An introduction into the area of inverse problems for the Schrödinger operators on metric graphs is given. The case of metric finite trees is treated in detail with the focus on matching conditions. For graphs with loops we show that for almost all matching conditions the potential on the loop is not determined uniquely by the Titchmarsh-Weyl function. The class of all admissible potentials is characterized.
Quantum graphs having one cycle are considered. It is shown that if the cycle contains at least three vertices, then the potential on the graph can be uniquely reconstructed from the corresponding Titchmarsh-Weyl function (Dirichlet-to-Neumann map) associated with graph's boundary, provided certain non-resonant conditions are satisfied.
We discuss lower and upper estimates for the spectral gap of the Laplace operator on a finite compact connected metric graph. It is shown that the best lower estimate is given by the spectral gap for the interval with the same total length as the original graph. An explicit upper estimate is given by generalizing Cheeger's approach developed originally for Riemannian manifolds.
The electron motion in a strong perpendicular magnetic field close to the impenetrable obstacle is considered by the semi-classical and quantum points of view. We investigated an influence of a shape of the forbidden region to the formation of the plateaux in the one electron energy spectrum and transmissions between dot and antidot states. In the semi-classical regime electrons can be treated as charged particles with well-defined trajectories pinned to the potential wall. This approach, combined with singular equation technique in quantum calculations, has given us a possibility to investigate stripe-shaped and bow-shaped antidots with sharp edges and to find a way for controlled manipulation of the parameters of systems with an effort to get desired physical properties.
We present a submicron magnetic field sensor with voltage-tunable magnetic field sensitivity. The device, based on magnetic tunnel junction, exhibits high tunnelling magnetoresistance ratio of up to 90%. Perpendicular magnetic anisotropy of thin ferromagnetic sensing layer in combination with an in-plane magnetized reference layer is used to obtain linear change in the sensor resistance in response to the in-plane magnetic field. The perpendicular anisotropy is further controlled by the bias voltage and, thus, the sensitivity of the sensor is changed. In addition, we evaluate the sensor selectivity for the magnetic field direction and present an influence of the temperature on the anisotropy.
Molecular electronics aims for scaling down electronics to its ultimate limits by choosing single molecules as the building blocks of active devices. The advantages of this approach are the high reproducibility of molecular synthesis on the nanometer scale, the ability of molecules to form large structures by self-assembly, and the huge versatility of molecular complexes. On the other hand, conventional contacting techniques cannot form contacts on the single molecule scale and imaging techniques nowadays cannot provide a detailed image of such junctions. Therefore, the fabrication has to rely to some degree on self-organization of the constituents. The proof that a molecule has been contacted successfully can only be given by indirect methods, for example by measuring the current transport through the junctions. Here we give an overview of various techniques that were used successfully to contact molecules and to characterize them electrically. The techniques range from methods to contact single molecules to such which can be used to characterize ensembles of molecules. Especially, the comparison between such different techniques shows that a single measurement is always prone to artefacts originating from the unknown microscopic details of the junctions. It is therefore necessary to perform a statistically relevant number of measurements in order to resolve molecular properties. Various properties of the molecules can be studied. Special examples are the influence of conformational changes of the molecules, differences between various coupling endgroups of the molecules and effects of light-irradiation onto the molecular junctions.
Calculations of the current-voltage characteristics of the core-multishell nanowires for different radii of the core and various thicknesses of the shells are presented. A role of the conducting core and shells in the coherent transport under the influence of the gate voltage is discussed.
The influence of the applied gate voltage on the coherent propagation of the conduction electrons through the InGaAs/InP core-multishell nanowires with the surrounding gate is considered. The solution of the three-dimensional Schrödinger equation within the effective mass approximation is found using the adiabatic method. The electrostatic potential distribution generated by the all-around gate is determined from the self-consistent procedure applied to the Schrödinger-Poisson problem. The Landauer-Büttiker formalism and quantum transmission boundary method are applied to calculate the transport properties of the considered nanosystem.
In this research we have studied physisorption of hydrogen molecules on armchair (3,3) boron-nitride nanotube using density functional methods. Optical properties of the boron-nitride nanotube, with and without adsorbed H₂ molecules, were investigated under parallel and perpendicular polarized electric fields. The results indicate that the nanotube optical gap slightly changes due to H₂ physisorption and increasing H₂ physisorption suppresses the boron-nitride nanotube optical spectrum. Also, the nanotube gets more transparent as the H₂ concentration increases, in other words boron-nitride nanotube dielectric function decreases. Anisotropic dielectric function is another result which is determined by random phase approximation method.
We witness a new revolution in electronic industry - a new generation of integrated circuits uses as a gate isolator HfO_{2}. This high-k oxide was deposited by the atomic layer deposition technique. The atomic layer deposition, due to a high conformality of deposited films and low growth temperature, has a large potential to be widely used not only for the deposition of high-k oxides, but also of materials used in solar cells and semiconductor/organic material hybrid structures. This opens possibilities of construction of novel memory devices with 3D architecture, photovoltaic panels of the third generation and stable in time organic light emitting diodes as discussed in this work.
The classical, electrodynamic definition of the ampere is incoherent with quantum electrodynamics. The problem, although insignificant at the macroscopic scale, manifests clearly at the nanostructure level, where the consistently quantum approach is necessary. In this paper, we consider the Casimir effect to quantify inconsistencies that could have resulted if electric metrology of microstructures and nanostructures (including graphene) had been based on classical electrodynamics and the current SI definition of the ampere. The issue is discussed in the context of the New SI program, where the base electric unit is to be redefined by fixing the numerical value of the elementary charge. The conclusion supports the case for a prompt redefinition of the base electric unit, which will make the electric metrology in general, and the electric metrology of nanostructures in particular, coherent with the international system of units.
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.