On the Critical Behavior of the Uniform Susceptibility of a Fermi Liquid Near an Antiferromagnetic Transition with Dynamic Exponent z=2 z = 2

We compute the leading behavior of the uniform magnetic susceptibility, $\chi$, of a Fermi liquid near an antiferromagnetic transition with dynamic exponent $z=2$. Our calculation clarifies the role of triangular ``anomaly'' graphs in the theory and justifies the effective action used in previous work \cite{Hertz}. We find that at the $z=2$ critical point of a two dimensional material, $lim_{q \rightarrow 0} \chi (q,0) = \chi_0 - D T$ with $\chi_0$ and $D$ nonuniversal constants. For reasonable band structures we find that in a weak coupling approximation $D$ is small and positive. Our result suggests that the behavior observed in the quantum critical regime of underdoped high-$T_c$ superconductors are difficult to explain in a $z=2$ theory.Comment: 12 pages, uuencoded Postscript fil

Covalency and the metal-insulator transition in titanate and vanadate perovskites

A combination of density functional and dynamical mean-field theory is applied to the perovskites SrVO$_3$, LaTiO$_3$ and LaVO$_3$. We show that DFT+DMFT in conjunction with the standard fully localized-limit (FLL) double-counting predicts that LaTiO$_3$ and LaVO$_3$ are metals even though experimentally they are correlation-driven ("Mott") insulators. In addition, the FLL double counting implies a splitting between oxygen $p$ and transition metal $d$ levels which differs from experiment. Introducing into the theory an \textit{ad hoc} double counting correction which reproduces the experimentally measured insulating gap leads also to a $p$-$d$ splitting consistent with experiment if the on-site interaction $U$ is chosen in a relatively narrow range ($\sim 6\pm 1$ eV). The results indicate that these early transition metal oxides will serve as critical test for the formulation of a general \textit{ab initio} theory of correlated electron metals.Comment: 5 pages, 3 figure

Spin Gaps and Bilayer Coupling in YBa2_2Cu3_3O7−δ_{7-\delta} and YBa2_2Cu4_4O8_8

We investigate the relevance to the physics of underdoped YBa$_2$Cu$_3$O$_{\rm 6+x}$ and YBa$_2$Cu$_4$O$_8$ of the quantum critical point which occurs in a model of two antiferromagnetically coupled planes of antiferromagnetically correlated spins. We use a Schwinger boson mean field theory and a scaling analysis to obtain the phase diagram of the model and the temperature and frequency dependence of various susceptibilities and relaxation rates. We distinguish between a low $\omega ,T$ coupled-planes regime in which the optic spin excitations are frozen out and a high $\omega ,T$ decoupled-planes regime in which the two planes fluctuate independently. In the coupled-planes regime the yttrium nuclear relaxation rate at low temperatures is larger relative to the copper and oxygen rates than would be naively expected in a model of uncorrelated planes. Available data suggest that in YBa$_2$Cu$_4$O$_8$ the crossover from the coupled to the decoupled planes regime occurs at $T 700K$ or $T \sim 200K$. The predicted correlation length is of order 6 lattice constants at $T=200K$. Experimental data related to the antiferromagnetic susceptibility of YBa$_2$Cu$_4$O$_8$ may be made consistent with the theory, but available data for the uniform susceptibility are inconsistent with the theory.Comment: RevTex 3.

On the Fermi Liquid to Polaron Crossover I: General Results

We use analytic techniques and the dynamical mean field method to study the crossover from fermi liquid to polaron behavior in models of electrons interacting with dispersionless classical phonons.Comment: 42 pages, 13 figure

On the Fermi Liquid to Polaron Crossover II: Double Exchange and the Physics of "Colossal" Magnetoresistance

We use the dynamical mean field method to study a model of electrons Jahn-Teller coupled to localized classical oscillators and ferromagnetically coupled to ``core spins'', which, we argue, contains the essential physics of the ``colossal magnetoresistance'' manganites $Re_{1-x} A_x MnO_3$. We determine the different regimes of the model and present results for the temperature and frequency dependence of the conductivity, the electron spectral function and the root mean square lattice parameter fluctuations. We compare our results to data, and give a qualitative discussion of important physics not included in the calculation. Extensive use is made of results from a companion paper titled: ``On the Fermi Liquid to Polaron Crossover I: General Results''.Comment: 34 pages, 10 figures. Depends on previous paper titled "On the Fermi Liquid to Poalron Crossover I: General Result

Quantum critical behavior of electrons at the edge of charge order

We consider quantum critical points (QCP) in which quantum fluctuations associated with charge rather than magnetic order induce unconventional metallic properties. Based on finite-T calculations on a two-dimensional extended Hubbard model we show how the coherence scale T* characteristic of Fermi liquid behavior of the homogeneous metal vanishes at the onset of charge order. A strong effective mass enhancement reminiscent of heavy fermion behavior indicates the possible destruction of quasiparticles at the QCP. Experimental probes on quarter-filled layered organic materials are proposed for unveiling the behavior of electrons across the quantum critical region.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

Orbital dynamics: The origin of the anomalous optical spectra in ferromagnetic manganites

We discuss the role of orbital degeneracy in the transport properties of perovskite manganites, focusing in particular on the optical conductivity in the metallic ferromagnetic phase at low temperatures. Orbital degeneracy and strong correlations are described by an orbital t-J model which we treat in a slave-boson approach. Employing the memory-function formalism we calculate the optical conductivity, which is found to exhibit a broad incoherent component extending up to bare bandwidth accompanied by a strong suppression of the Drude weight. Further, we calculate the constant of T-linear specific heat. Our results are in overall agreement with experiment and suggest low-energy orbital fluctuations as the origin of the strongly correlated nature of the metallic phase of manganites.Comment: To appear in: Phys. Rev. B 58 (Rapid Communications), 1 November 199

Effects of uniaxial strain in LaMnO_3

The effects of uniaxial strain on the structural, orbital, optical, and magnetic properties of LaMnO_3 are calculated using a general elastic energy expression, along with a tight-binding parameterization of the band theory. Tensile uniaxial strain of the order of 2 % (i.e., of the order of magnitude of those induced in thin films by lattice mismatch with substrates) is found to lead to changes in the magnetic ground state, leading to dramatic changes in the band structure and optical conductivity spectrum. The magnetostriction effect associated with the Neel transition of bulk(unstrained) LaMnO_3 is also determined. Due to the Jahn-Teller coupling, the uniform tetragonal distortion mode is softer in LaMnO_3 than in doped cubic manganates. Reasons why the observed (\pi \pi 0) orbital ordering is favored over a (\pi \pi \pi) periodicity are discussed.Comment: 9 figures, submitted in Phys. Rev.

Application of the scattering rate sum-rule to the interplane optical conductivity of high temperature superconductors: pseudogap and bi-layer effects

We use a recently proposed model of the interplane conductivity of high temperature superconductors to investigate the `scattering rate sum-rule' introduced by Basov and co-workers. We present a new derivation of the sum-rule. The quantal and thermal fluctuations of the order parameter which have been argued to produce the observed pseudogap behavior are shown to increase the total integrated `scattering rate' but may either increase or decrease the `quasiparticle' contribution from frequencies greater than twice the superconducting gap.Comment: 4 pages, 5 figures, revise