טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKira Anat
SubjectHoles in interacting Nano-scale systems: Models, Algorithms,
and Dynamics
DepartmentDepartment of Applied Mathematics
Supervisors Professor Uri Peskin
Professor Ofir Alon


Abstract

Hole transport is an important transport mechanism in solid state based electronic devices. In recent years charge transport through biomolecules (such as DNA) is also attributed to hole dynamics and/or kinetics. The presented study deals with fundamental aspects of quantum hole dynamics in Nano-scale systems. Using reduced models, the many-body dynamics of interacting electrons in the presence of a few (one or two) holes is followed and the validity of the interpretation of the many-body dynamics in terms of holes dynamics is investigated. In this work, specific models are described, and a new computational algorithm is developed, aiming at efficiently solving the many-body Schrödinger equation for these models. Already for the reduced models used in this study, an efficient algorithm is required owing to the Coulomb integrals terms that account for the electron-electron interactions. The number of Coulomb integrals to be calculated for a system characterized by N particles scales polynomial in N (typically ~N4), it is therefore crucial to reduce the computational complexity. By exploiting spatial symmetries in order to calculate the many-electron dynamics of extended systems, a particular algorithm was developed and implemented in this work for the reflection symmetry.    

The algorithm was tested and verified for several geometries of lattices. The algorithm was applied to linear chains in the study of holes dynamics. The results demonstrate intriguing aspects of holes dynamics in confined and extended systems, such as transition from holes repulsion to holes attraction induced by changes in the systems size, or in the electron-electron interaction parameter. Conclusions with respect to the common interpretation of holes in terms of effective positive charges are drawn. Numerical analysis of the system allows one to find the interaction strength parameters for which transitions between different phenotypes of holes repulsion/attraction should be observed. For this purpose, a theoretical tool was developed based on the identification of energy level crossings (or avoided crossings) between different eigenstates, associated with hole-localization in different regions of space. The ability to control holes dynamics by changing the effective interaction strength (via experimentally controlled parameters, such as confining potentials, particles densities, dielectric constants) should assist in future developments in the field of hole-dynamics based electronic devices.