Erratum: Quantum Criticality in Quasi-Two-Dimensional Itinerant Antiferromagnets [Phys. Rev. Lett. 115, 186405 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.115.186405.

Quantum Criticality in Quasi-Two-Dimensional Itinerant Antiferromagnets.

Quasi-two-dimensional itinerant fermions in the antiferromagnetic (AFM) quantum-critical region of their phase diagram, such as in the Fe-based superconductors or in some of the heavy-fermion compounds, exhibit a resistivity varying linearly with temperature and a contribution to specific heat or thermopower proportional to TlnT. It is shown, here, that a generic model of itinerant anti-ferromagnet can be canonically transformed so that its critical fluctuations around the AFM-vector Q can be obtained from the fluctuations in the long wavelength limit of a dissipative quantum XY model. The fluctuations of the dissipative quantum XY model in 2D have been evaluated recently, and in a large regime of parameters, they are determined, not by renormalized spin fluctuations, but by topological excitations. In this regime, the fluctuations are separable in their spatial and temporal dependence and have a spatial correlation length which is proportional to the logarithm of the temporal correlation length, i.e., for some purposes, the effective dynamic exponent z=∞. The time dependence gives ω/T scaling at criticality. The observed resistivity and entropy then follow. Several predictions to test the theory are also given.

Phase diagram of a three-orbital model for high-Tc cuprate superconductors.

We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.

Landau renormalizations of superfluid density in the heavy-fermion superconductor CeCoIn5.

The formation of heavy-fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid (3)He that Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth Λ quite different from that in BCS theory. Using Leggett's theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of Λ in high quality samples both Landau parameters F(0)(s) and F(1)(s); this has never been accomplished before. A modification of the temperature dependence of the electronic specific heat C(el), related to that of Λ, is also expected. We have carefully determined the magnitude and temperature dependence of Λ in CeCoIn(5) by muon spin relaxation rate measurements to obtain F(0)(s) = 36 ± 1 and F(1)(s) = 1.2 ± 0.3, and we find a consistent change in the temperature dependence of C(el). This, the first determination of F(1)(s) with a value ≪ F(0)(s) in a heavy-fermion compound, tests the basic assumption of the theory of heavy fermions, that the frequency dependence of the self-energy is much more important than its momentum dependence.

Sharp low-energy feature in single-particle spectra due to forward scattering in d-wave cuprate superconductors.

There is an enormous interest in the renormalization of the quasiparticle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature T_{c} because it enables the determination of the fluctuation spectrum to which the qp's are coupled. A remarkable discovery by angle-resolved photoemission spectroscopy (ARPES) is a sharp low-energy feature (LEF) in qp spectra well below the superconducting energy gap but with its energy increasing in proportion to T_{c} and its intensity increasing sharply below T_{c}. This unexpected feature needs to be reconciled with d-wave superconductivity. Here, we present a quantitative analysis of ARPES data from Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} (Bi2212) using Eliashberg equations to show that the qp scattering rate due to the forward scattering impurities far from the Cu-O planes is modified by the energy gap below T_{c} and shows up as the LEF. This is also a necessary step to analyze ARPES data to reveal the spectrum of fluctuations promoting superconductivity.

Coexistence of two sharp-mode couplings and their unusual momentum dependence in the superconducting state of Bi2Sr2CaCu2O(8+δ) revealed by laser-based angle-resolved photoemission.

High-resolution laser-based angle-resolved photoemission measurements have been carried out on Bi2Sr2CaCu2O(8+δ) (Bi2212) superconductors to investigate momentum dependence of electron coupling with collective excitations (modes). Two coexisting energy scales are clearly revealed over a large momentum space for the first time in the superconducting state of the overdoped Bi2212 superconductor. These two energy scales exhibit distinct momentum dependence: one keeps its energy near 78 meV over a large momentum space while the other changes its energy from ∼40 meV near the antinodal region to ∼70 meV near the nodal region. These observations provide a new picture on momentum evolution of electron-boson coupling in Bi2212 that electrons are coupled with two sharp modes simultaneously over a large momentum space in the superconducting states. Their unusual momentum dependence poses a challenge to our current understanding of electron-mode-coupling and its role for high-temperature superconductivity in cuprate superconductors.

