Session F25: Superconductivity in Cuprates: Theory I

Hole motion in the Hubbard model

The motion of a single hole in the half-filled two-dimensional Hubbard model is not fully understood, despite the fact that it constitutes a crucial first step in unravelling the doping evolution of the electronic properties. Here we unambiguously show, using analytical and numerical approaches applied to the various versions of the Hubbard and t-J models, that the hole dynamics is determined by a complex interplay between (i) the strong coupling of a hole to magnons {\it and} (ii) the strongly renormalized, but effectively free, next-nearest neighbor hopping resulting from additional delocalization pathways. By studying the changes in the hole dynamics in the one-to-two-dimensional crossover regime we comment on applicability of the spin-charge separation ansatz and the spin density wave dispersion picture in the single-particle dynamics of the two-dimensional Hubbard model.   

Spectral properties of the two-dimensional Hubbard model with next-nearest-neighbor hopping near the Mott transition

The single-particle spectral properties of the two-dimensional Hubbard model with next-nearest-neighbor hopping near the Mott transition are investigated using cluster perturbation theory [1]. Based on the consideration of how the next-nearest-neighbor hopping shifts the spectral-weight distribution, the spectral features are explained by tracing the origins back to those of the one-dimensional and two-dimensional Hubbard models [1-3]. From this viewpoint, various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors, such as the pseudogaps in different momentum regimes between hole-doped and electron-doped cuprates, are collectively explained as properties of a two-dimensional system with next-nearest-neighbor hopping near the Mott transition. \\[4pt] [1] M. Kohno, Phys. Rev. B 90, 035111 (2014). \\[0pt] [2] M. Kohno, Phys. Rev. Lett. 105, 106402 (2010). \\[0pt] [3] M. Kohno, Phys. Rev. Lett. 108, 076401 (2012).   

Origin of the quasiparticle dispersion kinks in Bi-2212 determined from angle-resolved inelastic electron scattering

The kink features in the low energy quasiparticle dispersion in cuprate superconductors have been extensively studied using angle-resolved photoemission spectroscopy (ARPES). The existence of these kinks is a signature of a renormalization of the fermionic quasiparticles due to coupling to some bosonic collective mode at a scale related to the kink energy. In this talk, I will present angle-resolved inelastic electron scattering studies of the bosonic collective excitations in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Performing a 2D momentum parameterization of these modes, we reconstruct the complete dynamical susceptibility, $\chi(q,\omega)$, which we use to perform a one-loop self energy correction to the quasiparticle dispersion. The result reproduces well the dispersion observed with ARPES, indicating that these excitations are the origin of the observed kinks. I will discuss the implications of our study for phonon vs.\ spin fluctuation interpretation of these effects.   

Ultrafast quenching of electron-boson interaction and superconducting gap in a cuprate superconductor

Ultrafast spectroscopy makes it possible to track similarities and correlations that are not evident near equilibrium. Time- and angle-resolved photoemission measurements on cuprate high-temperature superconductor reveals that below the superconductor's critical temperature, ultrafast excitations trigger a synchronous decrease of electron self-energy and superconducting gap. In contrast, electron-boson coupling is unresponsive to ultrafast excitations above the superconductor's critical temperature and in the metallic state of a related material. These findings open a new pathway for studying transient self-energy and correlation effects in solids.   

Calculation of RIXS spectra of cuprates using band structure parameters

We explore the quasi particle theory to study the Resonant Inelastic X-ray Scattering(RIXS) by using the band structure parameters. We use both the determinant method(D. Benjamin, I. Klich and E. Demler, Phys. Rev. Lett. 112, 247002(2014)) and the expansion in the core-hole potential. The methods are applied to the (Ca$_x$La$_{1?x}$)(Ba$_{1.75 -x}$La$_{0.25+x}$)Cu$_3$O$_y$, (x=$0.1$ and $0.4$). We find that by using the band structure alone we can obtain quantitative agreement with the experimental data, especially for the position of the peak.   

Nernst Effect in HTC cuprate from BDW

The pseudogap regime in low hole doped high $T_{c}$ cuprate superconductors exhibits peculiar experimental signatures like the detection of enhanced negative signals for Hall, Seebeck and Nernst coefficients. It has been suggested that some of these phenomena can be understood in terms of a competition between a bond density wave order and superconductivity. In this work, we theoretically studied the Nernst effect using a mean-field quasiparticle model with $\textbf{Q}_{1} = (0, 2\pi/3)$ and $\textbf{Q}_{2} = ( 2\pi/3,0)$. By employing semi-classical Boltzmann dynamics, we have shown that the thermoelectric coefficient depends linearly on the absolute value of order parameter for small values of the induced gap and the contribution mainly comes from the small area of hot spot.   

