Session W8: Superconductivity Theory: Phonons and Other Mechanisms

Anti-Jahn-Teller effect and d-wave phonon mechanism in cuprates

Undoped cuprates are Jahn-Teller (JT) Materials [1] and Mott AF insulators [2]. When holes are doped, the octahedrons or pyramids elongated by the JT effect shrink. We call such distortion against the JT effect ``\textbf{\textit{anti-Jahn-Teller effect}}''[3]. By the interplay of the \textit{anti-Jahn-Teller effect }and \textit{Mott physics}, the two multiplets, the Zhang-Rice singlet and the Hund's coupling triplet, become nearly degenerate, and thus the hole-carriers in the underdoped regime form a metallic state, by taking the two multiplets alternately in the presence of the local AF order without destroying it [3,4]. On the basis of this two-component K-S model with small Fermi surfaces, the mechanism of superconductivity is discussed by the interplay of the electron-phonon interactions and local AF order [5,3]. It is shown that (1) the phase difference of wave functions between up- and down-spin carriers leads to the gap of dx$^{2}$-y$^{2}$ symmetry, and (2) the calculated concentration dependences of Tc and of isotope effects for LSCO are consistent with recent experimental results including anomalous isotope effects [6]. Finally the origin of the high-energy pseudogap is discussed based on the K-S model [3]. \newline \newline [1] J.G. Bednorz and K.A. Mueller, \textit{Z. Phys}. \textbf{B64}, 189 (1986). \newline [2] P.W. Anderson, \textit{Science} \textbf{235}, 1196 (1987). \newline [3] H. Kamimura \textit{et al}., \textit{in Theory of Copper Oxide Superconductors} (Springer, Heidelberg, 2005). \newline [4] H. Kamimura and Y. Suwa, \textit{J. Phys. Soc. Jpn.}\textbf{ 62,} 3368 (1993). \newline [5] H. Kamimura \textit{et al.} \textit{Phys. Rev. Lett.}\textbf{ 77,} 723 (1996). \newline [6] A.R. Bishop \textit{et al}., \textit{J. Supercond}., to be published (2006).   

Effects of Inhomogeneous Magnetic Correlations on the Penetration Depth in d-Wave Superconductors

The influence of static magnetic correlations on the temperature-dependent superfluid density $\rho_s(T)$ is calculated for $d$-wave superconductors. In self-consistent calculations, itinerant holes form incommensurate spin density waves (SDW) which coexist with superconductivity. In the clean limit, the density of states is gapped, and $\rho_s(T\ll T_c)$ is exponentially activated. In inhomogeneously-doped cases, the SDW are disordered and both the density of states and $\rho_s(T)$ obtain forms indistinguishable from those in dirty but pure $d$-wave superconductors, in accordance with experiments. We conclude that the observed collapse of $\rho_s$ at $x\approx 0.35$ in underdoped $\backslash$YBCO may plausibly be attributed to the coexistence of SDW and superconductivity.   

Frustrated metallicity in the quasi-one-dimensional conductor PrBa$_2$Cu$_4$O$_8$

We have investigated the ground state of the extremely anisotropic quasi-one-dimensional metal PrBa$_2$Cu$_4$O$_8$ ($t_ {b}^2:t_{a}^2: t_{c}^2 \sim 4000: 2: 1$), the non- superconducting analogue of the high-T$_c$ cuprate YBa$_2$Cu$_4 $O$_8$, as a function of disorder content, introduced either through atomic-site substitution or electron irradiation. A common single disorder threshold is found to drive interchain and in-chain resistivities into a low temperature regime where they display $d\rho/dT<0$. The survival of a large magnetoresistance of orbital origin reveals the itinerancy of the electronic system not to be suppressed by the presence of disorder. We propose an interpretative scenario based on a microscopic fragmentation of the metallic chains, though in contrast to many previous theoretical proposals, coherent hopping between chains appears to remain a relevant perturbation within the disordered system.   

Critical Number of Fermions in Anisotropic QED$_{3}$; Application to the Pseudogap State of High-T$_c$ Cuprates

The low-energy physics of d-wave superconductors is marked by the presence of four nodal points where the gap function vanishes. This nodal structure can be used as the basis of an effective theory for fermionic quasiparticles, which turns out to be an incarnation of a two-dimensional quantum electrodynamics (QED$_3$), where the gauge field encodes quantum fluctuations in the phase of the gap function. The theory predicts the Fermi surface of the pseudogap state which is confined to the four nodal points and contains an intrinsic anisotropy reflecting the difference between the gap and Fermi velocities. In this context, the emergence of an antiferromagnetic order can be described as the dynamical generation of mass due to the phenomenon of spontaneous chiral symmetry breaking. Mass generation occurs when the number of fermionic species in the theory is less than some critical number N$_{c}$, the actual value of which is still much debated. Based on simple physical arguments we find that N$_{c}$ does depend on anisotropy and, more surprisingly, different regimes emerge depending on the ratio between the Fermi and gauge field velocities.   

Properties of the ``quasi-particles'' at a nodal nematic quantum critical point

We study the properties of a $d-$wave superconductor in the vicinity of a quantum critical transition to a nematic (or $d+s$ superconducting) phase. Most interactions have little effect on nodal quasiparticles, due to the limitted phase space available for scattering. The few critical modes that do couple effectively (such as the phase fluctuations treated in the context of QED3) produce a renormalized (fixed point) dispersion that is isotropic (pseudo-Lorentz invariant). This contrasts with the extreme anisotropy found in ARPES experiments on cuprate superconductors, which is often considerably larger even than anticipated from mean-field considerations based on the magnitude of $\Delta_0/E_F$ We find quantum fluctuations near a nodal nematic quantum critical point strongly enhance the dispersion anisotropy, and are efficient inelastic scatterers. The quantum field theory which describes the nodal nematic critical point is non-Lorentz invariant and the nodal quasiparticles display clear non-Fermi liquid behavior. The fermion spectral function displays nontrivial structure, which can be compared with those measured by ARPES in cuperate superconductors.   