Considerations on the mechanisms and transition temperatures of superconductivity induced by electronic fluctuations.

An overview of the momentum and frequency dependence of effective electron-electron interactions which favor electronic instability to a superconducting state in the angular-momentum channel ℓ and the properties of the interactions which determine the magnitude of the temperature T(c) of the instability is provided. Interactions induced through exchange of electronic fluctuations of spin density, charge density or current density are considered. Special attention is paid to the role of quantum-critical fluctuations (QCFs) including pairing due to their virtual exchange as well as de-pairing due to inelastic scattering. Additional insight is gained by reviewing empirical data and theory specific to superfluidity in liquid He(3), superconductivity in some of the heavy-fermion compounds, in cuprates, in pncitides and the valence skipping compound. The physical basis for the following observation is provided: the ratio of the maximum T(c) to the typical phonon frequency in phonon induced s-wave superconductivity is O(10(-1)); the ratio of p-wave T(c) to the renormalized Fermi energy in liquid He(3), a very strongly correlated Fermi liquid near its melting pressure, is only O(10(-3)); in the cuprates and the heavy fermions where d-wave superconductivity occurs in a region governed by QCFs, this ratio rises to O(10(-2)). These discussions also suggest factors important for obtaining higher T(c). Experiments and theoretical investigations are suggested to clarify the many unresolved issues.

Collective modes in the loop ordered phase of cuprate superconductors.

We show that the two branches of collective modes discovered recently in underdoped cuprates with a large spectral weight are a necessary consequence of the loop-current state. Such a state has been shown in earlier experiments to be consistent with the symmetry of the order parameter competing with superconductivity in four families of cuprates. We also predict a third branch of excitations which cannot be discovered by neutron scattering but may be discovered by other techniques. Using parameters to fit the observed modes, we show that quantum fluctuations change the direction of the effective moments in the ground state to lie at an angle to the c axis as observed in experiments.

Superconductivity in the fullerenes.

Intramolecular vibrations strongly scatter electrons near the Fermi-surface in doped fullerenes. A simple expression for the electron-phonon coupling parameters for this case is derived and evaluated by quantum-chemical calculations. The observed superconducting transition temperatures and their variation with lattice constants can be understood on this basis. To test the ideas and calculations presented here, we predict that high frequency H(2) modes acquire a width of about 20% of their frequency in superconductive fullerenes, and soften by about 5% compared to the insulating fullerenes.

Pseudogap in cuprates in the loop-current ordered state.

Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. The loop-current order, characterized by the anapole vector Ω, discovered in under-doped cuprates occurs in the same region of the temperature and doping as the pseudo gap observed in STM and ARPES experiments. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand for disorder coupling linearly to the different possible orientations of Ω, there can only be a finite temperature dependent static correlation length for the loop-current state at any temperature. This leads to formation of domains of the ordered state with different orientation and magnitude of Ω in each. For the characteristic size of the domains much larger than the Fermi-vectors [Formula: see text], the boundary of the domains leads to forward scattering of the Fermions. Such forward scattering is shown to push states near the chemical potential to energies both above and below it leading to a pseudo-gap with an angular dependence which is maximum in the [Formula: see text] directions because the single-particle energies are degenerate in these directions for all domains. The magnitude of the average gap systematically increases with the square of the average loop order parameter measured by polarized neutron scattering. This result is tested. A unique result of the gap due to forward scattering is the lack of a bump in the density of states at the 'edge' of the pseudo-gap so that the depletion of states near the chemical potential is recovered only in integration up to the edge of the band. This is also in agreement with a variety of experiments. Some predictions for further experiments are provided. Due to the finite correlation length, low frequency excitations are expected at long wavelength at all temperatures in the 'ordered' phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

Universality of single-particle spectra of cuprate superconductors.

