Tomi Ohtsuki

CORRECTIONS TO SCALING AT THE ANDERSON TRANSITION

We report a numerical analysis of corrections to finite size scaling at the Anderson transition due to irrelevant scaling variables and non-linearities of the scaling variables. By taking proper account of these corrections, the universality of the critical exponent for the orthogonal universality class for three different distributions of the random potential is convincingly demonstrated.

THE ANDERSON TRANSITION : TIME REVERSAL SYMMETRY AND UNIVERSALITY

We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes which occur in the field theory description of the transition. The critical conductance distribution at the Anderson transition has also been investigated and different distributions for the orthogonal and unitary classes obtained.

Random laser action in GaN nanocolumns

We report observations of random laser action in self-organized GaN nanocolumns. We have measured three samples with different filling fractions and investigated the dependence of the lasing property on the random configuration of nanocolumns. Numerical calculations based on a finite-difference time-domain method have also been performed and the comparison with the experimental results shows a clear relationship between the strength of light localization and the occurrence of random laser action.

Mesoscopic Stern-Gerlach spin filter by nonuniform spin-orbit interaction

A spin filtering in a two-dimensional electron system with nonuniform spin-orbit interactions (SOI) is theoretically studied. The strength of SOI is modulated perpendicular to the charge current. A spatial gradient of effective magnetic field due to the nonuniform SOI causes the Stern-Gerlach-type spin separation. The direction of the polarization is perpendicular to the current and parallel to the spatial gradient. Almost 100% spin polarization can be realized even without applying any external magnetic fields and without attaching ferromagnetic contacts. The spin polarization persists even in the presence of randomness.

Random network models and quantum phase transitions in two dimensions

An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for introducing the network model, the percolation model for electrons in spatial dimension 2 in a strong perpendicular magnetic field and a spatially correlated random potential is described. Based on this, the network model is established, using the concepts of percolating probability amplitude and tunneling. Its localization properties and its behavior at the critical point are discussed including a short survey on the statistics of energy levels and wave function amplitudes. Magneto-transport is reviewed with emphasis on some new results on conductance distributions. Generalizations are performed by establishing equivalent Hamiltonians. In particular, the significance of mappings to the Dirac model and the two-dimensional Ising model is discussed. A description of renormalization group treatments is given. The classification of two-dimensional random systems according to their symmetries is outlined. This provides access to the complete set of quantum phase transitions like the thermal Hall transition and the spin quantum Hall transition in two dimensions. The supersymmetric effective field theory for the critical properties of network models is formulated. The network model is extended to higher dimensions including remarks on the chiral metal phase at the surface of a multi-layer quantum Hall system.

Inverse Participation Number and Fractal Dimensionality of Electronic States in a Two Dimensional System in Strong Perpendicular Magnetic Field

We study the system size dependence of the inverse participation number (IPN) of the electronic eigenstates of a two-dimensional disordered system subject to a strong perpendicular magnetic field with periodic boundary condition in one direction, and Dirichlet boundary conditions in the other. Two types of random potentials are considered, random arrays of δ-function potentials, and of Gaussian potentials with a finite range of the order of the magnetic length. The fractal dimensionality d * of the most extended states is estimated to be 1.39 for the δ-potential case and 1.56 for the finite-ranged impurity model. The edge states have d * =1. Their insensitivity to the impurity potential is explicitly demonstrated. Through the analysis of the energy dependence of d * , it is found that there is a continuous change of states from the edge states to the bulk extended states with lowering energy.

Anderson transition in two-dimensional systems with spin-orbit coupling.

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent nu for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyze the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent nu=2.73+/-0.02.

Reconciling Conductance Fluctuations and the Scaling Theory of Localization

We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution, exp(), , and 1/, where g is the conductance in units of e(2)/h and R = 1/g is the resistance, and demonstrate that these quantities obey single parameter scaling laws. We obtain consistent estimates of the critical exponent from the scaling of all these quantities.

Spin polarization in a T-shaped conductor induced by strong Rashba spin-orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spinorbit interaction in a T-shaped conductor proposed by A.A. Kiselev and K.W. Kim (Appl. Phys. Lett. 78 775 (2001)). The recursive Green function method is used to calculate the three terminal spin dependent transmission probabilities. We focus on single-channel transport and show that the spin polarization becomes nearly 100% with a conductance close to e 2 /h for sufficiently strong spin-orbit coupling. This is interpreted by the fact that electrons with opposite spin states are deflected into an opposite terminal by the spin dependent Lorentz force. The influence of the disorder on the predicted effect is also discussed. Cases for multi-channel transport are studied in connection with experiments.

Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of a disordered Z2 topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent ν and the dynamical critical exponent z are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.