Numerical study of dephasing in disordered electron systems

在本项目中，我们研究了复杂量子干涉在无序电子系统中起重要作用的量子输运中的数值失相和相关主题。在低维系统，如二维电子系统（2DES）中，这种干涉尤为重要。由于与外部自由度（如热浴）的耦合而导致的干扰击穿是消相的根源。在数值计算中，将附加导线耦合到储层上是一种考虑失相的方法。因此，在本项目中，我们研究了以下内容：1)3端几何结构下的电子输运研究：考虑到失相，需要研究两个以上端的系统。我们开发了一个程序来研究这个问题，并计算了输运系数。作为副产物，我们分析了自旋轨道相互作用下自旋极化电流的产生。（论文2、4）自旋在量子输运现象中的作用研究：研究了自旋自由度在量子输运中的作用。特别令人感兴趣的是低维系统中具有强自旋轨道散射的系统。我们模拟了电导波动（论文10），2DES中的安德森跃迁（论文8和15）和二维以下的安德森跃迁（论文1）。通过假设一个时变势，研究了2DES中存在自旋轨道散射时的消相。3)随机相位模型的研究：为了研究相位在量子输运中的重要性，我们研究了随机相位模型（论文6和11）。4)量子网络模型研究：研究了用于研究量子输运现象的简化模型——网络模型（论文5）。由于模型很简单，我们可以在一个样本上附加许多线索。5)量子霍尔效应中边缘态的研究：已知量子霍尔边缘态具有超长的消相时间。我们已经详细研究了无序存在下的这些状态（论文3和7）。少

In this project, we have studied numerically dephasing and related topics in quantum transport in disordered electron systems where complex quantum interference plays an important role. The interference is especially important in low dimensional systems such as the 2 dimensional electron system (2DES). The breakdown of the interference due to the coupling to external degrees of freedom such as a heat bath is the origin of dephasing. Attaching extra lead(s) coupled to reservoir(s) is a way to take into account the dephasing in numerical calculations. In this project, therefore, we have studied the following :1) Study of electron transport in the 3 terminal geometry : to take into account the dephasing, study of systems with more than two terminals is needed. We have developed a program to study this issue, and have calculated the transport coefficients. As a byproduct, we have analyzed the generation of spin polarized current in the presence of spin-orbit interaction. (Papers 2 and 4.)2 … More ) Study of the role of spin in quantum transport phenomena : the role of the spin degree of freedom in quantum transport has been studied. Of particular interest is the system with strong spin-orbit scattering in low dimensional systems. We have simulated conductance fluctuations (paper 10), the Anderson transition in 2DES (papers 8 and 15) and the Anderson transition below 2 dimensions (paper 1). Dephasing in the presence of spin-orbit scattering has been studied in the 2DES by assuming a time-dependent potential (paper 14).3) Study of random phase model : to investigate the importance of phase in quantum transport, we have studied the random phase model (papers 6 and 11).4) Study of quantum network model : the network model that is a simplified model to study the quantum transport phenomena has been studied (paper 5). Since the model is simple, we are able to attach many leads to a sample.5) Study of edge states in the quantum Hall effect : the quantum Hall edge states are know to have extraordinary long dephasing time. We have studied these states in the presence of disorder in detail (papers 3 and 7). Less