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Journal of Physics Condensed Matter

Effects of strong correlations on the disorder-induced zero-bias anomaly in the extended Anderson–Hubbard model

Yun Song, Sinan Bulut, Rachel Wortis, W. A. Atkinson

Published Aug 27, 2009• 15 citations
Publisher

Abstract

We study the effect of strong correlations on the zero-bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model (EAHM) on a square lattice. The EAHM has both on-site and nearest-neighbour interactions and randomly chosen site energies. We use a mean-field theory that incorporates strong correlations and treats the disorder potential exactly. We use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit, and the off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half-filling, and enhance the ZBA gap when the interaction is finite ranged.

DOI
10.1088/0953-8984/21/38/385601

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We study the effect of strong correlations on the zero-bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model (EAHM) on a square lattice. The EAHM has both on-site and nearest-neighbour interactions and randomly chosen site energies. We use a mean-field theory that incorporates strong correlations and treats the disorder potential exactly. We use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit, and the off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half-filling, and enhance the ZBA gap when the interaction is finite ranged.
We study the effect of strong correlations on the zero bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model, which has both on-site and nearest-neighbor interactions on a square lattice. We use a variation of dynamical mean field theory in which the diagonal self-energy is solved self-consistently at each site on the lattice for each realization of the randomly-distributed disorder potential. Since the ZBA occurs in systems with both strong disorder and strong interactions, we use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit. The off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half filling, and enhance the Coulomb gap when the interaction is finite-ranged.
Several recent exact-diagonalization calculations have established that the Anderson-Hubbard model has a disorder-induced zero bias anomaly (ZBA) (also called a disorder-induced pseudogap) in the density of states. In order to understand the physics of the ZBA, we study a simplified problem---an ensemble of two-site molecules with random site energies---for which analytical results are possible. For this ensemble, we examine how the ZBA forms in both the weakly correlated (mean field) and strongly correlated limits. In the weakly correlated case, the ZBA can be understood as the result of level repulsion between bonding and antibonding molecular orbitals. A similar level repulsion occurs in the strongly correlated case too but a larger contribution to the ZBA comes from the suppression of a triplet excitation mode. This inherently many-body mechanism does not have a counterpart in mean-field models.
Using a combination of numerical and analytical calculations, we study the disorder-induced zero bias anomaly (ZBA) in the density of states of strongly correlated systems modeled by the two-dimensional Anderson-Hubbard model. We find that the ZBA comes from the response of the nonlocal inelastic self-energy to the disorder potential, a result which has implications for theoretical approaches that retain only the local self-energy. Using an approximate analytic form for the self-energy, we derive an expression for the density of states of the two-site Anderson-Hubbard model. Our formalism reproduces the essential features of the ZBA, namely that the width is proportional to the hopping amplitude ttt and is independent of the interaction strength and disorder potential.
To expand the framework available for interpreting experiments on disordered strongly correlated systems, and in particular to explore further the strong-coupling zero-bias anomaly found in the Anderson-Hubbard model, we ask how this anomaly responds to the addition of nonlocal electron-electron interactions. We use exact diagonalization to calculate the single-particle density of states of the extended Anderson-Hubbard model. We find that for weak nonlocal interactions the form of the zero-bias anomaly is qualitatively unchanged. The energy scale of the anomaly continues to be set by an effective hopping amplitude renormalized by the nonlocal interaction. At larger values of the nonlocal interaction strength, however, hopping ceases to be a relevant energy scale and higher energy features associated with charge correlations dominate the density of states.
Abstract The Anderson-Hubbard model considers the correlation between disorder and other interactions in a strongly correlated electron system. Both disorder and correlations drive the metal-insulator transition but the densities of states behave in different ways. The zero bias anomaly (ZBA) referring to the V-dip shape of the density of states at the Fermi energy occurs in the strong disorder and strong interaction regime instead of a hard Coulomb gap in an insulator phase of strongly correlated interacting systems. In this paper, we use a Gaussian distribution for disorder to examine a two-site Anderson-Hubbard model. We also explain comprehensively the relationship between the phase diagram of ground states with various numbers of electrons and the behavior of the density of states. Furthermore, we want to investigate the effect of disorder distribution on the formation of the ZBA which originates from a hopping mechanism in two specific configurations.
We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.