We present first-principles based calculations of the tunneling conductance and magnetoconductance of epitaxial Fe(100)͉MgO(100)͉Fe(100) sandwiches. Our results indicate that tunneling is much more interesting and complicated than the simple barrier model used previously. We obtain the following general results: ͑1͒ Tunneling conductance depends strongly on the symmetry of the Bloch states in the electrodes and of the evanescent states in the barrier layer. ͑2͒ Bloch states of different symmetry decay at different rates within the barrier. The decay rate is determined by the complex energy bands of the same symmetry in the barrier. ͑3͒ There may be quantum interference between the decaying states in the barrier. This leads to an oscillatory dependence of the tunneling current on k ʈ and a damped oscillatory dependence on barrier thickness. ͑4͒ Interfacial resonance states can allow particular Bloch states to tunnel efficiently through the barrier. For Fe(100)͉MgO(100)͉Fe(100) our calculations indicate that quite different tunneling mechanisms dominate the conductance in the two spin channels. In the majority channel the conductance is primarily via Bloch electrons with small transverse momentum. One particular state with ⌬ 1 symmetry is able to effectively couple from the Fe into the MgO. In the minority channel the conductance is primarily through interface resonance states especially for thinner layers. We predict a large magnetoresistance that increases with barrier thickness.

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The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the Dynamical Cluster Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.Despite years of active research, the understanding of pairing in the high-temperature "cuprate" superconductors (HTSC) remains one of the most important outstanding problems in condensed matter physics. While conventional superconductors are well described by the BCS theory, the pairing mechanism in HTSC is believed to be of entirely different nature. Strong electronic correlations play a crucial role in HTSC, not only for superconductivity but also for their unusual normal state behavior. Hence, models describing itinerant correlated electrons, in particular the two-dimensional (2D) Hubbard model and its strong-coupling limit, the 2D t-J model, were proposed to capture the essential physics of the CuO-planes in HTSC [1,2]. Despite the fact that these models are among the mostly studied models in condensed matter physics, the question of whether they contain enough ingredients to describe HTSC remains an unsolved problem.Many different techniques, from analytic to numerical have been applied to study superconductivity in these models. The Mermin-Wagner theorem [3] and the rigorous results in Ref.[4] preclude d x 2 −y 2 superconducting long-range order at finite temperatures in the 2D models. Superconductivity may however exist -as in the attractive Hubbard model -as topological order at finite temperatures below the Kosterlitz-Thouless (KT) transition temperature [5]. Recent renormalization group studies indicate that the ground-state of the doped weakcoupling 2D Hubbard model is superconducting with a d x 2 −y 2 -wave order parameter [6]. The possibility of d x 2 −y 2 -wave pairing in the 2D Hubbard and t-J models was also indicated in a number of numerical studies of finite system size (for a review see [7]). Only recent numerical calculations for the t-J model provided evidence for pairing at T = 0 in relatively large systems for physically relevant values of J/t [8]. Quantum Monte Carlo (QMC) simulations are also employed to search for such a transition [9]. These studies indicate an enhancement of the pairing correlations in the d x 2 −y 2 channel with decreasing temperature. Unfortunately the Fermion sign problem limits these studies to temperatures too high to study a possible KT transition. Another difficulty of these methods arises from their strong finite size effects, often ruling out the reliable extraction of low-energy scales. In fact, a reliable finite-size scaling has only recently been achieved in the negative-U model [10], where th...

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