通过光场调控HgTe/CdTe量子井拓扑性质的理论研究

A new material called the topological insulator (TI) has attracted our attention, of which the bulk state is gapped while the edge state (surface state) is gapless conducting and will be topologically protected. Especially the two-dimensional topological insulator, such as graphene, HgTe/CdTe quantum well and Bi2Se3 thin film, where the existence of such quantum spin Hall state has been predicted theoretically and supported by a few experiments. However, in the above materials, the edge state is due to the subtle band inversion which comes from changing the structural parameter of the system, so it may be not easy for the real manipulating. Now some research are trying to use the optically engineering stragegy to change the topological property of materials, to realize manual modulation. It is known to us that optical field is a powerful method to change material properties. As HgTe/CdTe quantum well is regarded as the most probable material for real application, in this project, we will investigate the response of the system to the optical field. We will use the Floquet theorem which is closely related to the time periodicity to study the quasi-spectrum of the system. By changing the parameters of the optical field, including the period and the amplitude to realize the possibility of the phase transition, from the trivial insulator phase to the nontrivial insulator phase. As the electron occupation is non-equilibrium, we will try to understand the transport property and ZB phenomenon (a rapid oscillation of electron) under optical radiation. Our studies will be of great significances to its real application of the material.

一类新的被称为拓扑绝缘体的物质引起了人们的兴趣。特别是二维拓扑绝缘体，比如石墨烯，HgTe/CdTe量子井及Bi2Se3薄膜中量子自旋霍尔态的存在已在理论上被预言且为一些实验所证明。但在上述材料中，无能隙的边缘态均来源于系统结构参数的改变所引发的很微妙的能带反演，不易于实际的操纵。有一些研究试图采用光操作的方法引发材料的拓扑相，以达到人工调控的目的。已知光场是一种改变材料性质的强有力的方法。HgTe/CdTe量子井系统作为可能最具备实际应用价值的材料，在本项目中，我们拟考察该系统对光场的响应。我们将利用同时间周期性有关的Floquet定理，来考察系统的准能谱。通过调节光场的参数，包括周期及振幅来实现系统的拓扑相变的可能性，从平庸绝缘体相到非平庸绝缘体相。由于在光操作下电子的占据是非平衡的，研究该系统在此情况下的输运性质及相关的ZB现象（一种电子的快速振荡现象）等对于实际应用具有重要的意义。

拓扑绝缘体近些年来引起了人们的极大兴趣，其特征是材料的边缘出现一种无能隙的导电态。本课题中, 我们试图在能呈现量子自旋霍尔效应的HgTe/CdTe 量子井材料中，通过外光场方法调控其性质。根据我们研究的进展，并结合国内外的最新研究动态，得到的研究成果如下：. 1. 我们采用一超短的激光脉冲场，调查用以描述HgTe/CdTe量子井的Bernevig-Hughes-Zhang模型中的电子的快速振荡现象 (Zitterbewegung)。为了得到一稳定的图象，我们在二维电子气中加上垂直磁场，把电子固定在朗道能级上。调节参数，我们研究了系统在量子自旋霍尔区的的ZB运动及电磁辐射。该研究论文题目为<Revivals of Zitterbewegung in Bernevig-Hughes-Zhang model in the quantum spin Hall regime with the laser pulse>，发表在 Chinese Physics B 期刊的2014年第3期。. 2. 我们研究了Haldane模型在垂直磁场下的量子霍尔效应。Haldane模型能够实现反常的量子霍尔效应而没有朗道能级，并且是能实现量子自旋霍尔效应的Kane-Mele模型的原型。我们选择单位元胞中的磁通同晶格结构相匹配。研究论文题目为 <Quantum Hall Effect of Haldane Model under magnetic field>，已发表在Europhysical Letters期刊的2014年第1期。. 除了这些之外，我们还有一些问题正在考虑。比如进一步地研究高阶光子的吸收和发射现象对拓扑相的调控并借助Bragg光谱仪的方法从理论上给出探测拓扑相的建议等，将作为后绪的研究逐渐开展。

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