All the available data for the dispersion and linewidth of the single-particle spectra above the superconducting gap and the pseudogap in metallic cuprates for any doping have universal features. The linewidth is linear in energy below a scale omega(c) and constant above. The cusp in the linewidth at omega(c) mandates, due to causality, a waterfall, i.e., a vertical feature in the dispersion. These features are predicted by a recent microscopic theory. We find that all data can be quantitatively fitted by the theory with a coupling constant lambda(0) and an upper cutoff at omega(c), which vary by less than 50% among the different cuprates and for varying dopings. The microscopic theory also gives these values to within factors of O(2).

Screening of point charge impurities in highly anisotropic metals: application to mu+-spin relaxation in underdoped cuprate superconductors.

We calculate the screening charge density distribution due to a point charge, such as that of a positive muon (mu+), placed between the planes of a highly anisotropic layered metal. In underdoped hole cuprates the screening charge converts the charge density in the metallic-plane unit cells in the vicinity of the mu+ to nearly its value in the insulating state. The current-loop-ordered state observed by polarized neutron diffraction then vanishes in such cells, and also in nearby cells over a distance of order the intrinsic correlation length of the loop-ordered state. This strongly suppresses the magnetic field at the mu+ site. We estimate this suppressed field in underdoped YBa2Cu3O6+x and La2-xSrxCuO4, and find consistency with the observed approximately 0.2 G field in the former case and the observed upper bound of approximately 0.2 G in the latter case. This resolves the controversy between the neutron diffraction and mu-spin relaxation experiments.

Theory of the quantum critical fluctuations in cuprate superconductors.

The statistical mechanics of the time-reversal and inversion symmetry breaking order parameter, possibly observed in the pseudogap region of the phase diagram of the cuprates, can be represented by the Ashkin-Teller model. We add kinetic energy and dissipation to the model for a quantum generalization and show that the spectrum of the quantum-critical fluctuations is of the form postulated in 1989 to give the marginal Fermi-liquid properties. The model solved and the methods devised are likely to be of interest also to other quantum phase transitions.

Josephson effect for superconductors lacking time-reversal and inversion symmetries.

Because of the absence of a center of inversion in some superconducting compounds, a p-wave admixture to the dominant d-wave (or s) order parameter must exist. If time reversal is also violated, an allowed invariant is the product of the d wave (or s wave), p wave, and an appropriately directed current. We show that this leads to a new and remarkable property of the Josephson current for tunneling into a s-wave superconductor along the direction parallel to the axis of the p-wave component. These ideas are applied to the heavy-fermion compounds which lack center of inversion due to crystalline symmetry, as well as time-reversal symmetry, such as CePt(3)Si. They also apply to the superconducting state of the cuprates in the pseudogap region of the phase diagram where in the normal phase some experiments have detected a time-reversal and inversion symmetry broken phase.

Helicity order: hidden order parameter in URu2Si2.

We propose that the "hidden order parameter" in URu2Si2 is a helicity order that must arise if the Pomeranchuk criteria for the spin-antisymmetric Landau parameters with respect to the stability of a Fermi liquid state are violated. In a simple model, we calculate the specific heat, the linear and nonlinear magnetic susceptibilities, and the change of transition temperature in a magnetic field with such an order parameter, and obtain quantitative agreement with experiments in terms of two parameters extracted from the data. The peculiar temperature dependence of the NMR linewidth and the nature of the loss of excitations in the ordered phase seen by neutron scattering are also explained, and experiments are suggested to directly confirm the proposed order parameter.

Undressing the Kondo effect near the antiferromagnetic quantum critical point.

The problem of a spin-1/2 magnetic impurity near an antiferromagnetic transition of the host lattice is shown to transform to a multichannel problem. A variety of fixed points is discovered asymptotically near the antiferromagnetic critical point. Among these is a new variety of stable fixed point of a multichannel Kondo problem which does not require channel isotropy. At this point Kondo screening disappears but coupling to spin fluctuations remains. In addition to its intrinsic interest, the problem is an essential ingredient in the problem of quantum critical points in heavy fermions.

What angle-resolved photoemission experiments tell about the microscopic theory for high-temperature superconductors.

Recent angular-resolved photoemission experiments on high-temperature superconductors are consistent with a phenomenological description of the normal state of these materials as marginal Fermi liquids. The experiments also provide constraints on microscopic theories.