P.A. Maksym

A theory of rheed

Abstract Elastic Reflection High Energy Electron Diffraction (RHEED) by solid surfaces is studied theoretically. First, the problem of finding the electron reflection and transmission coefficients of a crystal slab is formally solved. Following this, it is shown how the formal solution may be used in a practical computation of the diffracted beam intensities. These two results are applied to a study of high energy (20 keV) electron diffraction by the Ag(001) surface. Rocking curves are computed to illustrate the dependence of the reflection coefficients on the glancing angle of the incident beam, the incident beam azimuth being in the [110] direction. The curves are shown to have several features in common with a typical set of LEED I - V plots: primary Bragg peaks, secondary Bragg peaks and resonance peaks are all present. The dependence of the reflection coefficients on the deviation of the incident beam azimuth from the [110] direction is also described. Additional computations are made to illustrate the sensitivity of the RHEED pattern to the details of the surface structure: the relative heights of the peaks in the rocking curves are shown to be quite sensitive to the spacing of the topmost atomic layers.

Analysis of intensity data for RHEED by the MgO(001) surface

Rocking curves for elastic diffraction of 10 keV electrons incident on the MgO(001) surface, in the [010] azimuth, are computed and compared with experimental data. Very good agreement with experiment is obtained in spite of some uncertainty about the inelastic component of the data. Assuming that the possible presence of an inelastic component does not affect the subsequent analysis allows the spacing of the topmost atomic layers of the MgO(001) surface to be determined. The most likely value is found to be identical to the bulk layer spacing and the upper limit on any deviation from the bulk spacing is found to be a 3% expansion. This is consistent with the accepted LEED result. Further calculations are then used to show that RHEED could be used to find the rumpling of the MgO(001) surface as well as the topmost layer spacing. It is shown that the RHEED intensities are insensitive to rumpling when the incident beam azimuth lies in one of the [n10] directions with n even, but that they are very sensitive to rumpling when it lies in other directions. Use of this effect would enable the topmost spacing and rumpling to be determined by a systematic procedure for which the computational cost is particularly low. Some reasons for the apparent insignificance of inelastic scattering in the analysis of the RHEED data for diffraction by the MgO(001) surface are considered and the prospects of using RHEED as a general surface structure analysis technique are discussed.

RHEED from stepped surfaces and its relation to RHEED intensity oscillations observed during MBE

Abstract Multiple scattering theory is used to calculate the intensities of reflection high energy electron diffraction from periodic arrays of surface steps. The intensities are found to depend strongly on the direction of the incident beam azimuth. When the incident beam azimuth is parallel to the step edges, both the specular and diffracted beam intensities are diminished with respect to the intensities from a flat surface. When the incident beam azimuth is perpendicular to the edges, the intensities of all the beams are of the same order of magnitude as for a flat surface but some of the peak heights are oscillatory functions of the number of atoms in the topmost layer. These peak intensity oscillations are very similar to the intensity oscillations observed during molecular beam epitaxial film growth.

Theory of quantum dot helium

Abstract The competition between the Coulomb interaction and the binding forces due to the confinement and the magnetic field induces transitions of the ground state of quantum dots with few electrons. We demonstrate that for quantum dot helium these transitions occur between states with differently strong correlations between the electrons. By the response of quantum dot helium to far infrared radiation we exemplify that a proper treatment of the correlation effects may be essential for a correct interpretation of experimental data on quantum dots with few electrons.

Calculation of RHEED intensities from stepped surfaces

Abstract We consider the effect of surface steps on RHEED intensities. A multiple scattering theory of RHEED described by Maksym and Beeby is used to calculate intensities for RHEED by the Al(001) surface and the effect of steps is studied by considering periodic arrays of monolayer steps. The steps are found to cause two characteristic changes in the RHEED intensities. One is that the intensity of the specular spot is diminished when the incident beam azimuth is parallel to the step edges. The other is that when the incident beam azimuth is perpendicular to the step edges the heights of the peaks in the RHEED intensity curves depends systematically on the number of atoms in the topmost layer. The latter effect is consistent with the diffraction intensity oscillations recently reported in studies of molecular beam epitaxial film growth.

