The causal set approach to quantum gravity models spacetime as a discrete structure - a causal set. Recent research has led to causal set models for the retarded propagator for the Klein-Gordon equation and the dAlembertian operator. These models can
be compared to their continuum counterparts via a sprinkling process. It has been shown that the models agree exactly with the continuum quantities in the limit of an infinite sprinkling density - the continuum limit. This paper obtains the correction terms for these models for sprinkled causal sets with a finite sprinkling density. These correction terms are an important step towards testable differences between the continuum and discrete models that could provide evidence of spacetime discreteness.
Determinant quantum Monte Carlo (DQMC) simulations are used to study non-linear electron-phonon interactions in a two-dimensional Holstein-like model on a square lattice. We examine the impact of non-linear electron-lattice interactions on supercondu
ctivity and on Peierls charge-density-wave (CDW) correlations at finite temperatures and carrier concentrations. We find that the CDW correlations are dramatically suppressed with the inclusion of even a small non-linear interaction. Conversely, the effect of the non-linearity on superconductivity is found to be less dramatic at high temperatures; however, we find evidence that the non-linearity is ultimately detrimental to superconductivity. These effects are attributed to the combined hardening of the phonon frequency and a renormalization of the effective linear electron-phonon coupling towards weaker values. These results demonstrate the importance of non-linear interactions at finite carrier concentrations when one is addressing CDW and superconducting order and have implications for experiments that drive the lattice far from equilibrium.
We report a low-temperature specific heat study of high-quality single crystals of the heavily hole doped superconductor Ca$_{0.32}$Na$_{0.68}$Fe$_2$As$_2$. This compound exhibits bulk superconductivity with a transition temperature $T_c approx 34$,K
, which is evident from the magnetization, transport, and specific heat measurements. The zero field data manifests a significant electronic specific heat in the normal state with a Sommerfeld coefficient $gamma approx 53$ mJ/mol K$^{2}$. Using a multi-band Eliashberg analysis, we demonstrate that the dependence of the zero field specific heat in the superconducting state is well described by a three-band model with an unconventional s$_pm$ pairing symmetry and gap magnitudes $Delta_i$ of approximately 2.35, 7.48, and -7.50 meV. Our analysis indicates a non-negligible attractive intraband coupling,which contributes significantly to the relatively high value of $T_c$. The Fermi surface averaged repulsive and attractive coupling strengths are of comparable size and outside the strong coupling limit frequently adopted for describing high-$T_c$ iron pnictide superconductors. We further infer a total mass renormalization of the order of five, including the effects of correlations and electron-boson interactions.
We study a model for the metal-insulator (MI) transition in the rare-earth nickelates RNiO$_3$, based upon a negative charge transfer energy and coupling to a rock-salt like lattice distortion of the NiO$_6$ octahedra. Using exact diagonalization and
the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with ground state of predominantly $d^8ligand$ character, where $ligand$ denotes a ligand hole. For sufficiently large distortions ($delta d_{rm Ni-O} sim 0.05 - 0.10AA$), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with $(d^8ligand^2)_{S=0}(d^8)_{S=1}$ character, where $S$ is the total spin. Thus the MI transition may be viewed as being driven by an internal volume collapse where the NiO$_6$ octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the ($1/2,1/2,1/2$) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of a new type of charge ordering achieved without any actual movement of the charge.
Quasiparticle interference (QPI) by means of scanning tunneling microscopy/spectroscopy (STM/STS), angle resolved photoemission spectroscopy (ARPES), and multi-orbital tight bind- ing calculations are used to investigate the band structure and superc
onducting order parameter of LiFeAs. Using this combination we identify intra- and interband scattering vectors between the hole (h) and electron (e) bands in the QPI maps. Discrepancies in the band dispersions inferred from previous ARPES and STM/STS are reconciled by recognizing a difference in the $k_z$ sensitivity for the two probes. The observation of both h-h and e-h scattering is exploited using phase-sensitive scattering selection rules for Bogoliubov quasiparticles. From this we infer an s$_pm$ gap structure, where a sign change occurs in the superconducting order parameter between the e and h bands.
We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the f
illing and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half-filling.
We establish in a combination of ab initio theory and experiments that the tunneling process in scanning tunneling microscopy/spectroscopy on the A-122 iron pnictide superconductors - in this case BaFe$_{2-x}$Co$_x$As$_2$ - involve a strong adatom fi
ltering of the differential conductance from the near-EF Fe3d states, which in turn originates from the top-most sub-surface Fe layer of the crystal. The calculations show that the dominance of surface Ba-related tunneling pathways leaves fingerprints found in the experimental differential conductance data, including large particle-hole asymmetry and an energy-dependent contrast inversion.
Recently, neutron scattering spin echo measurements have provided high resolution data on the temperature dependence of the linewidth $Gamma({bf q},T)$ of acoustic phonons in conventional superconductors Pb and Nb. [P. Aynajian, et al, Science 319, 1
509 (2008)]. At low temperatures the merging of the $2Delta(T)$ structure in the linewidth with a peak associated with a low lying $hbaromega_{bf q_{KA}}$ Kohn anomaly suggested a coincidence between $2Delta(0)$ and $hbaromega_{bf q_{KA}}$ in Pb and Nb. Here we carry out a standard BCS calculation of the phonon linewidth to examine its temperature evolution and explore how close $2Delta(0)/hbaromega_{bf q_{KA}}$ must be to unity in order to be consistent with the neutron data.
Recent laser angle-resolved photoemission spectroscopy studies have established the presence of a new kink in the low-energy nodal dispersion of Bi$_2$Sr$_2$CaCu$_2$O$+{8+delta}$ (Bi-2212). The energy scale (~8-15 meV) of this kink appears below the
maximum of the superconducting gap $delta_0$. Therefore it is difficult to interpret this feature in terms of the usual coupling to a sharp dispersionless mode. In this paper we examine electron-phonon coupling to the in-plane acoustic phonon branch arising from the modulation of the screened Coulomb potential. We demonstrate that such a coupling has a strong forward scattering peak, and as a consequence, a kink occurs in the dispersion at an energy scale shifted by the local gap $delta(k)$. In addition, considerations for the reduction of screening with underdoping naturally explains the observed doping dependence of the low-energy kink. These results point to a strong coupling to the acoustic branch which is peaked in the forward scattering direction and has important implications for transport and pairing in the high-T$_c$ cuprates.
