Thomas A. Maier

Quantum Cluster Theories

Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative and are always in the thermodynamic limit. Their quality can be systematically improved, and they provide complementary information to finite size simulations. They have been studied intensively in recent years and are now well established. After a brief historical review, this article comparatively discusses the nature and advantages of these cluster techniques. Applications to common models of correlated electron systems are reviewed.

Near-degeneracy of several pairing channels in multiorbital models for the Fe pnictides

Weak-coupling approaches to the pairing problem in the iron pnictide superconductors have predicted a wide variety of superconducting ground states. We argue here that this is due both to the inadequacy of certain approximations to the effective low-energy band structure, and to the natural near degeneracy of different pairing channels in superconductors with many distinct Fermi surface sheets. In particular, we review attempts to construct two-orbital effective band models, the argument for their fundamental inconsistency with the symmetry of these materials, and compare the dynamical susceptibilities of two- and five-orbital tight-binding models. We then present results for the magnetic properties, pairing interactions and pairing instabilities within a five-orbital tight-binding random phase approximation model. We discuss the robustness of these results for different dopings, interaction strengths and variations in band structures. Within the parameter space explored, an anisotropic, sign-changing s-wave (A1g) state and a (B1g) state are nearly degenerate, due to the near nesting of Fermi surface sheets.

Spin fluctuations and superconductivity in a 3D tight-binding model for BaFe2As2

Despite the wealth of experimental data on the Fe-pnictide compounds of the KFe2As2 type, K=Ba, Ca, or Sr, the main theoretical work based on multiorbital tight-binding models has been restricted so far to the study of the related 1111 compounds. This can be ascribed to the more three-dimensional electronic structure found by ab initio calculations for the 122 materials, making this system less amenable to model development. In addition, the more complicated Brillouin zone BZ of the body-centered tetragonal symmetry does not allow a straightforward unfolding of the electronic band structure into an effective 1Fe/unit cell BZ. Here we present an effective five-orbital tight-binding fit of the full density functional theory band structure for BaFe2As2 including the kz dispersions. We compare the five-orbital spin fluctuation model to one previously studied for LaOFeAs and calculate the random-phase approximation enhanced susceptibility. Using the fluctuation ex- change approximation to determine the leading pairing instability, we then examine the differences between a strictly two-dimensional model calculation over a single kz cut of the BZ and a completely three-dimensional approach. We find pairing states quite similar to the 1111 materials, with generic quasi-isotropic pairing on the hole sheets and nodal states on the electron sheetsmorexa0» at kz=0, which however are gapped as the system is hole doped. On the other hand, a substantial kz dependence of the order parameter remains, with most of the pairing strength deriving from processes near kz=?. These states exhibit a tendency for an enhanced anisotropy on the hole sheets and a reduced anisotropy on the electron sheets near the top of the BZ.«xa0less

d-Wave Superconductivity in the Hubbard Model

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with the help of the dynamical cluster approximation. To solve the effective cluster problem we employ an extended noncrossing approximation, which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solutions with off-diagonal long-range order. The maximal T(c) approximately 150 K occurs for a doping delta approximately 20% and the doping dependence of the transition temperatures agrees well with the generic high- T(c) phase diagram.

Evolution of the superconducting state of Fe-based compounds with doping.

We introduce an effective low-energy pairing model for Fe-based superconductors with s- and d-wave interaction components and a small number of input parameters and use it to study the doping evolution of the symmetry and the structure of the superconducting gap. We argue that the model describes the entire variety of pairing states found so far in the Fe-based superconductors and allows one to understand the mechanism of the attraction in s(±) and d(x(2)-y(2)) channels, the competition between s- and d-wave solutions, and the origin of superconductivity in heavily doped systems, when only electron or only hole pockets are present.

Sensitivity of the superconducting state and magnetic susceptibility to key aspects of electronic structure in ferropnictides

Experiments on the iron–pnictide superconductors appear to show some materials where the ground state is fully gapped, and others where low-energy excitations dominate, possibly indicative of gap nodes. Within the framework of a five-orbital spin fluctuation theory for these systems, we discuss how changes in the doping, the electronic structure or interaction parameters can tune the system from a fully gapped to a nodal sign-changing gap with s-wave (A1g) symmetry (s±). In particular, we focus on the role of the hole pocket at the (π, π) point of the unfolded Brillouin zone, identified as crucial to the pairing by Kuroki et al (2009 Phys. Rev. B 79 224511), and show that its presence leads to additional nesting of hole and electron pockets, which stabilizes the isotropic s± state. The pockets contribution to the pairing can be tuned by doping, surface effects and by changes in interaction parameters, which we examine. Analytic expressions for orbital pairing vertices calculated within the random phase approximation (RPA) fluctuation exchange approximation allow us to draw connections between aspects of the electronic structure, interaction parameters and the form of the superconducting gap.

