A physical model for a mixed-valence impurity in a metal must satisfy the Friedel screening theorem for both valences. Such a model is shown, following earlier work which showed low energy singularities in it, to be supersymmetric, leading to a free
Majorana and a phase-shifted Majorana excitation. The theory extended approximately to a lattice of mixed-valence ions at appropriate filling gives, without fine-tuning the parameters, a protected gapless Majorana fermion band across the chemical potential, besides the mixed-valence particle and hole bands separated by gaps. In this situation the system is electrically neutral in linear response but has de Haas-van Alphen oscillations. This is used to explain the recently observed magneto-oscillations in mixed-valence insulators as well as their accompanying low energy thermodynamic and relaxation rate anomalies. Some predictions to test the validity of the theoretical results are provided, the most striking of which is that there should be extensive ground state entropy in such compounds.
We re-examine the experimental results for the magnetic response function $chi({bf q}, E, T)$, for ${bf q}$ around the anti-ferromagnetic vectors ${bf Q}$, in the quantum-critical region, obtained by inelastic neutron scattering, on an Fe-based super
conductor, and on a heavy Fermion compound. The motivation is to compare the results with a recent theory, which shows that the fluctuations in a generic anti-ferromagnetic model for itinerant fermions map to those in the universality class of the dissipative quantum-XY model. The quantum-critical fluctuations in this model, in a range of parameters, are given by the correlations of spatial and of temporal topological defects. The theory predicts a $chi({bf q}, E, T)$ (i) which is a separable function of $({bf q -Q})$ and of ($E$,$T$), (ii) at crticality, the energy dependent part is $propto tanh (E/2T)$ below a cut-off energy, (iii) the correlation time departs from its infinite value at criticality on the disordered side by an essential singularity, and (iv) the correlation length depends logarithmically on the correlation time, so that the dynamical critical exponent $z$ is $infty$ . The limited existing experimental results are found to be consistent with the first two unusual predictions from which the linear dependence of the resistivity on T and the $T ln T$ dependence of the entropy also follow. More experiments are suggested, especially to test the theory of variations on the correlation time and length on the departure from criticality.
The experimental study of the modulation of the envelope of spin-echo signals due to internal and external fields is an important spectroscopic tool to detect very small internal magnetic fields. We derive the free induction decay and the frequency s
pectrum and amplitude of spin-echo signals for arbitrary orientation of fields with respect to crystalline axis for nuclei in a crystal of orthorhombic symmetry. Results reproduce the results that no modulation should be observed in tetragonal crystals for fields either along the c-axis or any direction in the basal plane and give details of the signal as a function of the orthorhombicity parameter. They are used to discuss recent experimental results and provide guidelines for future experiments.
The loop-current state discovered in under-doped cuprates is characterized by a vector ${bf Omega}$ which has four possible orientations which correspond to different domains of order in a perfect sample. Since translational symmetry remains unchange
d in the pure limit, no gap occurs at the chemical potential. On the other hand Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. For disorder coupling also to the direction of ${bf Omega}$, there can only be a finite temperature dependent static correlation length for the loop-current state below the ordering temperature of the pure problem. It is shown that, in this situation, singular forward scattering of fermions for large correlation lengths induces an angle dependent pseudo-gap in the single-particle spectral function near the chemical potential. The peaks in the spectral function at the fermi-vectors are away from the chemical potential proportionally to the square of the average loop order parameter measurable by polarized neutron scattering. This result is tested. Due to the finite correlation length there always exist low frequency excitations 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.
The quantum critical Antiferromagnetic (AFM) fluctuation spectra measured by inelastic neutron scattering recently in two heavy fermion superconductors are used together with their other measured properties to calculate their D-wave superconducting t
ransition temperatures $T_{rm c}$. To this end, the linearized Eliashberg equations for D-wave superconductivity induced by AFM fluctuations are solved in models of fermions with various levels of nesting. The results for the ratio of $T_{rm c}$ to the characteristic spin-fluctuation energy are well parametrized by a dimensionless coupling constant and the AFM correlation length. Comparing the results with experiments suggests that one may reasonably conclude that superconductivity in these compounds is indeed caused by AFM fluctuations. This conclusion is strengthened by a calculation with the same parameters of the measured coefficient of the normal state quantum-critical resistivity $propto T^{3/2}$ characteristic of {it gaussian} AFM quantum-critical fluctuations. The calculations give details of the superconducting coupling as a function of the correlation length and the integrated fluctuation spectra useful in other compounds.
