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Register a new userAnomalously localized states and multifractal correlations of critical wavefunctions in two-dimensional electron systems with spin-orbital interactions
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Anomalously localized states (ALS) at the critical point of the Anderson transition are studied for the SU(2) model belonging to the two-dimensional symplectic class. Giving a quantitative definition of ALS to clarify statistical properties of them, the system-size dependence of a probability to find ALS at criticality is presented. It is found that the probability increases with the system size and ALS exist with a finite probability even in an infinite critical system, though the typical critical states are kept to be multifractal. This fact implies that ALS should be eliminated from an ensemble of critical states when studying critical properties from distributions of critical quantities. As a demonstration of the effect of ALS to critical properties, we show that the distribution function of the correlation dimension of critical wavefunctions becomes a delta function in the thermodynamic limit only if ALS are eliminated.
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We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.
We study the box-measure correlation function of quantum states at the Anderson transition point with taking care of anomalously localized states (ALS). By eliminating ALS from the ensemble of critical wavefunctions, we confirm, for the first time, the scaling relation z(q)=d+2tau(q)-tau(2q) for a wide range of q, where q is the order of box-measure moments and z(q) and tau(q) are the correlation and the mass exponents, respectively. The influence of ALS to the calculation of z(q) is also discussed.
The wavefunctions of a disordered two-dimensional electron gas at the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these characteristics in the spatially resolved local density of states of a two-dimensional mixed surface alloy Bi_xPb_{1-x}/Ag(111), by combining high-resolution scanning tunneling microscopy with spin and angle-resolved inverse-photoemission experiments. Our detailed knowledge of the surface alloy electronic band structure, the exact lattice structure and the atomically resolved local density of states enables us to construct a realistic Anderson tight binding model of the mixed surface alloy, and to directly compare the measured local density of states characteristics with those from our model calculations. The statistical analyses of these two-dimensional local density of states maps reveal their log-normal distributions and multifractal scaling characteristics of the underlying wavefunctions with a finite anomalous scaling exponent. Finally, our experimental results confirm theoretical predictions of an exact scaling symmetry for Anderson quantum phase transitions in the Wigner-Dyson classes.
We study spatial structures of anomalously localized states (ALS) in tail regions at the critical point of the Anderson transition in the two-dimensional symplectic class. In order to examine tail structures of ALS, we apply the multifractal analysis only for the tail region of ALS and compare with the whole structure. It is found that the amplitude distribution in the tail region of ALS is multifractal and values of exponents characterizing multifractality are the same with those for typical multifractal wavefunctions in this universality class.
Mesoscopic fluctuations of the local density of states encode multifractal correlations in disorderedelectron systems. We study fluctuations of the local density of states in a superconducting state of weakly disordered films. We perform numerical computations in the framework of the disordered attractive Hubbard model on two-dimensional square lattices. Our numerical results are explained by an analytical theory. The numerical data and the theory together form a coherent picture of multifractal correlations of local density of states in weakly disordered superconducting films.
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