Doping dependence of spin excitations and its correlations with high-temperature superconductivity in iron pnictides

High-temperature superconductivity in iron pnictides occurs when electrons and holes are doped into their antiferromagnetic parent compounds. Since spin excitations may be responsible for electron pairing and superconductivity, it is important to determine their electron/hole-doping evolution and connection with superconductivity. Here we use inelastic neutron scattering to show that while electron doping to the antiferromagnetic BaFe2As2 parent compound modifies the low-energy spin excitations and their correlation with superconductivity (<50u2009meV) without affecting the high-energy spin excitations (>100u2009meV), hole-doping suppresses the high-energy spin excitations and shifts the magnetic spectral weight to low-energies. In addition, our absolute spin susceptibility measurements for the optimally hole-doped iron pnictide reveal that the change in magnetic exchange energy below and above Tc can account for the superconducting condensation energy. These results suggest that high-Tc superconductivity in iron pnictides is associated with both the presence of high-energy spin excitations and a coupling between low-energy spin excitations and itinerant electrons.Meng Wang∗,1 Chenglin Zhang∗,2 Xingye Lu∗,1, 2 Guotai Tan,2 Huiqian Luo,1 Yu Song,2 Miaoyin Wang,2 Xiaotian Zhang,1 E. A. Goremychkin,3 T. G. Perring,3 T. A. Maier,4 Zhiping Yin,5 Kristjan Haule,5 Gabriel Kotliar,5 and Pengcheng Dai2, 1 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2 Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA 3 ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK 4 Center for Nanophase Materials Sciences and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6494, USA 5 Department of Physics, Rutgers University, Piscataway, NJ 08854, USA

Accuracy and performance of graphics processors: A Quantum Monte Carlo application case study

The tradeoffs of accuracy and performance are as yet an unsolved problem when dealing with Graphics Processing Units (GPUs) as a general-purpose computation device. Their high performance and low cost makes them a desirable target for scientific computation, and new language efforts help address the programming challenges of data parallel algorithms and memory management. But the original task of GPUs - real-time rendering - has traditionally kept accuracy as a secondary goal, and sacrifices have sometimes been made as a result. In fact, the widely deployed hardware is generally capable of only single precision arithmetic, and even this accuracy is not necessarily equivalent to that of a commodity CPU. In this paper, we investigate the accuracy and performance characteristics of GPUs, including results from a preproduction double precision-capable GPU. We then accelerate the full Quantum Monte Carlo simulation code DCA++, similarly investigating its tolerance to the precision of arithmetic delivered by GPUs. The results show that while DCA++ has some sensitivity to the arithmetic precision, the single-precision GPU results were comparable to single-precision CPU results. Acceleration of the code on a fully GPU-enabled cluster showed that any remaining inaccuracy in GPU precision was negligible; sufficient accuracy was retained for scientifically meaningful results while still showing significant speedups.

Structure of the pairing interaction in the two-dimensional Hubbard model.

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for dx2-y2 pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the Q=(pi, pi) spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.

Neutron Scattering Studies of spin excitations in hole-doped Ba0.67K0.33Fe2As2 superconductor

We report inelastic neutron scattering experiments on single crystals of superconducting Ba0.67K0.33Fe2As2 (Tc = 38u2005K). In addition to confirming the resonance previously found in powder samples, we find that spin excitations in the normal state form longitudinally elongated ellipses along the QAFM direction in momentum space, consistent with density functional theory predictions. On cooling below Tc, while the resonance preserves its momentum anisotropy as expected, spin excitations at energies below the resonance become essentially isotropic in the in-plane momentum space and dramatically increase their correlation length. These results suggest that the superconducting gap structures in Ba0.67Ka0.33Fe2As2 are more complicated than those suggested from angle resolved photoemission experiments.