Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two-dimensional (2D) electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and noncrossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k(R)l of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e. g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the nth Landau-level g(n) factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

Luminescence from two-dimensional electron gases in InAlN/GaN heterostructures with different In content

The luminescence properties of InxAl1−xN/GaN heterostructures are investigated systematically as a function of the In content (x = 0.067 − 0.208). The recombination between electrons confined in the two-dimensional electron gas and free holes in the GaN template is identified and analyzed. We find a systematic shift of the recombination with increasing In content from about 80 meV to only few meV below the GaN exciton emission. These results are compared with model calculations and can be attributed to the changing band profile and originating from the polarization gradient between InAlN and GaN.

SEMICLASSICAL THEORY OF MAGNETIZATION FOR A 2-DIMENSIONAL NONINTERACTING ELECTRON-GAS

We compute the semiclassical magnetization and susceptibility of non-interacting electrons, confined by a smooth two-dimensional potential and subjected to a uniform perpendicular magnetic field, in the general case when their classical motion is chaotic. It is demonstrated that the magnetization per particle m(B) is directly related to the staircase function N(E), which counts the single-particle levels up to energy E. Using Gutzwiller's trace formula for N, we derive a semiclassical expression for m. Our results show that the magnetization has a non-zero average, which arises from quantum corrections to the leading-order Weyl approximation to the mean staircase and which is independent of whether the classical motion is chaotic or not. Fluctuations about the average are due to classical periodic orbits and do represent a signature of chaos. This behaviour is confirmed by numerical computations for a specific system.

Interference effects in nonplanar wires with a two-dimensional electron gas

We have studied the universal conductance fluctuations (UCF) due to quantum interface in a two-dimensional electron gas (2DEG) grown on the substrates with pre-patterned, sub-micron wires. The dependence of UCF on the angle between the direction of the magnetic field and the substrate has been investigated. We found, that magnetoresistance traces for different angles are completely uncorrelated. A non-planar character of electron motion is responsible for these angular conductance fluctuations. We compared the experimental results with a simple geometrical model.

Three-dimensional electron microscopy of myriapod hemocyanin, planorbid snail acetylcholine-binding protein and cyanobacterial Vipp1

Three-dimensional electron microscopy (3-D EM) provides a framework for the analysis of large protein quaternary structures. The advantage over the generally higher resolving meth- od of X-ray crystallography is the embedding of the proteins in their physiological environ- ment. However, results of the two methods can be combined to obtain superior structural information. In this work, three different protein types – (i) Myriapod hemocyanin, (ii) vesi- cle-inducing protein in plastids 1 (Vipp1) and (iii) acetylcholine-binding protein (AChBP) – were structurally analyzed by 2-D and 3-D EM and, where possible, functionally interpreted.rnMyriapod hemocyanins have been previously shown to be 6x6-meric assemblies that, in case of Scutigera coleoptrata hemocyanin (ScoHc), show two 3x6-mer planes whith a stag- gering angle of approximately 60°. Here, previously observed structural differences between oxy- and deoxy-ScoHc could be substantiated. A 4° rotation between hexamers of two dif- ferent 3x6-mer planes was measured, which originates at the most central inter-hexamer in- terface. Further information about allosteric behaviour in myriapod hemocyanin was gained by analyzing Polydesmus angustus hemocyanin (PanHc), which shows a stable 3x6-mer and divergent histidine patterns in the inter-hexamer interfaces when compared to ScoHc. Both findings would conclusively explain the very different oxygen binding properties of chilopod and diplopod hemocyanin.rnVipp1 is a protein found in cyanobacteria and higher plants which is essential for thyla- koid membrane function and forms highly variable ring-shaped structures. In the course of this study, the first 3-D analysis of Vipp1 was conducted and yielded reconstructions of six differently sized Vipp1 rings from negatively stained images at resolutions between 20 to 30 Å. Furthermore, mutational analyses identified specific N-terminal amino acids that are essential for ring formation. On the basis of these analyses and previously published results, a hypothetical model of the Vipp1 tertiary and quaternary structure was generated.rnAChBP is a water-soluble protein in the hemolymph of mollusks. It is a structural and functional homologue of the ligand-binding domain of nicotinic acetylcholine receptors. For the freshwater snail Biomphalaria glabrata, we previously described two types of AChBP (BgAChBP1 and BgAChBP2). In this work, a 6 Å 3-D reconstruction of native BgAChBP is presented, which shows a dodecahedral assembly that is unprecedented for an AChBP. Single particle analysis of recombinantely expressed BgAChBP types led to preliminary results show- ing a dodecahedral assembly of BgAChBP1 and a dipentameric assembly of BgAChBP2. This indicates divergent biological functions of the two types.

