Theory of Electron Dynamics of One-dimensional Lattice in an Electric Field

• Main Authors: Cong-Huei Pan, 潘聰輝
• Other Authors: Fangyeong Guo
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/kwu6hp

碩士 === 國立彰化師範大學 === 物理學系 === 102 === Abstract The first part of this thesis concerns with the electron dynamics in single-band lattice under a constant electric field. The Bloch oscillation (BO) was important and usually demomstrated, by using the semiclassical approach, in infinite periodic lattices for electrons initially prepared with delocalized wave packet in real space. However, the fully quantum mechanical calculations predict “breathing mode” oscillation due to localized initial wave packet prepared. Thus, we numerically study the oscillation dynamics of these two modes in finite-length lattices in which the ends of the lattice may strongly influence the wave packet when it reaches the ends. We explicitly take the undimerized polyacetylene as a lattice model of the single band and use the tight-binding approximation to study the “oscillatory” and “breathing” oscillations. Our results show that except for chain length long enough, the wave packets will be reflected at the ends, resulting in the dephasing of the oscillations. The second part of this thesis deals with the Bloch-Zener (BZ) oscillations that are recently the subject interested by researchers, since it may have useful applications as matter wave beam splitter and Mach-Zehnder interferometer. The BZ oscillations can be described in two-band lattice chain when the applied electric field is strong enough and tunneling through the band gap occurs. In our study, we take the (dimerized) trans-polyacetylene as a lattice model and again use the tight-binding approximation to calculate the BZ oscillations. We show that the period of a complete BZ oscillation is indeed determined by the ratio of two time scales as described by Breid et. al. We also propose a novel method to design a BZ oscillation with a specific period.