Theoretical Study of Two Dimensional Electronic States in Random Magnetic Fields and Their Transport

本研究的目的是利用我们迄今为止开发的各种数值技术，如强迫振子法、有限尺寸多重分形分析和均匀磁场中的传递矩阵技术，阐明二维电子在随机磁场中的量子态及其输运性质。为此，本学年我们主要研究了具有长程相关的随机磁场作用下连续系统中二维电子的输运性质。为了在随机磁场中实验实现二维电子系统，一种可能的方法是在二维电子系统表面附近随机配置铁磁性小粒子。为了从理论上研究这类系统的量子输运，我们用递归格林函数法计算了单磁粒子在非均匀磁场作用下系统的电导。对于磁场，我们在电子表面有一条闭合的线，在这条线上B_z=0。电子绕着这条线（蛇形轨道）迂回。由于磁通量穿过这个环，我们可以预料到阿哈罗诺夫-玻姆效应。用递归格林函数法计算的电导显示了这种效应。考虑到电子自旋，发现了由于围绕电子绝热旋转的磁场而产生的贝里相效应。此外，我们还发现，随着磁场强度的增加，阿哈罗诺夫-玻姆振荡周期缩短。这是因为电子的入射能量根据电子的自旋被塞曼能量所转移。在本研究中，我们还研究了临界点处异常局域态的统计性质，以阐明随机磁场波动的影响。特别地，我们对属于辛类的二维临界波函数进行了初步计算。结果表明，即使在有限概率的无限系统中，临界点处也存在异常局域状态。这意味着标度理论或重整化群论只能应用于典型状态。少

The aim of this research is to clarify quantum states of two-dimensional electrons in a random magnetic field and their transport properties by using various numerical techniques which we have developed so far, such as the forced oscillator method, the finite-size multifractal analysis, and the transfer matrix technique in in homogeneous magnetic fields. To this end, we have mainly studied transport properties of two-dimensional electrons in continuous systems subject to random magnetic fields with long range correlations in this year. For realizing a two-dimensional electron system in a random magnetic field experimentally, a possible method is to configure randomly ferromagnetic small particles near the surface of the two-dimensional electron system. In order to study theoretically quantum transport of such a system, we have calculated conductance of a system subject to an in homogeneous magnetic field made by a single magnetic particle by the recursive Green's function method. For t … More his magnetic field, we have a closed line on the electron surface at which B_z=0. Electrons meander around this line (snake orbit). We can expect the Aharonov-Borm effect due to magnetic fluxes threading this loop. The conductance calculated by the recursive Green's function method shows this type of effects. Considering electron spins, the effect of the Berry phase due to a magnetic field rotating adiabatically around the electron has been found. Furthermore, we discovered that the period of Aharonov-Borm oscillation becomes shortened as increasing the strength of the magnetic field. This is because the incident energy of the electron is shifted by the Zeeman energy depending on the electron spin. In this study, we also examined statistical properties of anomalously localized states at the critical point to clarify the effect of fluctuations of random magnetic fields. In particular, we performed preliminary calculations for two-dimensional critical wave functions belonging to the symplectic class. As a result, we found that anomalously localized states at the critical point exist even in infinite systems with a finite probability. This implies that a scaling theory or renormalization group theory can be applied only to typical states. Less