Electronic structure of La$_2$CuO$_4$ within self-consistent GW approximation

La$_2$CuO$_4$, the parent compound of the high-temperature superconductor, is a classic strongly-correlated material. We present a first-principles study on the excitations spectrum of La$_2$CuO$_4$ within the self-consistent GW approximation based on full-potential linearized augmented-plane-wave methods. We compare the results of the Quasiparticle (QP) self-consistency and the fully self consistent approach. We find that the spin-polarized self-consistent GW calculation succeed in predicting the insulating ground state and anti-ferromagnetic ordering. It also describes charge-transfer character of the top of the valence band and reproduce the experimental spectral function well, including the weight of the copper $d$ and the position of the lanthanum levels, but it overestimates the bandgap by 75\%. We comment on the implications of our results for the implementation of GW+DMFT in a one shot, QP, and fully self consistent version.   

Strong Correlation of Electron Saddle Point Singularities to the Anomalous Isotope Effect in Zr, Nb$_{3}$Sn, and YBa$_{2}$Cu$_{3}$O$_{7}$

Anomalously small isotope effect in some high and low T$_{\mathrm{c}}$ superconductors such as Zr, Nb$_{3}$Sn, and YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO) created a great challenge for understanding. It has been shown by experiments and first-principles calculations that there exist extended saddle point singularities in the electronic structures of these materials. In this work, a new methodology is further implemented by integrating first-principles calculations of electronic structures of the materials into the theory of many-body physics for superconductivity. The aim is to seek a unified methodology to calculate the electronic and superconducting properties of these materials. It is demonstrated from first-principles that the extended saddle point singularities in Zr, Nb$_{3}$Sn, and YBCO strongly correlate to the anomalous isotope effect in these superconductors. However, there still exist some differences between the calculated and experimental results that require further research work.   

Resonant tunneling of fluctuation Cooper pairs: Shapiro steps above superconducting critical temperature

Superconducting fluctuations have proved to be an irreplaceable source of information about microscopic and macroscopic material parameters that could be inferred from experiments. According to common wisdom, the effect of thermodynamic fluctuations in the vicinity of the superconducting transition temperature, $T_c$, is to round off all of the sharp corners and discontinuities, which otherwise would have been expected to occur at $T_c$. Here we report the current spikes due to radiation-induced resonant tunneling of fluctuation Cooper pairs between two superconductors which grow even sharper and more pronounced upon approach to $T_c$. This striking effect offers an unprecedented tool for direct measurements of fluctuation Cooper pairs' lifetime, which is key to our understanding of the fluctuation regime, most notably to nature of the pseudogap state in high temperature superconductors. Our finding marks a radical departure from the conventional view of superconducting fluctuations as blurring and rounding phenomenon.   

Inhomogeneities in a strongly correlated d-wave superconductors in the limit of strong disorder

The complex interplay of the strong correlations and impurities in a high temperature superconductor is analyzed within a Hartree-Fock-Bogoliubov theory, augmented with Gutzwiller approximation for taking care of the strong electronic repulsion. The inclusion of such correlations is found to play a crucial role in reducing inhomogeneities in both qualitative and quantitative manner. This difference is comprehended by investigating the underlying one-particle ``normal states'' that includes the order parameters in the Hartree and Fock channels in the absence of superconductivity. This amounts to the renormalization of disorder both on the lattice sites and also on links. These two components of disorder turn out to be spatially anti-correlated through self-consistency. Interestingly, a simple pairing theory in terms of these normal states is found to describe the complex behaviors of dirty cuprates with reasonable accuracy. However, this framework needs modifications in the limit where disorder strengths are comparable to the band width. We will discuss appropriate updates in the formalism to describe physics of inhomogeneities with strong disorder.   

Effects of thermal disorder on electronic structure, electron-phonon coupling and spin-fluctuations in high-$T_C$ cuprates

The superconducting $T_C$'s are estimated from the values of electron-phonon and spin-phonon coupling in typical high-$T_C$ cuprates. It is shown that the couplings are peaked for just a few q-vectors because of the 2-dimensional Fermi surface shape. The involvement of few selective spin-phonon modes compensates for the low electronic density-of-states, which allows for a high $T_C$ [1]. Thermal disorder at moderately high temperature perturbs the strongly coupled modes through incoherent potential fluctuations of the Madelung terms, and electronic structure calculations show that the effective spin-phonon coupling suffers from lattice disorder. This effect puts a limit on long-range superconductivity, while fluctuations can persist to higher temperature. BCS-type model calculations are used to show how disorder modifies the superconducting gap and reduces $T_C$. Some ideas of how to recuperate a higher $T_C$ from superconducting fluctuations are discussed. \\[4pt] [1] T. Jarlborg, Solid State Commun. {\bf 181}, 15, (2014).   

