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

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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