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

Spatially dependent Kondo effect in Quantum Corrals

We study the Kondo screening of a single magnetic impurity inside a non-magnetic quantum corral located on the surface of a metallic host system. We show that the spatial structure of the corral's eigenmodes lead to a spatially dependent Kondo effect whose signatures are spatial variations of the Kondo temperature, $T_K$. Moreover, we predict that the Kondo screening is accompanied by the formation of multiple Kondo resonances with characteristic spatial patterns. Our results open new possibilities to manipulate and explore the Kondo effect by using quantum corrals.Comment: 4 pages 5 figure

Defects in Heavy-Fermion Materials: Unveiling Strong Correlations in Real Space

Complexity in materials often arises from competing interactions at the atomic length scale. One such example are the strongly correlated heavy-fermion materials where the competition between Kondo screening and antiferromagnetic ordering is believed to be the origin of their puzzling non-Fermi-liquid properties. Insight into such complex physical behavior in strongly correlated electron systems can be gained by impurity doping. Here, we develop a microscopic theoretical framework to demonstrate that defects implanted in heavy-fermion materials provide an opportunity for unveiling competing interactions and their correlations in real space. Defect-induced perturbations in the electronic and magnetic correlations possess characteristically different spatial patterns that can be visualized via their spectroscopic signatures in the local density of states or non-local spin susceptibility. These real space patterns provide insight into the complex electronic structure of heavy-fermion materials, the light or heavy character of the perturbed states, and the hybridization between them. The strongly correlated nature of these materials also manifests itself in highly non-linear quantum interference effects between defects that can drive the system through a first-order phase transition to a novel inhomogeneous ground state.Comment: 11 pages, 7 figure

Antiferromagnetic Vortex Core of Tl_2Ba_2CuO_{6+x} Studied by Nuclear Magnetic Resonance

Spatially-resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally-doped Tl_2Ba_2CuO_{6+x} (Tc=85 K). The NMR relaxation rate 1/T_1 at Tl site provides a direct evidence that the AF spin correlation is significantly enhanced in the vortex core region. In the core region Cu spins show a local AF ordering with moments parallel to the layers at T_N=20K. Above T_N the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T*~120 K), indicating that the pseudogap disappears within cores.Comment: 4 pages, 4 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

Hidden Order Transition in URu2Si2 and the Emergence of a Coherent Kondo Lattice

Using a large-N approach, we demonstrate that the differential conductance and quasi-particle interference pattern measured in recent scanning tunneling spectroscopy experiments (A.R. Schmidt et al. Nature 465, 570 (2010); P. Aynajian et al., PNAS 107, 10383 (2010)) in URu2Si2 are consistent with the emergence of a coherent Kondo lattice below its hidden order transition (HOT). Its formation is driven by a significant increase in the quasi-particle lifetime, which could arise from the emergence of a yet unknown order parameter at the HOT.Comment: 5 pages, 3 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

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

Luttinger theorem for a spin-density-wave state

We obtained the analog of the Luttinger relation for a commensurate spin-density-wave state. We show that while the relation between the area of the occupied states and the density of particles gets modified in a simple and predictable way when the system becomes ordered, a perturbative consideration of the Luttinger theorem does not work due to the presence of an anomaly similar to the chiral anomaly in quantum electrodynamics.Comment: 4 pages, RevTeX, 1 figure embedded in the text, ps-file is also available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm