Ohtsuki Tomi

We review the new method of obtaining the phase diagrams of quantum phase transitions in random electron systems. The method is based on the image recognition using the multilayer convolutional neural network, deep learning. Applications to the Anderson transition as well as quantum percolations are demonstrated.

ニューラルネットワークを使った物性物理学の現状を解説した。

Self-organized GaN nanocolumns are one-dimensional columnar nano-crystals, which have about 100nm in diameter and 1μm in height. Nanocolumns have high optical properties due to almost dislocation-free nature. And also, strong localization of light is expected in nanocolumns due to it's randomly distribution. In this study, we observed the random laser action in self-organized GaN nanocolumns for the first time. Polarization behavior, sample dependence, and theoretical approach using 2D-FDTD method will be also presented.

The quantum phase diagram of disordered quantum wires in a strong magnetic field is reviewed. For uncorrelated disorder potential the 2-terminal conductance, as calculated with the numerical transfer matrix method, shows zero temperature discontinuous transitions between exactly integer plateau values and zero. This is explained by the dimensional crossover of the bulk localisation length, which drives a transition from delocalised to localised edge states. In the thermodynamic limit, fixing the aspect ratio of the wire, there is a transition from the one dimensional chiral metal of extended edge states to localisation along the wire. In the vicinity of this chiral metal insulator transition (CMIT), states are identified which are superpositions of edge states with opposite chirality. The bulk contribution of such states is found to decrease with increasing wire width. Based on exact diagonalisation results for the eigenstates and their participation ratios, we conclude that these states are characteristic for the CMIT, and have the appearance of nonchiral edges states. Thereby these states are distinguishable from other states in the quantum Hall wire, namely, extended edge states, two-dimensionally (2D) localized, quasi 1D localized, and 2D critical states. In the presence of spatially correlated random potential we find with the numerical transfermatrix method that the potential correlation results in a shift of quantized conductance plateaus in long wires proportional to the strength of the random potential. This shift is found to be insensitive to the strength of magnetic fields and the same for all plateaus. A semiclassical explanation of this effect is proposed. We conclude with an outlook on modfications of the quantum phase diagram due to the spin degree of freedom of the electrons and their interactions. We discuss the stability of the phase diagram at finite temperature.