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This paper is dedicated to study the thin polycrystalline films of semiconductor chalcogenide materials (CdS, CdSe, and PbS) obtained by ammonia-free chemical bath deposition. The obtained material is of polycrystalline nature with crystallite of a size that, from a general point of view, should not result in any noticeable quantum confinement. Nevertheless, we were able to observe blueshift of the fundamental absorption edge and reduced refractive index in comparison with the corresponding bulk materials. Both effects are attributed to the material porosity which is a typical feature of chemical bath deposition technique. The blueshift is caused by quantum confinement in pores, whereas the refractive index variation is the evident result of the density reduction. Quantum mechanical description of the nanopores in semiconductor is given based on the application of even mirror boundary conditions for the solution of the Schrödinger equation; the results of calculations give a reasonable explanation of the experimental data.

The recent creation of electron vortex beams and their first practical application motivates a better understanding of their properties. Here, we develop the theory of free electron vortices with quantized angular momentum, based on solutions of the Schrödinger equation for cylindrical boundary conditions. The principle of transformation of a plane wave into vortices with quantized angular momentum, their paraxial propagation through round magnetic lenses, and the effect of partial coherence are discussed.

Highlights

► Theory of vortex electrons. ► Proof that free electrons can carry quantized orbital momentum. ► Proof that electron vortices are stable and robust under spherical aberration. ► Demonstration of the strong influence of partial coherence.

A 3-D quantum transport solver based on the spectral element method (SEM) and perfectly matched layer (PML) is introduced to solve the 3-D Schrödinger equation with a tensor effective mass. In this solver, the influence of the environment is replaced with the artificial PML open boundary extended beyond the contact regions of the device. These contact regions are treated as waveguides with known incident waves from waveguide mode solutions. As the transmitted wave function is treated as a total wave, there is no need to decompose it into waveguide modes, thus significantly simplifying the problem in comparison with conventional open boundary conditions. The spectral element method leads to an exponentially improving accuracy with the increase in the polynomial order and sampling points. The PML region can be designed such that less than −100 dB outgoing waves are reflected by this artificial material. The computational efficiency of the SEM solver is demonstrated by comparing the numerical and analytical results from waveguide and plane-wave examples, and its utility is illustrated by multiple-terminal devices and semiconductor nanotube devices.

We have developed a hierarchical process that combines linear triblock copolymers into concentric globular sub-units through strong chemical bonds and is followed by their supramolecular assembly via weak non-covalent interactions to afford one-dimensionally-assembled, dynamic cylindrical nanostructures. The molecular brush architecture forces triblock copolymers to adopt some intramolecular interactions within confined frameworks and then drives their intermolecular interactions in the mixtures of organic solvent and water. In contrast, the triblock copolymers, when not pre-connected into the molecular brush architectures, organize only into globular assemblies.

It has been widely reported that twin boundaries strengthen nanowires regardless of their morphology—that is, the strength of nanowires goes up as twin spacing goes down. This article shows that twin boundaries do not always strengthen nanowires. Using classical molecular dynamics simulations, the authors show that whether twin boundaries strengthen nanowires depends on the necessary stress for dislocation nucleation, which in turn depends on surface morphologies. When nanowires are circular cylindrical, the necessary stress of dislocation nucleation is high and the presence of twin boundaries lowers this stress; twin boundaries soften nanowires. In contrast, when nanowires are square cylindrical, the necessary stress of dislocation nucleation is low, and a higher stress is required for dislocations to penetrate twin boundaries; they strengthen nanowires.

It has been widely reported that twin boundaries strengthen nanowires regardless of their morphology—that is, the strength of nanowires goes up as twin spacing goes down. This article shows that twin boundaries do not always strengthen nanowires. Using classical molecular dynamics simulations, the authors show that whether twin boundaries strengthen nanowires depends on the necessary stress for dislocation nucleation, which in turn depends on surface morphologies. When nanowires are circular cylindrical, the necessary stress of dislocation nucleation is high and the presence of twin boundaries lowers this stress; twin boundaries soften nanowires. In contrast, when nanowires are square cylindrical, the necessary stress of dislocation nucleation is low, and a higher stress is required for dislocations to penetrate twin boundaries; they strengthen nanowires.

