Plasmonic Enhancement of Solar Cells Efficiency: Material Dependence in Semiconductor Metallic Surface Nano-Modification

Recent experimental data shown a promising direction in employing nano-plasmonics for increasing efficiencies of the solar cells. The effect is due to metallic nanoparticles’ plasmons mediating energy transfer from the incoming e-m wave to the semiconductor in a regime violating limits in energy transitions imposed by the momentum conservation, due to translational invariance departure in surface nano-modified system. The chapter presents analysis of material dependence of near-field coupling to band electrons of surface plazmons in metallic nanoparticles deposited on the top of semiconductor substrate in nano-modified solar cells. Various materials for metal and substrate are comparatively studied upon the quantum Fermi Golden Rule approach in theoretical quantitative modeling of the plasmon-electron coupling that enhances ordinary PV effect. The material dependence of the plasmon-mediated efficiency growth in two types of solar cells, multi-crystalline Si and CIGS (copper-indium-gallium-diselenide), modified by various surface-deposited metallic nanoparticles is additionally illustrated by the experimental data

Bilayer Graphene as the Material for Study of the Unconventional Fractional Quantum Hall Effect

Fractional quantum Hall effect (FQHE) discovered experimentally in 1982 is still mysterious, not fully understood phenomenon. It fundaments are linked with a nontrivial topological effects in 2D space going beyond the standard description of FQHE with local quantum mechanics. The study of integer and fractional QHE in graphene might be helpful in resolution of this fundamental problem in many body quantum physics. FQHE has been observed both in monolayer and bilayer graphene with an exceptional accuracy due to advances in experimental techniques and purity of graphene samples. Recent experimental observations of FQHE in the bilayer graphene reveal different FQHE behavior than in the monolayer samples or in conventional semiconductor 2D materials. This unexpected phenomena related to Hall physics in the bilayer systems allows to better understand more than 30 years old puzzle of FQHE. In the chapter we will summarize the recent and controversial experimental observations of FQHE in bilayer graphene and describe the topology foundations which may explain the oddness of correlated multiparticle states in the bilayer system. These topological arguments shed also a new light on understanding of heuristic CF concept for FQHE and deeper the topological sense of the famous Laughlin function describing this strongly correlated state

Forbidden trajectories for path integrals

The problem of the availability of trajectories for the Feynman path integral is considered. Forbidden trajectories for single particle integrals are featured in the case of quantum tunneling across barriers. In the case of multiparticle systems of indistinguishable identical particles, some limits for the availability of cyclotron braid trajectories are demonstrated, which leads to the explanation of statistics and correlation in quantum Hall systems of interacting 2D electrons. The homotopy-type restrictions for trajectories close to general-relativity singularities are discussed with indication of quantum properties of black holes manifesting themselves at quasar luminosity or at neutron star merger collapses. The related supplementation to conventional models of accretion disk luminosity in the close vicinity of the event horizon of a super massive black hole is proposed and compared with observations

Application of path-integral quantization to indistinguishable particle systems topologically confined by a magnetic field

We demonstrate an original development of path-integral quantization in the case of a multiply connected configuration space of indistinguishable charged particles on a 2D manifold and exposed to a strong perpendicular magnetic field. The system occurs to be exceptionally homotopy-rich and the structure of the homotopy essentially depends on the magnetic field strength resulting in multi loop trajectories at specific conditions. We have proved, by a generalization of the Bohr-Sommerfeld quantization rule, that the size of a magnetic field flux quantum grows for multi loop orbits like $(2k+1)\frac{h}{c}$ with the number of loops $k$. Utilizing this property for electrons on the 2D substrate jellium we have derived upon the path integration a complete FQHE hierarchy in excellent consistence with experiments. The path-integral has been next developed to a sum over configurations, displaying various patterns of trajectory homotopies (topological configurations), which in the nonstationary case of quantum kinetics reproduces some unclear formerly details in the longitudinal resistivity observed in experiments