Properties of excited state of polaron in quantum disk in finite depth parabolic potential well

Abstract

Studies of single quantum state measurement and the relevant physics are very important for the fields of quantum information and quantum coupution. In recent years, quantum dots as information carrier have become a hotpoint of research. The study on quantum dot properties has atracted a lot of attetion and made a series of progress.#br#In this paper, we formulate a theoretical method that can be used to investigate polaron properties in low-dimensional structures in finite depth potential well. We assume that an electron in a quantum disk which is in other medium is in parabolic potential field, but the effect of the medium on the electron in quantum disk is equivalent to a potential barrier with height V1 and width d. By expanding the finite height potential barrier as plane waves and Lee-Low-Pines unitary transformation for Hamiltonian, as well as variation for expectation value of Hamiltonian where trial wave functions are obtained by solving the energy eigen-value equation, the ground state energy, the first excited state energy, and excitation energy of polaron are drived.#br#Numerical calculation by using polaron unit, numerical results indicate that the first excited state energy and excitation energy of polaron increase with increasing the width or height of the potential barrier, because the probability of electron penetrating potential barrier will decrease as the width or height of potential barrier increases, so that electronic energy, the first excited state energy and excitation energy of polaron all increase. Numerical results also show that energies mentioned earlier decrease with increasing radius of quantum disk, which illustrates that the quantum disk has obvious quantum size effect.#br#It is also found from numerical results that the first excited state energy of polaron decreases with increasing effective confine length, it falls quickly when effective confine length is less than 0.3 and is a little change when effective confine length is more than 0.3. The longer the effective confine length, the more weakly the electron is bounded and the smaller the potential energy is, so that the first excited state energy of polaron decreases. Oppositely, the excitation energy of polaron increases with increasing effective confine length, because the first excited state energy decreases more slowly than the ground state energy.