Three-dimensional electron beam dose calculations

The MDAH pencil-beam algorithm developed by Hogstrom et al (1981) has been widely used in clinics for electron beam dose calculations for radiotherapy treatment planning. The primary objective of this research was to address several deficiencies of that algorithm and to develop an enhanced version. Two enhancements have been incorporated into the pencil-beam algorithm; one models fluence rather than planar fluence, and the other models the bremsstrahlung dose using measured beam data. Comparisons of the resulting calculated dose distributions with measured dose distributions for several test phantoms have been made. From these results it is concluded (1) that the fluence-based algorithm is more accurate to use for the dose calculation in an inhomogeneous slab phantom, and (2) the fluence-based calculation provides only a limited improvement to the accuracy the calculated dose in the region just downstream of the lateral edge of an inhomogeneity. The source of the latter inaccuracy is believed primarily due to assumptions made in the pencil beam's modeling of the complex phantom or patient geometry.^ A pencil-beam redefinition model was developed for the calculation of electron beam dose distributions in three dimensions. The primary aim of this redefinition model was to solve the dosimetry problem presented by deep inhomogeneities, which was the major deficiency of the enhanced version of the MDAH pencil-beam algorithm. The pencil-beam redefinition model is based on the theory of electron transport by redefining the pencil beams at each layer of the medium. The unique approach of this model is that all the physical parameters of a given pencil beam are characterized for multiple energy bins. Comparisons of the calculated dose distributions with measured dose distributions for a homogeneous water phantom and for phantoms with deep inhomogeneities have been made. From these results it is concluded that the redefinition algorithm is superior to the conventional, fluence-based, pencil-beam algorithm, especially in predicting the dose distribution downstream of a local inhomogeneity. The accuracy of this algorithm appears sufficient for clinical use, and the algorithm is structured for future expansion of the physical model if required for site specific treatment planning problems. ^

N-dimensional electron in an anharmonic potential:the large-N limit

We show that the energy levels predicted by a frac(1, N)-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared with numerical results.

DEVELOPMENT OF A 2-DIMENSIONAL FINITE VOLUME MODEL TO ASSESS HYDRODYNAMIC AND MICROBIAL CONTROLS ON DNAPL DISSOLUTION AND DETOXIFICATION

Tetrachloroethene (PCE) and trichloroethene (TCE) form dense non-aqueous phase liquids (DNAPLs), which are persistent groundwater contaminants. DNAPL dissolution can be "bioenhanced" via dissolved contaminant biodegradation at the DNAPL-water interface. This research hypothesized that: (1) competitive interactions between different dehalorespiring strains can significantly impact the bioenhancement effect, and extent of PCE dechlorination; and (2) hydrodynamics will affect the outcome of competition and the potential for bioenhancement and detoxification. A two-dimensional coupled flowtransport model was developed, with a DNAPL pool source and multiple microbial species. In the scenario presented, Dehalococcoides mccartyi 195 competes with Desulfuromonas michiganensis for the electron acceptors PCE and TCE. Simulations under biostimulation and low velocity (vx) conditions suggest that the bioenhancement with Dsm. michiganensis alone was modestly increased by Dhc. mccartyi 195. However, the presence of Dhc. mccartyi 195 enhanced the extent of PCE transformation. Hydrodynamic conditions impacted the results by changing the dominant population under low and high vx conditions.

Quantum Hall Effect near the Charge Neutrality Point in a Two-Dimensional Electron-Hole System

We study the transport properties of HgTe-based quantum wells containing simultaneously electrons and holes in a magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity sigma(xy) approximate to 0 and in a minimum of diagonal conductivity sigma(xx) at nu = nu(p) - nu(n) = 0, where nu(n) and nu(p) are the electron and hole Landau level filling factors. We suggest that the transport at the CNP point is determined by electron-hole ""snake states'' propagating along the nu = 0 lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in a random magnetic field with a zero mean value.

Many-Body Effects on the rho(xx) Ringlike Structures in Two-Subband Wells

The longitudinal resistivity rho(xx) of two-dimensional electron gases formed in wells with two subbands displays ringlike structures when plotted in a density-magnetic-field diagram, due to the crossings of spin-split Landau levels (LLs) from distinct subbands. Using spin density functional theory and linear response, we investigate the shape and spin polarization of these structures as a function of temperature and magnetic-field tilt angle. We find that (i) some of the rings ""break'' at sufficiently low temperatures due to a quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of spin polarization (similar to 50%) within, consistent with the NMR data of Zhang et al. [Phys. Rev. Lett. 98, 246802 (2007)], and (ii) for increasing tilting angles the interplay between the anticrossings due to inter-LL couplings and the exchange-correlation effects leads to a collapse of the rings at some critical angle theta(c), in agreement with the data of Guo et al. [Phys. Rev. B 78, 233305 (2008)].

