Parabolic Quantum Dot In Weak Coupling Polaron Ground State Energy

Polaron is the quasi particle of the electron-longitude optical phonon coupling system, which is an important subject in the condensed matter physics. The study on this subject plays an important role in explaining the phenomena of light transition and transport in the ionic crystal and polar semiconductor. In recent years, there has been a great deal of interest in the investigation of polarons in the quantum dots, and some useful results are obtained.Some basic concepts of polaron and quantum dot and investigation methods are expounded in the first place. The thesis concerns mainly about the ground state energy of weak coupling polaron in a parabolic quantum dot. An item which stands for two-phonon correlation is introduced into the ground-state vector. Under the Lee-Low-Pines canonical transformation and the combination of linearoperators of the electron, the correction of phonon correlation to the ground-state energy of this system is obtained. We find that the energy E_o resulted includingthe phonon correlation is lower than E'_o obtained without correlation. Thispaper focuses on the following aspects:1. We calculate the ground-state energy E_o of a polaron confined in aparabolic quantum dot. The relation between E₀ and effective confinement length l0 and coupling constant α is discussed. The calculation shows that E_o decreases as l₀ and a increase;when l₀ > 1.0 E_o nearly remains steady;when a varies from 0 to 2.5, the difference between E_o and E'_ois negligible.2. In the presence of two-phonon correlation, we consider the effect of anexternal magnetic field B on a weak coupling polaron confined in the hydrogenized impurity. It indicates that E_o increases as B increases, and falls asl₀, α and coulomb bound potential β increase.