We report on various self-assembled In(Ga)As nanostructures by droplet epitaxy on GaAs substrates using molecular beam epitaxy. Depending on the growth condition and index of surfaces, various nanostructures can be fabricated: quantum dots (QDs), ring-like and holed-triangular nanostructures. At near room temperatures, by limiting surface diffusion of adatoms, the size of In droplets suitable for quantum confinement can be fabricated and thus InAs QDs are demonstrated on GaAs (100) surface. On the other hand, at relatively higher substrate temperatures, by enhancing the surface migrations of In adatoms, super lower density of InGaAs ring-shaped nanostructures can be fabricated on GaAs (100). Under an identical growth condition, holed-triangular InGaAs nanostructures can be fabricated on GaAs type-A surfaces, while ring-shaped nanostructures are formed on GaAs (100). The formation mechanism of various nanostructures can be understood in terms of intermixing, surface diffusion, and surface reconstruction.

We report on various self-assembled In(Ga)As nanostructures by droplet epitaxy on GaAs substrates using molecular beam epitaxy. Depending on the growth condition and index of surfaces, various nanostructures can be fabricated: quantum dots (QDs), ring-like and holed-triangular nanostructures. At near room temperatures, by limiting surface diffusion of adatoms, the size of In droplets suitable for quantum confinement can be fabricated and thus InAs QDs are demonstrated on GaAs (100) surface. On the other hand, at relatively higher substrate temperatures, by enhancing the surface migrations of In adatoms, super lower density of InGaAs ring-shaped nanostructures can be fabricated on GaAs (100). Under an identical growth condition, holed-triangular InGaAs nanostructures can be fabricated on GaAs type-A surfaces, while ring-shaped nanostructures are formed on GaAs (100). The formation mechanism of various nanostructures can be understood in terms of intermixing, surface diffusion, and surface reconstruction.

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potentials and also a stress tensor. Correspondingly, a viscous double-layer potential is defined. The properties of all these potentials are investigated.

By representing the scattered field as a combination of a single-layer viscous potential and a double-layer viscous potential the problem is reduced to the solution of a singular vectorial integral equation of Fredholm type of the second kind.

In the case where the stress vector on the boundary is the main quantity of interest the corresponding boundary singular integral equation is proved to have a unique solution.

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

We have studied ultrafast carrier dynamics in nanocrystalline silicon films with thickness of a few nanometers where boundary-related states and quantum confinement play an important role. Transient non-degenerated photoinduced absorption measurements have been employed to investigate the effects of grain boundaries and quantum confinement on the relaxation dynamics of photogenerated carriers. An observed long initial rise of the photoinduced absorption for the thicker films agrees well with the existence of boundary-related states acting as fast traps. With decreasing the thickness of material, the relaxation dynamics become faster since the density of boundary-related states increases. Furthermore, probing with longer wavelengths we are able to time-resolve optical paths with faster relaxations. This fact is strongly correlated with probing in different points of the first Brillouin zone of the band structure of these materials.

An analysis is presented of the diffraction of a pressure wave by a periodic grating including the influence of the air viscosity. The direction of the incoming pressure wave is arbitrary. As opposed to the classical nonviscous case, the problem cannot be reduced to a plane problem having a definite 3-D character. The system of partial differential equations used for solving the problem consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to a system of two hypersingular integral equations for determining the velocity components in the slits’ plane and a hypersingular integral equation for the normal component of velocity. These equations are solved by using Galerkin’s method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in MEMS technology. In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The analysis indicates that the openings in the screen should be on the order of 10 microns in order to avoid excessive attenuation of the signal. This paper also provides the variation of the transmission coefficient with frequency in the acoustical domain.

More recently, motivated by extensively technical applications of carbon nanostructures, there is a growing interest in exploring novel non-carbon nanostructures. As the nearest neighbor of carbon in the periodic table, boron has exceptional properties of low volatility and high melting point and is stronger than steel, harder than corundum, and lighter than aluminum. Boron nanostructures thus are expected to have broad applications in various circumstances. In this contribution, we have performed a systematical study of the stability and electronic and magnetic properties of boron nanowires using the spin-polarized density functional calculations. Our calculations have revealed that there are six stable configurations of boron nanowires obtained by growing along different base vectors from the unit cell of the bulk α-rhombohedral boron (α-B) and β-rhombohedral boron (β-B). Well known, the boron bulk is usually metallic without magnetism. However, theoretical results about the magnetic and electronic properties showed that, whether for the α-B-based or the β-B-based nanowires, their magnetism is dependent on the growing direction. When the boron nanowires grow along the base vector [001], they exhibit ferromagnetism and have the magnetic moments of 1.98 and 2.62 μB, respectively, for the α-c [001] and β-c [001] directions. Electronically, when the boron nanowire grows along the α-c [001] direction, it shows semiconducting and has the direct bandgap of 0.19 eV. These results showed that boron nanowires possess the unique direction dependence of the magnetic and semiconducting behaviors, which are distinctly different from that of the bulk boron. Therefore, these theoretical findings would bring boron nanowires to have many promising applications that are novel for the boron bulk.