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Strong reduction of V(4+) amount in vanadium oxide/hexadecylamine nanotubes by doping with Co(2+) and Ni(2+) ions: Electron paramagnetic resonance and magnetic studies

In this work we present a complete characterization and magnetic study of vanadium oxide/hexadecylamine nanotubes (VO(x)/Hexa NT's) doped with Co(2)+ and Ni(2+) ions. The morphology of the NT's has been characterized by transmission electron microscopy, while the metallic elements have been quantified by the instrumental neutron activation analysis technique. The static and dynamic magnetic properties were studied by collecting data of magnetization as a function of magnetic field and temperature and by electron paramagnetic resonance. At difference of the majority reports in the literature, we do not observe magnetic dimers in vanadium oxide nanotubes. Also, we observed that the incorporation of metallic ions (Co(2+), S = 3/2 and Ni(2+), S = 1) decreases notably the amount of V(4+) ions in the system, from 14-16% (nondoped case) to 2%-4%, with respect to the total vanadium atoms (fact corroborated by XPS experiments) anyway preserving the tubular nanostructure. The method to decrease the amount of V(4+) in the nanotubes improves considerably their potential technological applications as Li-ion batteries cathodes. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3580252]

Nomograms of fetal thyroid measurements estimated by 2-dimensional sonography

Purpose. To build nomograms of fetal thyroid circumference (FTC), fetal thyroid area (FTA), and fetal thyroid transverse diameter (FTTD) throughout gestational age (GA). Method. Between January 2006 and July 2006, FTC, FTA, and FTTD were measured once in 196 normal fetuses examined at a GA of 22-35 weeks. Inclusion criteria were a healthy mother with normal maternal thyrotropin level during pregnancy, a singleton pregnancy with normal fetal morphology on sonography, and GA confirmed via first-trimester sonographic examination. Results. Mean FTC, FTA, and FTTD ranged from 3.21 cm, 0.58 cm(2), and 1.19 cm at 22 weeks to 5.11 cm, 1.69 cm(2), and 1.89 cm at 35 weeks, respectively. Linear regression analysis yielded the following formulas for FTC, FTA, and FTTD according to GA: FTC (cm) = 0.146 X GA (weeks); FTA (cm(2)) = -1.289 + 0.085 X GA (weeks); FTTD (cm) = 0.054 X GA (weeks). The following logarithmic formulas were obtained for the expected fetal thyroid measurements according to estimated fetal weight (FW): FTC (cm) = -4.791 + 1.265 X logN FW; FTA (cm(2)) = -1.676 + 0.455 X logN FW; and FTTD (cm) = 0.399 + 0.001 X logN FW. Conclusion. We describe new nomograms of fetal thyroid measurements throughout gestation that may be useful in case of thyroid dysfunction. (C) 2008 Wiley Periodicals, Inc.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Evaluation of organ-specific peripheral doses after 2-dimensional, 3-dimensional and hybrid intensity modulated radiation therapy for breast cancer based on Monte Carlo and convolution/superposition algorithms: implications for secondary cancer risk assessment.

To make a comprehensive evaluation of organ-specific out-of-field doses using Monte Carlo (MC) simulations for different breast cancer irradiation techniques and to compare results with a commercial treatment planning system (TPS). Three breast radiotherapy techniques using 6MV tangential photon beams were compared: (a) 2DRT (open rectangular fields), (b) 3DCRT (conformal wedged fields), and (c) hybrid IMRT (open conformal+modulated fields). Over 35 organs were contoured in a whole-body CT scan and organ-specific dose distributions were determined with MC and the TPS. Large differences in out-of-field doses were observed between MC and TPS calculations, even for organs close to the target volume such as the heart, the lungs and the contralateral breast (up to 70% difference). MC simulations showed that a large fraction of the out-of-field dose comes from the out-of-field head scatter fluence (>40%) which is not adequately modeled by the TPS. Based on MC simulations, the 3DCRT technique using external wedges yielded significantly higher doses (up to a factor 4-5 in the pelvis) than the 2DRT and the hybrid IMRT techniques which yielded similar out-of-field doses. In sharp contrast to popular belief, the IMRT technique investigated here does not increase the out-of-field dose compared to conventional techniques and may offer the most optimal plan. The 3DCRT technique with external wedges yields the largest out-of-field doses. For accurate out-of-field dose assessment, a commercial TPS should not be used, even for organs near the target volume (contralateral breast, lungs, heart).