Analysis of RHEED data from the GaAs(001)2 × 4 surface

Abstract Dynamical calculations of sets of elastic RHEED rocking curves from the (2 × 4)-reconstructed GaAs(001) surface, using 12.5 keV electrons incident in the [110] azimuth, are presented. Comparison of theoretical curves with experimental data permits an estimate of the values of the parameters present in the assumed surface model. The reliability of the parameters obtained is discussed with reference to factors possibly limiting the closeness of fit attainable between theory and experiment, notably inconsistencies in the experimental data and the neglect of the possible effects of surface disorder and defects on the theoretical rocking curves. Discrepancies present between theory and experiment mean that the values obtained for the surface model parameters should be regarded as only provisional. The effect upon rocking curves of varying the As surface coverage is then investigated. The experiment/theory comparison supports the 75% coverage of As observed using the STM, but a consideration of this RHEED data alone cannot exclude a 50% As coverage. Calculations employing unit cells containing surface defects suggest that such defects have very little effect upon sets of rocking curves. A consideration of the kinematic surface structure factor shows that surface disorder may markedly reduce the intensities of fractional-order diffraction features, yet have less effect upon whole-order features.

Vertically coupled double quantum dots in magnetic fields

Ground- and excited-state properties of vertically coupled double quantum dots are studied by exact diagonalization. Magic-number total angular momenta that minimize the total energy are found to reflect a crossover between electron configurations dominated by intralayer correlation and those dominated by interlayer correlation. The position of the crossover is governed by the strength of the interlayer electron tunneling and magnetic field. The magic numbers should have an observable effect on the far-infrared optical-absorption spectrum, since Kohns theorem [Phys. Rev. 123, 1242 (1961)] does not hold when the confinement potential is different for two dots. This is indeed confirmed here from a numerical calculation that includes Landau-level mixing. Our results take full account of the effect of spin degrees of freedom. A key feature is that the total spin S of the system and the magic-number angular momentum are intimately linked because of strong electron correlation. Thus S jumps hand in hand with the total angular momentum as the magnetic field is varied. One important consequence of this is that the spin blockade (an inhibition of single-electron tunneling) should occur in some magnetic field regions because of a spin selection rule. Owing to the flexibility arising from the presence of both intralayer and interlayer correlations, the spin blockade is easier to realize in double dots than in single dots.

Magic numbers and optical-absorption spectrum in vertically coupled quantum dots in the fractional quantum Hall regime.

Exact diagonalization is used to study the quantum states of vertically coupled quantum dots in strong magnetic fields. We find a new sequence of angular momentum magic numbers which are a consequence of the electron correlation in the double dot. The new sequence occurs at low angular momenta and changes into the single dot sequence at a critical angular momentum determined by the strength of the inter-dot electron tunneling. We also propose that the magic numbers can be investigated experimentally in vertically coupled dots. Because of the generalized Kohn theorem, the far-infrared optical absorption spectrum of a single dot is unaffected by correlation but the theorem does not hold for two vertically coupled dots which have different confining potentials. We show that the absorption energy of the double dot should exhibit discontinuities at the magnetic fields where the total angular momentum changes from one magic number to another.

Calculation of MEED intensities in the 5–10 keV electron energy range

Abstract A method for computing MEED intensities in the 5–10 keV electron energy range is described. The method is based on improving the computational efficiency of a RHEED program so that it can be used to handle the larger matrices involved in MEED calculations. As an example of its use rocking curves are computed for 5 keV electrons incident on the Al(110) surface in the 110 azimuth. Further numerical results are then presented to show that smaller scale calculations, in which only beams in the zeroth Laue zone are taken into account, can give a useful approximation to the exact rocking curves. Finally, the conditions under which these calculations are likely to be valid are discussed.

Unraveling Quantum Hall Breakdown in Bilayer Graphene with Scanning Gate Microscopy

Investigating the structure of quantized plateaus in the Hall conductance of graphene is a powerful way of probing its crystalline and electronic structure and will also help to establish whether graphene can be used as a robust standard of resistance for quantum metrology. We use low-temperature scanning gate microscopy to image the interplateau breakdown of the quantum Hall effect in an exfoliated bilayer graphene flake. Scanning gate images captured during breakdown exhibit intricate patterns where the conductance is strongly affected by the presence of the scanning probe tip. The maximum density and intensity of the tip-induced conductance perturbations occur at half-integer filling factors, midway between consecutive quantum Hall plateau, while the intensity of individual sites shows a strong dependence on tip-voltage. Our results are well-described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering in a network of saddle points separating localized states.