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Register a new userCoherent potential approximation for spatially correlated disorder
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The coherent potential approximation (CPA) is extended to describe satisfactorily the motion of particles in a random potential which is spatially correlated and smoothly varying. In contrast to existing cluster-CPA methods, the present scheme preserves the simplicity of the conventional CPA in using a single self-energy function. Its accuracy is checked by a comparison with the exact moments of the Greens function, and with the spectral function from numerical simulations. The scheme is applied to excitonic absorption spectra in different spatial dimensions.
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Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion of classical particles in a random environment and ($ii$) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown to correspond to the boson peak in the vibrational model. The anomalous regimes above the crossover are governed by a complex, frequency-dependent self energy. The boson peak is shown to be stronger for non-Gaussian disorder than for Gaussian disorder. We demonstrate that the low-frequency non-analyticity of the off-lattice version of the CPA leads to the correct long-time tails of the velocity autocorrelation function in the hopping problem and to low-frequency Rayleigh scattering in the wave problem. Furthermore we show that the present version of the CPA is capable to treat the percolative aspects of hopping transport adequately.
Electronic structure calculations performed on very large supercells have shown that the local charge excesses in metallic alloys are related through simple linear relations to the local electrostatic field resulting from distribution of charges in the whole crystal. By including local external fields in the single site Coherent Potential Approximation theory, we develop a novel theoretical scheme in which the local charge excesses for random alloys can be obtained as the responses to local external fields. Our model maintains all the computational advantages of a single site theory but allows for full charge relaxation at the impurity sites. Through applications to CuPd and CuZn alloys, we find that, as a general rule, non linear charge rearrangements occur at the impurity site as a consequence of the complex phenomena related with the electronic screening of the external potential. This nothwithstanding, we observe that linear relations hold between charge excesses and external potentials, in quantitative agreement with the mentioned supercell calculations, and well beyond the limits of linearity for any other site property.
We investigate a $d$-dimensional model ($d$ = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field-theoretical effective-medium theory (self-consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debyes $omega^{d-1}$ law (``boson peak) as a result of disorder. This anomay becomes reinforced for increasing correlation length $xi$. The theory predicts that $xi$ times the width of the Brillouin line should be a universal function of $xi$ times the wavenumber. Such a scaling is found in the 2d simulation data, so that they can be represented in a universal plot. In the low-wavenumber regime, where the lattice structure is irrelevant there is excellent agreement between the simulation at small disorder. At larger disorder the continuum theory deviates from the lattice simulation data. It is argued that this is due to an instability of the model with stronger disorder.
The individual building blocks of van der Waals (vdW) heterostructures host fascinating physical phenomena, ranging from ballistic electron transport in graphene to striking optical properties of MoSe2 sheets. The presence of bonded and non-bonded cohesive interactions in a vdW heterostructure, promotes diversity in their structural arrangements, which in turn profoundly modulate the properties of their individual constituents. Here, we report on the presence of correlated structural disorder coexisting with the nearly perfect crystallographic order along the growth direction of epitaxial vdW heterostructures of Bi2Se3/graphene/SiC. Using the depth penetration of X-ray diffraction microscopy and scattering, we probed their crystal structure from atomic to mesoscopic length scales, to reveal that their structural diversity is underpinned by spatially correlated disorder states. The presence of the latter induces on a system, widely considered to behave as a collection of nearly independent 2-dimensional units, a pseudo-3-dimensional character, when subjected to epitaxial constraints and ordered substrate interactions. These findings shed new light on the nature of the vast structural landscape of vdW heterostructures and could enable new avenues in modulating their unique properties by correlated disorder.
Electronic structure calculations performed on very large supercells have shown that the local charge excesses in metallic alloys are related through simple linear relations to the local electrostatic field resulting from distribution of charges in the whole crystal. By including local external fields in the single site Coherent Potential Approximation theory, we develop a novel theoretical scheme in which the local charge excesses for random alloys can be obtained as the responses to local external fields. Our model maintains all the computational advantages of a single site theory but allows for full charge relaxation at the impurity sites. Through applications to CuPd and CuZn alloys, we find that, as a general rule, non linear charge rearrangements occur at the impurity site as a consequence of the complex phenomena related with the electronic screening of the external potential. This nothwithstanding, we observe that linear relations hold between charge excesses and external potentials, in quantitative agreement with the mentioned supercell calculations, and well beyond the limits of linearity for any other site property.
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