Dirac and Weyl semimetals with linearly crossing bands are the focus of much recent interest in condensed matter physics. Although they host fascinating phenomena, their physics can be understood in terms of weakly interacting electrons. In contrast,
more than 40 years ago, Abrikosov pointed out that quadratic band touchings are generically strongly interacting. We have performed terahertz spectroscopy on films of the conducting pyrochlore Pr$_2$Ir$_2$O$_7$, which has been shown to host a quadratic band touching. A dielectric constant as large as $tilde{varepsilon }/epsilon_0 sim 180 $ is observed at low temperatures. In such systems the dielectric constant is a measure of the relative scale of interactions, which are therefore in our material almost two orders of magnitude larger than the kinetic energy. Despite this, the scattering rate exhibits a $T^2$ dependence, which shows that for finite doping a Fermi liquid state survives, however with a scattering rate close to the maximal value allowed.
We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known
to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the critical exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov exponent instead of the smallest positive Lyapunov exponent. We find a value for the critical exponent $ u=2.73 pm 0.02$ that is consistent with that for topologically trivial symplectic systems.
We study the surface and bulk electronic structure of the room-temperature ferromagnet Co:TiO2 anatase films using soft and hard x-ray photoemission spectroscopy with probe sensitivities of ~1 nm and ~10 nm, respectively. We obtain direct evidence of
metallic Ti$^{3+}$ states in the bulk, which get suppressed to give a surface semiconductor, thus indicating a surface-bulk dichotomy. X-ray absorption and high-sensitivity resonant photoemission spectroscopy reveal Ti$^{3+}$ electrons at the Fermi level (E$_F$) and high-spin Co$^{2+}$ electrons occurring away from E$_F$. The results show the importance of the charge neutrality condition: Co$^{2+}$ + V$_{O}$$^{2-}$ + 2Ti$^{4+}$ $leftrightarrow$ Co$^{2+}$ + 2Ti$^{3+}$ (V$_O$ is oxygen vacancy), which gives rise to the elusive Ti 3d carriers mediating ferromagnetism via the Co 3d-O 2p-Ti 3d exchange interaction pathway of the occupied orbitals.
We study numerically the charge conductance distributions of disordered quantum spin-Hall (QSH) systems using a quantum network model. We have found that the conductance distribution at the metal-QSH insulator transition is clearly different from tha
t at the metal-ordinary insulator transition. Thus the critical conductance distribution is sensitive not only to the boundary condition but also to the presence of edge states in the adjacent insulating phase. We have also calculated the point-contact conductance. Even when the two-terminal conductance is approximately quantized, we find large fluctuations in the point-contact conductance. Furthermore, we have found a semi-circular relation between the average of the point-contact conductance and its fluctuation.
We investigate numerically the spin polarization of the current in the presence of Rashba spin-orbit interaction in a T-shaped conductor proposed by A.A. Kiselev and K.W. Kim (Appl. Phys. Lett. {bf 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.
We present a theoretical study of spin-dependent transport through a ferromagnetic domain wall. With an increase of the number of components of the exchange coupling, we have observed that the variance of the conductance becomes half. As the strength
of the domain wall magnetization is increased, negative magnetoresistance is also observed.
The two terminal conductance for two dimensional systems is calculated in the presence of the spin-orbit scattering. The level statistics of the transmission eigenvalue is shown to be sensitive to the asymmetry of the spin population in the lead. The
nearest neighbor spacing is GUE instead of GSE when sufficiently large Zeeman splitting is assumed in one of the lead.
The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both wit
h and without an additional random scalar potential. We find the critical exponent $ u$ for the localization length to be $1.45 pm 0.09$ with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered.
We find a critical exponent of $ u=1.45pm0.09$ with random scalar potential. Without it, $ u$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.
The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $ u$ of the localization length is extracted and estimated to be $ u = 1.3 pm 0.2$. The level sta
tistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.
