research output reaches the public domain. Fewer still get to appreciate that the hard part of originality in science is to ask the right questions. . At the University of Leicester we have introduced a module to explicitly cover these areas. Our Physics students and Natural Sciences students learn about scientific publishing and peer review by acting as authors, referees, and editors of their own scientific journal. Split into small research groups, the students come up with original ideas, conduct research and write short scientific papers. They peer-review the work of other groups in a process overseen by a student editorial board who, based on the referees’ reports, have the final say on whether or not a paper is published. We use professional Open Journal Systems software to run the submission, review and publication processes of the journal online and, since 2008, all the students’ published work has been publically available from the journal website. The student experience is now a true reflection of that of professional research scientists and, as an added incentive to the students, some of the more creative published papers have recently gone viral, including interviews on Radio 4 and CNN international. In this presentation we shall report on the development of the module and its scalabilit