Abstract: In this article we study excitons and trions in fractional dimensional spaces using the model suggested by C. Palmer [ J. Phys. A: Math. Gen. 37 6987 (2004)] through variational quantum Monte Carlo. We present a direct approach for estimating the exciton binding energy and discuss the von Neumann rejection- and Metropolis sampling methods. A simple variational estimate of trions is presented which shows good agreement with previous calculations done within the fractional dimensional model presented by D. R. Herrick and F. H. Stillinger [ Phys. Rev. A 11 42 (1975) and J. Math. Phys. 18 1224 (1977)]. We explain the spatial physics of the positive and negative trions by investigating angular and inter-atomic distances. We then examine the wave function and explain the differences between the positive and negative trions with heavy holes. As applications of the fractional dimensional model we study three systems: First we apply the model to estimate the energy of the hydrogen molecular ion H2+. Then we estimate trion binding energies in GaAs-based quantum wells and we demonstrate a good agreement with other theoretical work as well as experimentally observed binding energies. Finally, we apply the results to carbon nanotubes. We find good agreement with recently observed binding energies of the positively charged trion.

Abstract: We show by extensive numerical simulations, that far-from-equilibrium experiments on dusty plasmas and on dipole particles in a circular cavity are good candidates for the verification of the Jarzynski equality, the Crooks relation and, to a lesser extent, of the recently obtained microscopic expression for the dissipated work.

Abstract: The valley splitting of the conduction-band states in a thin silicon-on-insulator layer is investigated using the 30-band k . p theory. The system composed of a few nm thick Si layer embedded within thick SiO2 layers is analyzed. The valley split states are found to cross periodically with increasing quantum well width, and therefore the energy splitting is an oscillatory function of the quantum well width, with period determined by the wave vector K-0 of the conduction band minimum. Because the valley split states are classified by parity, the optical transition between the ground hole state and one of those valley split conduction band states is forbidden. The oscillations in the valley splitting energy decrease with electric field and with smoothing of the composition profile between the well and the barrier by diffusion of oxygen from the SiO2 layers to the Si quantum well. Such a smoothing also leads to a decrease of the interband transition matrix elements. The obtained results are well parametrized by the effective two-valley model, but are found to disagree from previous 30-band calculations. This discrepancy could be traced back to the fact that the basis for the numerical solution of the eigenproblem must be restricted to the first Brillouin zone in order to obtain quantitatively correct results for the valley splitting.

Abstract: We theoretically investigate the ground-state properties of a quantum dot defined on the surface of a strong three-dimensional time-reversal invariant topological insulator. Confinement is realized by ferromagnetic barriers and Coulomb interaction is treated numerically for up to seven electrons in the dot. Experimentally relevant intermediate interaction strengths are considered. The topological origin of the dot has several consequences: (i) spin polarization increases and the ground state exhibits quantum phase transitions at specific angular momenta as a function of interaction strength, (ii) the onset of Wigner correlations takes place mainly in one spin channel, and (iii) the ground state is characterized by a robust persistent current that changes sign as a function of the distance from the center of the dot.

Abstract: Chrome yellow refers to a group of synthetic inorganic pigments that became popular as an artists material from the second quarter of the 19th century. The color of the pigment, in which the chromate ion acts as a chromophore, is related to its chemical composition (PbCr1-xSxO4, with 0≤x≤0.8) and crystalline structure (monoclinic/orthorhombic). Their shades range from the yellow-orange to the paler yellow tones with increasing sulfate amount. These pigments show remarkable signs of degradation after limited time periods. Pure PbCrO4 (crocoite in its natural form) has a deep yellow color and is relatively stable, while the co-precipitate with lead sulfate (PbCr1-xSxO4) has a paler shade and seems to degrade faster. This degradation is assumed to be related to the reduction of Cr(VI) to Cr(III). We show that on increasing the sulfur(S)-content in chrome yellow, the band gap increases. Typically, when increasing the band gap, one might assume that a decrease in photo activity is the result. However, the photo activity relative to the Cr content, and thus Cr reduction, of sulfur-rich PbCr1-xSxO4 is found to be much higher compared to the sulfur-poor or non-doped lead chromates. This discrepancy can be explained by the evolution of the crystal and electronic structure as function of the sulfur content: first-principles density functional theory calculations show that both the absorption coefficient and reflection coefficients of the lead chromates change as a result of the sulfate doping in such a way that the generation of electron-hole pairs under illumination relative to the total Cr content increases. These changes in the material properties explain why paler shade yellow colors of this pigment are more prone to discoloration. The electronic structure calculations also demonstrate that lead chromate and its co-precipitates are p-type semiconductors, which explains the observed reduction reaction. As understanding this phenomenon is valuable in the field of cultural heritage, this study is the first joint action of photo-electrochemical measurements and first-principles calculations to approve the higher tendency of sulfur-rich lead chromates to darken.

