We present electron and phonon spectral functions calculated from determinant quantum Monte Carlo simulations of the half-filled two-dimensional Hubbard-Holstein model on a square lattice. By tuning the relative electron-electron ($e$-$e$) and electr
on-phonon ($e$-$ph$) interaction strengths, we show the electron spectral function evolving between antiferromagnetic insulating, metallic, and charge density wave insulating phases. The phonon spectra concurrently gain a strong momentum dependence and soften in energy upon approaching the charge density wave phase. In particular, we study how the $e$-$e$ and $e$-$ph$ interactions renormalize the spectra, and analyze how the interplay of these interactions influence the spectral renormalizations. We find that the presence of both interactions suppresses the amount of renormalization at low energy, thus allowing the emergence of a metallic phase. These findings demonstrate the importance of considering the influence of multiple interactions in spectroscopically determining any one interaction strength in strongly correlated materials.
Using the non-equilibrium Keldysh formalism, we solve the equations of motion for electron-phonon superconductivity, including an ultrafast pump field. We present results for time-dependent photoemission spectra out of equilibrium which probes the dy
namics of the superconducting gap edge. The partial melting of the order by the pump field leads to oscillations at twice the melted gap frequency, a hallmark of the Higgs or amplitude mode. Thus the Higgs mode can be directly excited through the nonlinear effects of an electromagnetic field and detected without any additional symmetry breaking.
We study three proposals for broken symmetry in the cuprate pseudogap - oxygen antiferromagnetism, $Theta_{II}$ orbital loop currents, and circulating currents involving apex oxygens - through numerical exploration of multi-orbital Hubbard models. Ou
r numerically exact results show no evidence for the existence of oxygen antiferromagnetic order or the $Theta_{II}$ phase in the three-orbital Hubbard model. The model also fails to sustain an ordered current pattern even with the presence of additional apex oxygen orbitals. We thereby conclude that it is difficult to stabilize the aforementioned phases in the multi-orbital Hubbard models for parameters relevant to cuprate superconductors. However, the $Theta_{II}$ phase might be stabilized through explicit flux terms. We find an enhanced propensity for circulating currents with such terms in calculations simulating applied stress or strain, which skew the copper-oxygen plane to resemble a kagome lattice. We propose an experimental viewpoint to shed additional light on this problem.
The redistribution of electrons in an ultrafast pump-probe experiment causes significant changes to the effective interaction between electrons and bosonic modes. We study the influence of these changes on pump-probe photoemission spectroscopy for a
model electron-phonon coupled system using the nonequilibrium Keldysh formalism. We show that spectral rearrangement due to the driving field preserves an overall sum rule for the electronic self-energy, but modifies the effective electron-phonon scattering as a function of energy. Experimentally, this pump-modified scattering can be tracked by analyzing the fluence or excitation energy dependence of population decay rates and transient changes in dispersion kinks.
We identify dd-excitations in the quasi-one dimensional compound Ca$_2$Y$_2$Cu$_5$O$_{10}$ using resonant inelastic x-ray scattering. By tuning across the Cu L$_3$-edge, we observe abrupt shifts in the dd-peak positions as a function of incident phot
on energy. This observation demonstrates orbital-specific coupling of the high-energy excited states of the system to the low-energy degrees of freedom. A Franck-Condon treatment of electron-lattice coupling, consistent with other measurements in this compound, reproduces these shifts, explains the Gaussian lineshapes, and highlights charge-orbital-lattice renormalization in the high energy d-manifold.
High resolution resonant inelastic x-ray scattering has been performed to reveal the role of lattice-coupling in a family of quasi-1D insulating cuprates, Ca$_{2+5x}$Y$_{2-5x}$Cu$_5$O$_{10}$. Site-dependent low energy excitations arising from progres
sive emissions of a 70 meV lattice vibrational mode are resolved for the first time, providing a direct measurement of electron-lattice coupling strength. We show that such electron-lattice coupling causes doping-dependent distortions of the Cu-O-Cu bond angle, which sets the intra-chain spin exchange interactions. Our results indicate that the lattice degrees of freedom are fully integrated into the electronic behavior in low dimensional systems.
The unoccupied states of complex materials are difficult to measure, yet play a key role in determining their properties. We propose a technique that can measure the unoccupied states, called time-resolved Compton scattering, which measures the time-
dependent momentum distribution (TDMD). Using a non-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to a lattice in a pump-probe setup. We find a direct relation between temporal oscillations in the TDMD and the dispersion of the underlying unoccupied states, suggesting that both can be measured by time-resolved Compton scattering. We demonstrate the experimental feasibility by applying the method to a model of MgB$_2$ with realistic material parameters.
We consider several aspects of high-order harmonic generation in solids: the effects of elastic and inelastic scattering; varying pulse characteristics; and inclusion of material-specific parameters through a realistic band structure. We reproduce ma
ny observed characteristics of high harmonic generation experiments in solids including the formation of only odd harmonics in inversion-symmetric materials, and the nonlinear formation of high harmonics with increasing field. We find that the harmonic spectra are fairly robust against elastic and inelastic scattering. Furthermore, we find that the pulse characteristics play an important role in determining the harmonic spectra.
In this paper we examine the effects of electron-hole asymmetry as a consequence of strong correlations on the electronic Raman scattering in the normal state of copper oxide high temperature superconductors. Using determinant quantum Monte Carlo sim
ulations of the single-band Hubbard model, we construct the electronic Raman response from single particle Greens functions and explore the differences in the spectra for electron and hole doping away from half filling. The theoretical results are compared to new and existing Raman scattering experiments on hole-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ and electron-doped Nd$_{2-x}$Ce$_{x}$CuO$_{4}$. These findings suggest that the Hubbard model with fixed interaction strength qualitatively captures the doping and temperature dependence of the Raman spectra for both electron and hole doped systems, indicating that the Hubbard parameter U does not need to be doping dependent to capture the essence of this asymmetry.
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.
