Dynamical spin susceptibility and the resonance peak in the pseudogap region of the underdoped cuprate superconductors

We present a study of the dynamical spin susceptibility in the pseudogap region of the high-T$_c$ cuprate superconductors. We analyze and compare the formation of the so-called resonance peak, in three different ordered states: the $d_{x^2-y^2}$-wave superconducting (DSC) phase, the $d$-density wave (DDW) state, and a phase with coexisting DDW and DSC order. An analysis of the resonance's frequency and momentum dependence in all three states reveals significant differences between them. In particular, in the DDW state, we find that a nearly dispersionless resonance excitation exists only in a narrow region around ${\bf Q}=(\pi,\pi)$. At the same time, in the coexisting DDW and DSC state, the dispersion of the resonance peak near ${\bf Q}$ is significantly changed from that in the pure DSC state. Away from $(\pi,\pi)$, however, we find that the form and dispersion of the resonance excitation in the coexisting DDW and DSC state and pure DSC state are quite similar. Our results demonstrate that a detailed experimental measurement of the resonance's dispersion allows one to distinguish between the underlying phases - a DDW state, a DSC state, or a coexisting DDW and DSC state - in which the resonance peak emerges.Comment: 9 pages, 9 figure

Comment on "A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems" by A. H. Castro-Neto and B. A. Jones

In a recent paper Castro-Neto and Jones argue that because the observability of quantum Griffiths-McCoy effects in metals is controlled by non-universal quantities, the quantum Griffiths-McCoy scenario may be a viable explanation for the non-fermi-liquid behavior observed in heavy fermion compounds. In this Comment we point out that the important non-universal quantity is the damping of the spin dynamics by the metallic electrons; quantum Griffiths-McCoy effects occur only if this is parametrically weak relative to other scales in the problem, i.e. if the spins are decoupled from the carriers. This suggests that in heavy fermion materials, where the Kondo effect leads to a strong carrier-spin coupling, quantum Griffiths-McCoy effects are unlikely to occur.Comment: 2 page

The Resonance Peak in Sr2_2RuO4_4: Signature of Spin Triplet Pairing

We study the dynamical spin susceptibility, $\chi({\bf q}, \omega)$, in the normal and superconducting state of Sr$_2$RuO$_4$. In the normal state, we find a peak in the vicinity of ${\bf Q}_i\simeq (0.72\pi,0.72\pi)$ in agreement with recent inelastic neutron scattering (INS) experiments. We predict that for spin triplet pairing in the superconducting state a {\it resonance peak} appears in the out-of-plane component of $\chi$, but is absent in the in-plane component. In contrast, no resonance peak is expected for spin singlet pairing.Comment: 4 pages, 4 figures, final versio

Multiband Superconductivity in Spin Density Wave Metals

We study the emergence of multiband superconductivity with $s$- and $d-$wave symmetry on the background of spin density wave (SDW). We show that the SDW coherence factors renormalize the momentum dependence of the superconducting (SC) gap, yielding a SC state with an \emph{unconventional} s-wave symmetry. Interband Cooper pair scattering stabilizes superconductivity in both symmetries. With increasing SDW order, the s-wave state is more strongly suppressed than the d-wave state. Our results are universally applicable to two-dimensional systems with a commensurate SDW.Comment: 4 pages, 3 figure

Direct Evidence for a Magnetic f-electron Mediated Cooper Pairing Mechanism of Heavy Fermion Superconductivity in CeCoIn5

To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference (QPI) imaging, to reveal quantitatively the momentum-space (k-space) structure of the f-electron magnetic interactions of CeCoIn5. Then, by solving the superconducting gap equations on the two heavy-fermion bands $E_k^{\alpha,\beta}$ with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn5, then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by the f-electron magnetism.Comment: 19 pages, 4 figures, Supplementary Information: 31 pages, 5 figure

Spin susceptibility in bilayered cuprates: resonant magnetic excitations

We study the momentum and frequency dependence of the dynamical spin susceptibility in the superconducting state of bilayer cuprate superconductors. We show that there exists a resonance mode in the odd as well as the even channel of the spin susceptibility, with the even mode being located at higher energies than the odd mode. We demonstrate that this energy splitting between the two modes arises not only from a difference in the interaction, but also from a difference in the free-fermion susceptibilities of the even and odd channels. Moreover, we show that the even resonance mode disperses downwards at deviations from ${\bf Q}=(\pi,\pi)$. In addition, we demonstrate that there exists a second branch of the even resonance, similar to the recently observed second branch (the $Q^*$-mode) of the odd resonance. Finally, we identify the origin of the qualitatively different doping dependence of the even and odd resonance. Our results suggest further experimental test that may finally resolve the long-standing question regarding the origin of the resonance peak.Comment: 8 pages, 5 figure

Magnetic Coherence as a Universal Feature of Cuprate Superconductors

Recent inelastic neutron scattering (INS) experiments on La$_{2-x}$Sr$_x$CuO$_4$ have established the existence of a {\it magnetic coherence effect}, i.e., strong frequency and momentum dependent changes of the spin susceptibility, $\chi''$, in the superconducting phase. We show, using the spin-fermion model for incommensurate antiferromagnetic spin fluctuations, that the magnetic coherence effect establishes the ability of INS experiments to probe the electronic spectrum of the cuprates, in that the effect arises from the interplay of an incommensurate magnetic response, the form of the underlying Fermi surface, and the opening of the d-wave gap in the fermionic spectrum. In particular, we find that the magnetic coherence effect observed in INS experiments on La$_{2-x}$Sr$_x$CuO$_4$ requires that the Fermi surface be closed around $(\pi,\pi)$ up to optimal doping. We present several predictions for the form of the magnetic coherence effect in YBa$_2$Cu$_3$O$_{6+x}$ in which an incommensurate magnetic response has been observed in the superconducting state.Comment: 9 pages, 12 figures; extended version of Phys. Rev B, R6483 (2000

Identifying Collective Modes via Impurities in the Cuprate Superconductors

We show that the pinning of collective charge and spin modes by impurities in the cuprate superconductors leads to qualitatively different fingerprints in the local density of states (LDOS). In particular, in a pinned (static) spin droplet, the creation of a resonant impurity state is suppressed, the spin-resolved LDOS exhibits a characteristic spatial pattern, and the LDOS undergoes significant changes with increasing magnetic field. Since all of these fingerprints are absent in a charge droplet, impurities are a new probe for identifying the nature and relative strength of collective modes.Comment: 4 pages, 4 figure

Striped superconductors in the extended Hubbard model

We present a minimal model of a doped Mott insulator that simultaneously supports antiferromagnetic stripes and d-wave superconductivity. We explore the implications for the global phase diagram of the superconducting cuprates. At the unrestricted mean-field level, the various phases of the cuprates, including weak and strong pseudogap phases, and two different types of superconductivity in the underdoped and the overdoped regimes, find a natural interpretation. We argue that on the underdoped side, the superconductor is intrinsically inhomogeneous -- striped coexistence of of superconductivity and magnetism -- and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. On the overdoped side, the state is overall homogeneous and the superconductivity is of the classical BCS type.Comment: 5 pages, 3 eps figures. Effect of t' on stripe filling + new references are adde