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

随机磁场中二维电子态及其输运的理论研究

• 批准号: 14540317
• 负责人: YAKUBO Kousuke
• 金额: $ 2.18万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540317/
• 关键词: two-dimensional electron; random magnetic field; scaling theory; forced oscillator method; multifractal analysis; transfer matrix method; metal-insulator transition

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

本研究的目的是利用我们迄今为止开发的各种数值技术，例如受迫振荡法、有限尺寸多重分形分析、为此，我们今年主要研究长程相关随机磁场下二维电子的传输特性。在随机磁场中在实验上，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，我们计算了受到均匀磁场影响的系统的电导。通过递归格林函数方法，我们在电子表面上有一条闭合线，其中 B_z=0 。可以预期由于穿过该环路的磁通量而产生的阿哈罗诺夫-博姆效应。通过递归格林函数方法计算的电导显示了这种类型的效应，考虑到电子自旋，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-鲍姆振荡的周期会缩短，这是因为电子的入射能量根据塞曼能量而移动。在这项研究中，我们还研究了临界点的异常局域态的统计特性，以阐明随机磁场涨落的影响，特别是，我们对属于辛类的二维临界波函数进行了初步计算。结果，我们发现即使在具有有限概率的无限系统中也存在临界点的异常局部状态，这意味着标度理论或重整化群理论只能应用于典型状态。

项目成果

Correlation exponent and anomalously localized states at the critical point of the Anderson transition

安德森转变临界点的相关指数和异常局域态

• 发表时间: 2004
• 期刊: Journal of the Physical Society of Japan 73・8
• 作者: A.Takeyama;S.Tadano;H.Shima;H.Shima;H.Shima;H.Shima;H.Shima;H.Obuse;H.Shima;H.Obuse;H.Shima;H.Obuse
• 通讯作者: H.Obuse

Spatial structures of anomalously localized states in tail regions at the Anderson transition

安德森转变尾部区域异常局域态的空间结构

• 期刊: Journal of the Physical Society of Japan Supplement (発表予定)
• 作者: 桑島豊;重原孝臣;H.Shima;T.Nakayama;H.Obuse
• 通讯作者: H.Obuse

K.Yakubo: "AC current due to photon-assisted tunneling in driven mesoscopic systems"Physica E. 18. 97-98 (2003)

K.Yakubo：“驱动介观系统中光子辅助隧道效应产生的交流电流”Physica E. 18. 97-98 (2003)

H.Obuse: "Non-universal exponents at the Anderson transition"Physica E. 18. 276-277 (2003)

H.Obuse：“安德森转变时的非通用指数”Physica E. 18. 276-277 (2003)

Low-temperature anomalies of crystalline Ge with 0-impurities

0-杂质晶体Ge的低温异常

• 发表时间: 2004
• 期刊: Journal of the Physical Society of Japan 73・9
• 作者: A.Takeyama;S.Tadano;H.Shima;H.Shima;H.Shima;H.Shima;H.Shima;H.Obuse;H.Shima;H.Obuse;H.Shima;H.Obuse;H.Shima
• 通讯作者: H.Shima