A microscopic theory is presented for electron cotunneling through doubly occupied quantum dots in the Coulomb blockade regime. Beyond the semiclassic framework of phenomenological models, a fully quantum mechanical solution for cotunneling of electrons through a one-dimensional quantum dot is obtained using a quantum transmitting boundary method without any fitting parameters. It is revealed that the cotunneling conductance exhibits strong dependence on the spin configuration of the electrons confined inside the dot. Especially for the triplet configuration, the conductance shows an obvious deviation from the well-known quadratic dependence on the applied bias voltage. Furthermore, it is found that the cotunneling conductance reveals more sensitive dependence on the barrier width than the height.

The electronic structure and size-scaling of optoelectronic properties in cycloparaphenylene carbon nanorings are investigated using time-dependent density functional theory (TDDFT). The TDDFT calculations on these molecular nanostructures indicate that the lowest excitation energy surprisingly becomes larger as the carbon nanoring size is increased, in contradiction with typical quantum confinement effects. In order to understand their unusual electronic properties, I performed an extensive investigation of excitonic effects by analyzing electron-hole transition density matrices and exciton binding energies as a function of size in these nanoring systems. The transition density matrices allow a global view of electronic coherence during an electronic excitation, and the exciton binding energies give a quantitative measure of electron-hole interaction energies in the nanorings. Based on overall trends in exciton binding energies and their spatial delocalization, I find that excitonic effects play a vital role in understanding the unique photoinduced dynamics in these carbon nanoring systems.

A non-adiabatic theory of Electron Transfer (ET), which improves the standard theory near the inversion point and becomes equivalent to it far from the inversion point, is presented. The complex amplitudes of the electronic wavefunctions at different sites are used as Kramers variables for describing the quantum tunneling of the electron in the deformable potential generated by its environment (nonadiabaticity) which is modeled as a harmonic classical thermal bath. After exact elimination of the bath, the effective electron dynamics is described by a discrete nonlinear Schrödinger equation with norm preserving dissipative terms and a Langevin random force, with a frequency cut-off, due to the thermalized phonons.

This theory reveals the existence of a specially interesting marginal case when the linear and nonlinear coefficients of a two electronic states system are appropriately tuned for forming a Coherent Electron-Phonon Oscillator (CEPO). An electron injected on one of the electronic states of a CEPO generates large amplitude charge oscillations (even at zero temperature) associated with coherent phonon oscillations and electronic level oscillations. This fluctuating electronic level may resonate with a third site which captures the electron so that Ultrafast Electron Transfer (UFET) becomes possible. Numerical results are shown where two weakly interacting sites, a donor and a catalyst, form a CEPO that triggers an UFET to an acceptor. Without a catalytic site, a very large energy barrier prevents any direct ET. This UFET is shown to have many qualitative features similar to those observed in the primary charge separation in photosynthetic reaction centers. We suggest that more generally, CEPO could be a paradigm for understanding many selective chemical reactions involving electron transfer in biosystems.

The electronic states of a singly ionized on-axis double-donor complex (D2+) confined in two identical vertically coupled, axially symmetrical quantum dots in a threading magnetic field are calculated. The solutions of the Schrödinger equation are obtained by a variational separation of variables in the adiabatic limit. Numerical results are shown for bonding and antibonding lowest-lying artificial molecule states corresponding to different quantum dot morphologies, dimensions, separation between them, thicknesses of the wetting layers, and magnetic field strength.

We analyze the energy spectrum of a positively charged exciton confined in a semiconductor heterostructure formed by two vertically coupled, axially symmetrical type II quantum dots located close to each other. The electron in the structure is mainly located inside the dots, while the holes generally move in the exterior region close to the symmetry axis. The solutions of the Schrödinger equation are obtained by a variational separation of variables in the adiabatic limit. Numerical results are shown for bonding and anti-bonding lowest-lying of the trion states corresponding to the different quantum dots morphologies, dimensions, separation between them, thicknesses of the wetting layers, and the magnetic field strength.

Within the linear response theory, a local bond-polarization model based on the displacement–displacement Green’s function and the Born potential including central and non-central interatomic forces is used to investigate the Raman response and the phonon band structure of Ge nanostructures. In particular, a supercell model is employed, in which along the [001] direction empty-column pores and nanowires are constructed preserving the crystalline Ge atomic structure. An advantage of this model is the interconnection between Ge nanocrystals in porous Ge and then, all the phonon states are delocalized. The results of both porous Ge and nanowires show a shift of the highest-energy Raman peak toward lower frequencies with respect to the Raman response of bulk crystalline Ge. This fact could be related to the confinement of phonons and is in good agreement with the experimental data. Finally, a detailed discussion of the dynamical matrix is given in the appendix section.