Excitons in QED$_3$ and spin response in a phase-fluctuating $d$-wave superconductor

We study the particle-hole exciton mode in the QED$_3$ theory of a phase-fluctuating $d$-wave superconductor in ladder approximation. We derive a Schr\"odinger-like equation for the exciton bound state and determine the conditions for its existence. We find the dispersion of this mode below the particle-hole continuum and compare our results with the resonance observed in neutron scattering measurements in cuprates. See http://www.physics.ubc.ca/~babak/march07/ for a list of references on this work.   

Effects of inhomogeneities and thermal fluctuations on the spectral function of a model d-wave superconductor

We compute the spectral function of a model for high-temperature superconductors, at both zero and finite temperatures $T$. The model consists of a two-dimensional BCS Hamiltonian with $d$-wave symmetry, which has a spatially varying, thermally fluctuating, complex gap $\Delta$. Thermal fluctuations are governed by a Ginzburg-Landau free energy functional. We assume that a fraction $c_{\beta}$ of the superconductor area has a large $\Delta$ ($\beta$ regions), while the rest has a smaller $\Delta$ ($\alpha$ regions). $\alpha$ and $\beta$ regions are randomly distributed in space. We find that the inhomogeneous gap distribution of $\Delta$ affects the spectral function primarily near $\mathbf k = (\pi,0)$. For $c_{\beta}\simeq 0.5$, a split band appears if the difference between the gap magnitudes in the $\alpha$ and $\beta$ regions is sufficiently large; otherwise, the band is only broadened. Thermal fluctuations also affect the spectral function most strongly near $\mathbf k = (\pi,0)$, where the peaks that are sharp and high at zero temperature become reduced, widened, and shifted toward smaller energies as $T$ increases through the Kosterlitz-Thouless transition temperature.   

Enhanced superconductivity due to inhomogeneous bond order in a doped Mott insulator

At half filling, the ground state of SrCu2(BO3)2, a half filled Mott insulator on the Shastry-Sutherland lattice, is exactly described by a valence bond wave function. Using a resonating valence bond wavefunction for the doped system, that includes the correct limit at half-filling, we find that the doped quantum magnet shows long ranged superconducting order. The superconductivity is boosted by the spontaneous emergence of a checker board pattern of the pairing strength on the bonds. We further find a strong asymmetry between hole and electron doping.   

Mott transition in Kagom{\'e} lattice Hubbard model

We investigate the Mott transition in the Kagom{\'e} lattice Hubbard model using the cellular dynamical mean field theory. The calculation of the double occupancy, the density of states, the static and dynamical spin correlation functions demonstrates that the system undergoes the first-order Mott transition at the Hubbard interaction $U/W \sim 1.4$ ($W$: bandwidth). In the metallic phase close to the Mott transition, we find the strong renormalization of three distinct bands, giving rise to the formation of heavy quasiparticles with strong frustrated interactions. It is elucidated that the quasiparticle states exhibit anomalous behavior in the temperature-dependent spin correlation functions. We also find a dramatic change of the dominant spin fluctuations around the Mott transition. The spin fluctuations in the insulating phase favor down to the lowest temperature a spatial spin configuration in which antiferromagnetic correlations are strong only in one chain direction but almost vanishing in the others.   

Spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model

We will discuss recent dynamic cluster quantum Monte Carlo studies of the effective pairing interaction responsible for d-wave pairing in the doped two-dimensional Hubbard model with an on-site Coulomb interaction U equal to the bandwidth. Motivated by earlier studies that show that the dominant contribution to the pairing interaction comes from the spin S=1 channel, we study a simple spin susceptibility representation of the particle-particle irreducible vertex. We find that with an effective temperature dependent coupling $\bar{U}(T)$ and the numerically calculated spin susceptibility $\chi(K-K')$, the d-wave pairing interaction is well approximated by $\frac{3}{2}\bar{U}^2(T) \chi(K-K')$.   

Electron-Phonon Interaction and Antiferromagnetic Correlations

Recent experiments suggesting sizeable lattice effects in the cuprates raisethe issue of the the role of electron-phonon (e-ph) interaction in strongly correlated systems. By means of Dynamical Mean-Field Theory, we show that, in the Hubbard-Holstein model, antiferromagnetic (AF) correlations strongly enhance the effects of the e-ph coupling with respect to the paramagnetic phase,even though the net effect of the Coulomb interaction is a moderate suppression of the e-ph interaction. Doping weakens the AF correlations and reduces the effects of the e-ph, leading to a scenario in which the tendency to polaron formation is weakened by doping, in agreement with the experimental results [1]. \newline \newline [1] G. Sangiovanni {\it et al.}, Phys. Rev. Lett. {\bf 97}, 046404 (2006)   

High Energy Kinks in the Cuprates

Tunneling studies in conventional superconductors are well known to reveal details of the electron-phonon interaction responsible for pairing. Similar features--low energy kinks in the 40-70 meV range--have also been observed in the cuprates, but their origin and possible role in pairing have been hotly debated. Recently, even higher energy kinks above 200 meV have been reported in the ARPES spectra of several cuprates. In this connection we discuss the roles of electron-plasmon as well as electron-magnon effects and show that collective modes in the charge and spin channels in the cuprates yield band renormalizations at low energies and anomalous features in band dispersion at higher energies, which are in substantial accord with experimental results.