In the Eliashberg integral equations for d-wave superconductivity, two different functions $(alpha^2 F)_n(omega, theta)$ and $(alpha^2 F)_{p,d}(omega)$ determine, respectively, the normal and the pairing self-energies. We present a quantitative analy
sis of the high-resolution laser based ARPES data on the compound Bi-2212 to deduce the function$(alpha^2 F)_n(omega, theta)$. Besides its detailed $omega$ dependence, we find the remarkable result that this function is nearly independent of $theta$ between the ($pi,pi$)-direction and 25 degrees from it. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function $(alpha^2 F)_{p,d}(omega)$ required for the d-wave pairing instability at high temperatures as well as the deduced $(alpha^2 F)_n(theta, omega)$. We show that the deduced $(alpha^2 F)_n(theta, omega)$ can only be obtained from Antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using $(alpha^2 F)_{p,d}(omega)$ consistent with such a correlation length and the symmetry of matrix-elements scattering fermions off AFM fluctuations, we calculate $T_c$ an show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantum-critical fluctuations derived microscopically as the fluctuations of the observed loop-current order discovered in the under-doped cuprates. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the $theta$ and $omega$ dependence of the deduced $(alpha^2 F)_n(omega, theta)$. The pairing kernel $(alpha^2 F)_{p,d}(omega)$ calculated using the experimental values in the Eliashberg equation gives $d-wave$ instability at $T_c$ comparable to the experiments.
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 $ell$ and the properties of the interactions which determin
e $T_c$ is provided. Both interactions induced through exchange of phonons as well as purely electronic fluctuations of spin density, charge density or current density are considered. Special attention is paid to the role of quantum critical fluctuations including pairing due to their virtual exchange as well as de-pairing due to inelastic scattering. In light of the above, empirical data and theory specific to phonon induced superconductivity, in cold atoms, superfluidity in liquid $He^3$, superconductivity in some of the heavy fermion compounds, in Cuprates, in pncitides and the valence skipping compound, is reviewed. The physical basis for the following observation is provided: The universal ratio of s-wave $T_c$ to Fermi-energy for fermions at the unitarity limit with attractive interactions is about 0.15, the ratio of the maximum $T_c$ to the typical phonon frequency in phonon induced s-wave superconductivity is of the same order; 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 a special class of quantum-critical fluctuations, this ratio rises to $O(10^{-2})$. These discussions also suggest factors important for obtaining higher $T_c$.
The loop-current state discovered in the pseudogap phase of cuprates breaks time reversal symmetry and lowers the point group symmetry of the crystal. The order parameter and the magnetic structure within each unit cell which is associated with it ca
n be described by a toroidal moment parallel to the copper-oxide planes. We discuss lattice point group symmetry of the magnetic structure. As an application, we discuss a few effects that necessarily accompany order parameter in the pseudogap phase. The magnitude estimated for these specific effects makes them hard to observe because they rely on the small magnetic fields associated with the order parameter. Effects, associated with the electronic energies are much larger. Some of them have already been discussed.
The coupling between localized spins and phonons can lead to shifts in the dielectric constant of insulating materials at magnetic ordering transitions. Studies on isostructural SeCuO3 (ferromagnetic) and TeCuO3 (antiferromagnetic) illustrate how the
q-dependent spin-spin correlation function couples to phonon frequencies leading to a shift in the dielectric constant. A model is discussed for this spin-phonon coupling. The magnetodielectric coupling in multiferroic materials can be very large at a ferroelectric transition temperature. This coupling is investigated in the recently identified multiferroic Ni3V2O8.
Systematic theoretical results for the effects of a dilute concentration of magnetic impurities on the thermodynamic and transport properties in the region around the quantum critical point of a ferromagnetic transition are obtained. In the quasi-cla
ssical regime, the dynamical spin fluctuations enhance the Kondo temperature. This energy scale decreases rapidly in the quantum fluctuation regime, where the properties are those of a line of critical points of the multichannel Kondo problem with the number of channels increasing as the critical point is approached, except at unattainably low temperatures where a single channel wins out.