Abstract: The effect of B and P dopants on the band structure of Si nanowires is studied using electronic structure calculations based on density functional theory. At low concentrations a dispersionless band is formed, clearly distinguishable from the valence and conduction bands. Although this band is evidently induced by the dopant impurity, it turns out to have purely Si character. These results can be rigorously analyzed in the framework of effective mass theory. In the process we resolve some common misconceptions about the physics of hydrogenic shallow impurities, which can be more clearly elucidated in the case of nanowires than would be possible for bulk Si. We also show the importance of correctly describing the effect of dielectric confinement, which is not included in traditional electronic structure calculations, by comparing the obtained results with those of G(0)W(0) calculations.

Abstract: It is commonly believed that solids with spatial inversion symmetry do not display spinorbit effects. However, first-principles calculations now reveal unexpected spin structure for centrosymmetric crystals

Abstract: Black phosphorus (BP) has recently triggered an unprecedented interest in the 2D community. However, many of its unique properties are not exploited and the well-known environmental vulnerability is not conquered. Herein, a type-I mixed-dimensional (0D-1D) van der Waals heterojunction is developed, where three-atomic-layer BP quantum dots (QDs) are assembled on a single ZnO nanorod (NR). By adjusting the indium (In) content in ZnO NRs, the degree and even the direction of surface charge transfer doping within the heterojunction can be tuned, which result in selective Raman scattering enhancements between ZnO and BP. The maximal enhancement factor is determined as 4340 for BP QDs with sub-ppm level. Furthermore, an unexpected long-term ambient stability (more than six months) of BP QDs is revealed, which is ascribed to the electron doping from ZnO:In NRs. The first demonstration of selective Raman enhancements between two inorganic semiconductors as well as the improved stability of BP shed light on this emerging 2D material.

Abstract: Electro-optical modulators, which use an electric voltage (or an electric field) to modulate a beam of light, are essential elements in present-day telecommunication devices. Using a self-consistent tight-binding approach combined with the standard Kubo formula, we show that the optical conductivity and the linear dichroism of few-layer phosphorene can be modulated by a perpendicular electric field. We find that the field-induced charge screening plays a significant role in modulating the optical conductivity and the linear dichroism. Distinct absorption peaks are induced in the conductivity spectrum due to the strong quantum confinement along the out-of-plane direction and to the field-induced forbidden-to-allowed transitions. The field modulation of the linear dichroism becomes more pronounced with increasing number of phosphorene layers. We also show that the Faraday rotation is present in few-layer phosphorene even in the absence of an external magnetic field. This optical Hall effect is induced by the reduced lattice symmetry of few-layer phosphorene. The Faraday rotation is greatly influenced by the field-induced charge screening and is strongly dependent on the strength of perpendicular electric field and on the number of phosphorene layers.

Abstract: Sodium-ion batteries (SIBs) are potential cost-effective solutions for stationary energy storage applications. Unavailability of suitable anode materials, however, is one of the important barriers to the maturity of SIBs. Here, we report a Na2+xTi4O9/C composite as a promising anode candidate for SIBs with high capacity and cycling stability. This anode is characterized by a capacity of 124 mAh g(-1) (plus 11 mAh g(-1) contributed by carbon black), an average discharge potential of 0.9 V vs Na/Na+, a good rate capability and a high stability (89% capacity retention after 250 cycles at a rate of 1 degrees C). The mechanisms of sodium insertion/deinsertion and of the formation of Na2+xTi4O9/C are investigated with the aid of various ex/in situ characterization techniques. The in situ formed carbon is necessary for the formation of the reduced sodium titanate. This synthesis method may enable the convenient synthesis of other composites of crystalline phases with amorphous carbon.

Abstract: The anomalous Hall effect (AHE) is studied on the surface of a 3D magnetic topological insulator. By applying a modified semiclassical framework, all three contributions to the AHE, the Berry curvature effect, the side jump effect and the skew scattering effects are systematically treated, and analytical expressions for the conductivities are obtained in terms of the Fermi level, the spatial orientation of the surface magnetization and the concentration of magnetic and nonmagnetic impurities. We demonstrate that the AHE can change sign by altering the orientation of the surface magnetization, the concentration of the impurities and also the position of the Fermi level, in agreement with recent experimental observations. We show how each contribution to the AHE, or even the whole AHE, can be turned off by properly adjusting the given parameters. For example, one can turn off the anomalous hall conductivity in a system with in-plane magnetization by pushing the system into the fully metallic regime.