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发展的各种数值方法，如受迫振子方法、有限尺寸多重分形分析和均匀磁场中的转移矩阵技术，阐明二维电子在随机磁场中的量子态及其输运性质。为此，我们主要研究了连续系统中的二维电子输运性质的随机磁场与长程关联在今年。为了在实验上实现随机磁场中的二维电子系统，一种可能的方法是在二维电子系统的表面附近随机配置铁磁小粒子。为了从理论上研究这种系统的量子输运，我们用递归绿色函数方法计算了一个系统在单个磁性粒子产生的非均匀磁场中的电导。对于t ...更多信息 在磁场中，我们在电子表面有一条闭合线，在这条线上B_z=0。电子绕着这条线（蛇形轨道）蜿蜒。我们可以预期Aharonov-Borm效应由于磁通量穿过这个环。由递归绿色函数方法计算的电导显示了这种类型的效果。在考虑电子自旋的情况下，我们发现了磁场绕电子作自旋旋转时的Berry相位效应，并发现Aharonov-Borm振荡的周期随磁场强度的增大而缩短。这是因为电子的入射能量根据电子自旋而偏移塞曼能量。在这项研究中，我们还研究了在临界点的随机局域态的统计特性，以澄清随机磁场的波动的影响。特别是，我们进行了初步计算属于辛类的二维临界波函数。结果发现，即使在无限大的系统中，临界点处也存在有限概率的非线性局域态。这意味着标度理论或重整化群理论只能应用于典型态。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