非微扰场论方法对多层石墨烯体系和Weyl半金属体系的能带结构研究

项目名称： 非微扰场论方法对多层石墨烯体系和Weyl半金属体系的能带结构研究

项目编号： No.11504276

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 贾俊基

作者单位： 武汉大学

项目金额： 20万元

中文摘要： 石墨烯和Weyl半金属体系在电子工程方面有巨大的应用前景，它们的低能能带结构有相似性，并且都受相互作用的深刻影响。然而传统的紧束缚模型和第一性原理的计算无法完全包含一些由虚粒子过程引起的动力学效应。本项目拟采用非微扰场论中的Schwinger-Dyson (SD) 方程这一重要手段，来研究多层石墨烯和Weyl半金属体系中的准粒子间有极化的库仑相互作用、其他激发元诱导的多准粒子间相互作用、以及准粒子与外场的相互作用的动力学。项目中将计算这些相互作用、多层石墨烯层数等因素对极化函数的影响，并求解SD方程来获得体系的各广义能带隙、及其对应的低能能带结构和相能量，给出体系在外场空间的基态、相界和相图。同时项目还将从极化函数出发研究相互作用对光电导率的影响并与实验比较。本项目的实施将揭示体系内的非微扰动力学因素对体系能带的一般性作用，为多层石墨烯和潜在Weyl半金属体系的电子学工程应用提供理论指导。

中文关键词： 非微扰动力学；多层石墨烯；Weyl半金属；能带结构；极化函数

英文摘要： Graphene and Weyl semimetal are two systems with great electric engineering potentials. They have similarities in their low-energy band structures, which are also critically influenced by their corresponding quasiparticle interactions. However, traditional tight-binding theories and first principle calculations are limited when virtual particle dynamics are need to take into account. In this project we propose using a non-perturbative field theory approach, the Schwinger-Dyson equation, to study the dynamics of the polarized Coulomb interaction, interactions induced by other excitations and interactions with external fields in these two systems. The effects of these interaction and number of layers of multilayer graphene etc on the polarization function will be calculated. The generalized band gaps, low-energy band structure and various corresponding phases will be obtained by solving the SD equations. A phase diagram with ground states and phase boundaries in the external field space will be produced. In addition, starting from the above obtained polarization function, optical conductivities of these systems will be investigated and compared with experiments. The program will reveal the general effects of non-perturbative dynamics on the energy bands of these systems, and provide a guide for the future electrical engineering of the systems.

英文关键词： Non-perturbative dynamics;Multilayer graphene;Weyl semimetal;Band Structure;Polarization function