Temperature dependence of the zero-bias anomaly in the two-site Anderson-Hubbard model

Rachel Wortis, W. A. Atkinson, Hongyi Chen

Rachel Wortis, Hongyi Chen, W. A. Atkinson

Rachel Wortis, Malcolm P. Kennett

Rachel Wortis, W. A. Atkinson

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.

Hong‐Yi Chen, Rachel Wortis, W. A. Atkinson

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 $t$ and is independent of the interaction strength and disorder potential.

Hong-Yi Chen, W. A. Atkinson

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.