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Register a new userPower-law Localization in 2D, 3D with Off-diagonal Disorder
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We describe non-conventional localization of the midband E=0 state in square and cubic finite bipartite lattices with off-diagonal disorder by solving numerically the linear equations for the corresponding amplitudes. This state is shown to display multifractal fluctuations, having many sparse peaks, and by scaling the participation ratio we obtain its disorder-dependent fractal dimension $D_{2}$. A logarithmic average correlation function grows as $g(r) sim eta ln r$ at distance $r$ from the maximum amplitude and is consistent with a typical overall power-law decay $|psi(r)| sim r^{-eta}$ where $eta $ is proportional to the strength of off-diagonal disorder.
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We report the development and application of a new method for carrying out computational investigations of the effects of mass and force-constant (FC) disorder on phonon spectra. The method is based on the recently developed typical medium dynamical cluster approach (TMDCA), which is a Greens function approach. Excellent quantitative agreement with previous exact diagonalization results establishes the veracity of the method. Application of the method to a model system of binary mass and FC-disordered system leads to several findings. A narrow resonance, significantly below the van Hove singularity, that has been termed as the boson peak, is seen to emerge for low soft particle concentrations. We show, using the typical phonon spectrum, that the states constituting the boson peak cross over from being completely localized to being extended as a function of increasing soft particle concentration. In general, an interplay of mass and FC disorder is found to be cooperative in nature, enhancing phonon localization over all frequencies. However, for certain range of frequencies, and depending on material parameters, FC disorder can delocalize the states that were localized by mass disorder, and vice-versa. Modeling vacancies as weakly bonded sites with vanishing mass, we find that vacancies, even at very low concentrations, are extremely effective in localizing phonons. Thus, inducing vacancies is proposed as a promising route for efficient thermoelectrics. Finally, we use model parameters corresponding to the alloy system, Ni1-xPtx, and show that mass disorder alone is insufficient to explain the pseudogap in the phonon spectrum; the concomitant presence of FC disorder is necessary.
The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $gamma$ from the localization center.
We generalize the typical medium dynamical cluster approximation (TMDCA) and the local Blackman, Esterling, and Berk (BEB) method for systems with off-diagonal disorder. Using our extended formalism we perform a systematic study of the effects of non-local disorder-induced correlations and of off-diagonal disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three-dimensional Anderson model with configuration dependent hopping and find fast convergence with modest cluster sizes. Our results are in good agreement with the data obtained using exact diagonalization, and the transfer matrix and kernel polynomial methods.
We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $ell$ as a power-law $1/ell^alpha$. Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a long-distance algebraic decay of correlations within disordered-localized phases, for all exponents $alpha$. The exponent of algebraic decay depends only on $alpha$, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave-functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular and solid-state physics.
We study quantum transport in anisotropic 3D disorder and show that non rotation invariant correlations can induce rich diffusion and localization properties. For instance, structured finite-range correlations can lead to the inversion of the transport anisotropy. Moreover, working beyond the self-consistent theory of localization, we include the disorder-induced shift of the energy states and show that it strongly affects the mobility edge. Implications to recent experiments are discussed.
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