Pairing glue at finite temperature in high-temperature superconductors

Even though the presence of a magnetic pairing glue analogous to the phonon glue of conventional superconductivity has been documented in the weak to intermediate correlation regime, the strong-correlation limit is still largely unexplored.[1] One of the best ways to access the frequencies relevant for the unconventional pairing dynamics present in doped Mott insulators is to study the anomalous spectral function associated with the frequency-dependent Gorkov function. Already studied at zero temperature,[2-4] that anomalous spectral function is difficult to obtain at finite temperature when one needs maximum entropy continuation methodology.[5] Indeed, this method requires a non-negative spectral function. In this talk we present the solution to this problem. Then we show our results for the Hubbard model on a 2$\times$2 cluster solved with Cluster Dynamical Mean Field Theory (CDMFT) using Continuous-Time Quantum Monte-Carlo (CTQMC) in the hybridization expansion as an impurity solver. \\[4pt] [1] P. W. Anderson, Science 316, 1705 (2007). [2] T. A. Maier, et al., Phys. Rev. Lett. 100, 237001 (2008). [3] B. Kyung, et al., Phys. Rev. B 80, 205109 (2009). [4] D. S\'{e}n\'{e}chal, et al., Phys. Rev. B 87, 075123 (2013). [5] M. Jarrell and J. Gubernatis, Phys. Reports 269, 133 (1996).   

DMRG simulations of a 3 band Hubbard model for the cuprates

While both the hole and electron doped cuprates can exhibit $d_{x^2-y^2}$-wave superconductivity, the local distribution of the doped carriers is known to be significantly different with the doped holes going primarily on the O sites while the doped electrons go on the Cu sites. Here we report the results of a density-matrix-renormalization-group calculation for a three-orbital model of a CuO$_2$ lattice. In addition to the asymmetric dependence of the intra-unit-cell occupation of the Cu and O for hole and electron doping, we find important differences in the longer range spin and charge correlations. As expected, the pairfield response has an $d_{x^2-y^2}$-like structure for both the hole and electron doped systems.   

DMFT+FLEX approach to unconventional superconductivity

We propose to combine the dynamical mean field theory (DMFT) with the fluctuation exchange approximation (FLEX) to investigate strongly correlated systems and especially to obtain a phase diagram for d-wave superconductors such as the cuprates. The DMFT+FLEX method, which can also be viewed as a proposal for a new Luttinger-Ward functional, describes the momentum-dependent effective pairing interaction, so that the method can describe anisotropic pairing along with the local correlation effect that is important in Mott physics. We have applied the formalism to the two-dimensional repulsive Hubbard model to obtain superconducting transition temperature. The result does indeed exhibit a Tc-dome structure. We have traced back the origin of the dome to the local vertex correction from DMFT that gives a filling-dependent effect on the FLEX self-energy.   

Quantum oscillation signatures of spin-orbit interactions controlling the residual nodal bilayer-splitting in underdoped high-$T_{\rm c}$ cuprates

We investigate the origin of the small residual nodal bilayer-splitting in the underdoped high-$T_{\rm c}$ superconductor YBa$_2$Cu$_3$O$_{6+x}$ using the results of recently published angle-resolved quantum oscillation data [Sebastian {\it et al.}, Nature {\bf 511}, 61 (2014)]. A crucial clue to the origin of the residual bilayer-splitting is found to be provided by the anomalously small Zeeman-splitting of some of the observed cyclotron orbits. We show that such an anomalously Zeeman-splitting (or small effective {\it g}-factor) for a subset of orbits can be explained by spin-orbit interactions, which become significant in the nodal regions as a result of the vanishing bilayer coupling. The primary effect of spin-orbit interactions is to cause quasiparticles traversing the nodal region of the Brillouin zone to undergo a spin flip. We suggest that the Rashba-like spin-orbit interactions, naturally present in bilayer systems, have the right symmetry and magnitude to give rise to a network of coupled orbits consistent with experimental observations in underdoped YBa$_2$Cu$_3$O$_{6+x}$. This work is supported by the DOEm BES proposal LANLF100, while the magnet lab is supported by the NSF and Florida State.