Intraband Hopping Research Articles

Communication: Fragment-based Hamiltonian model of electronic charge-excitation gaps and gap closure.

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) model uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transfer hopping integrals T and on-fragment parameters U((FH)). The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. We demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U((FH)), thus providing new insight into the nature of metal-insulator transitions. This result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.

Study of multiband disordered systems using the typical medium dynamical cluster approximation

We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include inter-band and intra-band hopping and an intra-band disorder potential. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. We apply the method to K$_x$Fe$_{2-y}$Se$_2$ with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.

Antiferromagnetic exchange and spin-fluctuation pairing in cuprate superconductors

Abstract A microscopic theory of superconductivity is formulated within an effective p - d Hubbard model for a CuO 2 plane. By applying the Mori-type projection technique, the Dyson equation is derived for the Green functions in terms of Hubbard operators. The antiferromagnetic exchange caused by interband hopping results in pairing of all carries in the conduction subband and high T c proportional to the Fermi energy. Kinematic interaction in intraband hopping is responsible for the conventional spin-fluctuation pairing. Numerical solution of the gap equation proves the d -wave gap symmetry and defines T c doping dependence. Oxygen isotope shift and pressure dependence of T c are also discussed.

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

We propose a microscopical theory of superconductivity in CuO$_2$ layer within the effective two-band Hubbard model in the strong correlation limit. By applying a projection technique for the matrix Green function in terms of the Hubbard operators, the Dyson equation is derived. It is proved that in the mean-field approximation d-wave superconducting pairing mediated by the conventional exchange interaction occurs. Allowing for the self-energy corrections due to kinematic interaction, a spin-fluctuation d-wave pairing is also obtained. $T\sb{c}$ dependence on the hole concentration and $\bf k$-dependence of the gap function are derived. The results show that the exchange interaction (which stems from the interband hopping) prevails over the kinematic interaction (which stems from the intraband hopping).

Antiferromagnetism and superconductivity in cuprates

A microscopical theory of superconducting pairing within the p–d Hubbard model is reviewed. The results for d-wave symmetry gap function and T c for different hole concentrations are presented. The retardation effects for the superexchange pairing are unimportant due to large interband excitation energy that results in the pairing of all electrons in the conduction band and high T c∝ E F. The spin-fluctuation pairing mediated by kinematic interaction in the intraband hopping further enhances T c.

Electronic pairing due to interband and intraband hopping dependence on oxygen covalency in YBaCuO superconductors

We consider the electronic extended model for the superconducting ceramics. In this model the broad electron band formed in the Cu–O 2 plane interacts with the narrow level created by vacancies on the Cu–O chains. It has been assumed that both; the interband hopping integral and the intraband hopping integral depend on the oxygen occupancy. We derive the pairing potential using the diagonalization method for the two band system and subsequently we look for the pairing terms in the remaining interactions, which are; the Coulomb on site repulsion in the broad band and the occupational difference in the intraband and interband hopping interaction. In the result we obtain the pairing potential with reduced Coulomb repulsion and with negative terms, which are proportional to the differences in the oxygen hopping integrals. The effective pairing potential is analysed for the possibility of superconducting transition. It has been shown that the high temperature superconductivity is possible at the reduced values of the Coulomb Δ t=( ii|1/ r| ij) quasi hopping term. The reduction is due to the occupational difference, Δ V, in the interband hopping interaction between O 2− and O 1− oxygen ions and the narrow level. The Coulomb repulsion on the narrow level also reduces required Δ t but at the much smaller amount.