Multilayer In0.4Ga0.6As/GaAs quantum dot (QD) chain samples are investigated by means of cw and time-resolved photoluminescence (PL) spectroscopy in order to study the peculiarities of interdot coupling in such nanostructures. The temperature dependence of the PL has revealed details of the confinement. Non-thermal carrier distribution through in-chain, interdot wave function coupling is found. The peculiar dependences of the PL decay time on the excitation and detection energies are ascribed to the electronic interdot coupling and the long-range coupling through the radiation field. It is shown that the dependence of the PL decay time on the excitation wavelength is a result of the superradiance effect.

Multilayer In0.4Ga0.6As/GaAs quantum dot (QD) chain samples are investigated by means of cw and time-resolved photoluminescence (PL) spectroscopy in order to study the peculiarities of interdot coupling in such nanostructures. The temperature dependence of the PL has revealed details of the confinement. Non-thermal carrier distribution through in-chain, interdot wave function coupling is found. The peculiar dependences of the PL decay time on the excitation and detection energies are ascribed to the electronic interdot coupling and the long-range coupling through the radiation field. It is shown that the dependence of the PL decay time on the excitation wavelength is a result of the superradiance effect.

Peptide amphiphiles are a class of molecules that combine the structural features of amphiphilic surfactants with the functions of bioactive peptides and are known to assemble into a variety of nanostructures. A specific type of peptide amphiphiles are known to self-assemble into one-dimensional (1D) nanostructures under physiological conditions, predominantly nanofibers with a cylindrical geometry. The resultant nanostructures could be highly bioactive and are of great interest in many biomedical applications, including tissue engineering, regenerative medicine and drug delivery. In this context, we highlight our strategies for using molecular self-assembly as a toolbox to produce peptide amphiphile nanostructures and materials and efforts to translate this technology into applications as therapeutics. We also review our recent progress in using these materials for treating spinal cord injury, inducing angiogenesis, and for hard tissue regeneration and replacement.

The effect of electrostatic shielding of the polarization fields in nanostructures at high carrier densities is studied. A simplified analytical model, employing screened, exponentially decaying polarization potentials, localized at the edges of a QW, is introduced for the ES-shielded quantum confined Stark effect (QCSE). Wave function trapping within the Debye-length edge-potential causes blue shifting of energy levels and gradual elimination of the QCSE red-shifting with increasing carrier density. The increase in the e−h wave function overlap and the decrease of the radiative emission time are, however, delayed until the “edge-localization” energy exceeds the peak-voltage of the charged layer. Then the wave function center shifts to the middle of the QW, and behavior becomes similar to that of an unbiased square QW. Our theoretical estimates of the radiative emission time show a complete elimination of the QCSE at doping densities ≥1020 cm−3, in quantitative agreement with experimental measurements.

The effect of electrostatic shielding of the polarization fields in nanostructures at high carrier densities is studied. A simplified analytical model, employing screened, exponentially decaying polarization potentials, localized at the edges of a QW, is introduced for the ES-shielded quantum confined Stark effect (QCSE). Wave function trapping within the Debye-length edge-potential causes blue shifting of energy levels and gradual elimination of the QCSE red-shifting with increasing carrier density. The increase in the e−h wave function overlap and the decrease of the radiative emission time are, however, delayed until the “edge-localization” energy exceeds the peak-voltage of the charged layer. Then the wave function center shifts to the middle of the QW, and behavior becomes similar to that of an unbiased square QW. Our theoretical estimates of the radiative emission time show a complete elimination of the QCSE at doping densities ≥1020 cm−3, in quantitative agreement with experimental measurements.

The esteemed physicist Erwin Schrödinger, whose name is associated with the most notorious equation of quantum mechanics, also wrote a brief essay entitled ‘What is Life?’, asking: ‘How can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?’ The 60+ years following this seminal work have seen enormous developments in our understanding of biology on the molecular scale, with physics playing a key role in solving many central problems through the development and application of new physical science techniques, biophysical analysis and rigorous intellectual insight. The early days of single-molecule biophysics research was centred around molecular motors and biopolymers, largely divorced from a real physiological context. The new generation of single-molecule bioscience investigations has much greater scope, involving robust methods for understanding molecular-level details of the most fundamental biological processes in far more realistic, and technically challenging, physiological contexts, emerging into a new field of ‘single-molecule cellular biophysics’. Here, I outline how this new field has evolved, discuss the key active areas of current research and speculate on where this may all lead in the near future.