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Journal of Physics Conference Series

Zero bias anomaly in the two-site Anderson-Hubbard model with Gaussian distribution for disorder

Oanh Thi Kim Nguyen, Nam Van Tran, Giang H. Bach

Published Jul 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/1274/1/012008

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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.
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.
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.
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.
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.
The combined effects of strong disorder, strong correlations, and hopping in the Anderson-Hubbard model have been shown to produce a zero-bias anomaly which has an energy scale proportional to the hopping and minimal dependence on interaction strength, disorder strength, and doping. Disorder-induced suppression of the density of states for a purely local interaction is inconsistent with both the Efros-Shklovskii Coulomb gap and the Altshuler-Aronov anomaly, and moreover the energy scale of this anomaly is inconsistent with the standard energy scales of both weak- and strong-coupling pictures. We demonstrate that a density of states anomaly with similar features arises in an ensemble of two-site systems, and we argue that the energy scale ttt emerges in strongly correlated systems with disorder due to the mixing of lower and upper Hubbard orbitals on neighboring sites.
Motivated by experiments on doped transition metal oxides, this paper considers the interplay of interactions, disorder, kinetic energy and temperature in a simple system. An ensemble of two-site Anderson-Hubbard model systems has already been shown to display a zero-bias anomaly (Wortis and Atkinson 2010 Phys. Rev. B 82 073107) which shares features with that found in the two-dimensional Anderson-Hubbard model (Chiesa et al 2008 Phys. Rev. Lett. 101 086401). Here the temperature dependence of the density of states of this ensemble is examined. In the atomic limit, there is no zero-bias anomaly at zero temperature, but one develops at small nonzero temperatures. With hopping, small temperatures augment the zero-temperature kinetic-energy-driven zero-bias anomaly, while at larger temperatures the anomaly is filled in.