arXiv subjects

Elihu Abrahams

Publications and source records attributed to Elihu Abrahams.

At least 19 recordsLinked to original sources

arXiv2025

What Does The Korringa Ratio Measure?

We present an analysis of the Korringa ratio in a dirty metal, emphasizing the case where a Stoner enhancement of the uniform susceptibilty is present. We find that the relaxation rates are significantly enhanced by disorder, and that the inverse problem of determining the bare density of states from a study of the change of the Knight shift and relaxation rates with some parameter, such as pressure, has rather constrained solutions, with the disorder playing an important role. Some preliminary applications to the case of chemical substitution in the Rb$_{3-x}$K$_x $C$_{60}$ family of superconductors is presented and some other relevant systems are mentioned.

cond-mat↗

arXiv2020

Quantum critical nematic fluctuations and spin excitation anisotropy in iron pnictides

Quantum criticality in iron pnictides involves both the nematic and antiferromagnetic degrees of freedom, but the relationship between the two types of fluctuations has yet to be clarified. Here we study this problem in the presence of a small external uniaxial potential, which breaks the $C_4$-symmetry in the B$_{1g}$ sector. We establish an identity that connects the spin excitation anisotropy, which is the difference of the dynamical spin susceptibilities at $\vec{Q}_1=\left(π,0\right)$ and $\vec{Q}_2=\left(0,π\right)$, with the dynamical magnetic susceptibility and static nematic susceptibility. Using this identity, we introduce a scaling procedure to determine the dynamical nematic susceptibility in the quantum critical regime, and illustrate the procedure for the case of the optimally Ni-doped BaFe$_2$As$_2$[Y. Song \textit{et al.}, Phys. Rev. B 92, 180504 (2015)]. The implications of our results for the overall physics of the iron-based superconductors are discussed.

cond-mat.str-el↗

arXiv2019

Effective Exchange Interactions for Bad Metals and Implications for Iron-based Superconductors

The experimentally observed bad metal behavior in parent iron pnictides and chalcogenides suggests that these systems contain strong electronic correlations and are on the verge of a metal-to-insulator transition. The magnetic excitations in this bad-metal regime mainly derive from the incoherent part of the electronic spectrum away from the Fermi energy. We present a microscopic study of the exchange interactions in such a regime within a slave rotor approach. We find that the exchange interaction is maximized near the Mott transition. Generalizations to the multi-orbital case are discussed, as are the implications for the strength of superconducting pairing amplitude in the iron-based superconductors.

cond-mat.str-el↗

arXiv2018

Superconductivity at an antiferromagnetic quantum critical point: the role of energy fluctuations

Motivated by recent experiments reporting superconductivity only at very low temperature in a class of heavy fermion compounds, we study the impact of energy fluctuations with small momentum transfer on the pairing instability near an antiferromagnetic quantum critical point. While these fluctuations, formed by composite spin fluctuations, were proposed to explain the thermodynamic and transport properties near the quantum critical point of compounds such as YbRh$_{2}$Si$_{2}$ and CeCu$_{6-x}$Au$_{x}$ at $x\approx0.1$, here they are found to strongly suppress $T_{c}$ of the $d$-wave pairing of the hot quasiparticles promoted by the spin fluctuations. Interestingly, if energy fluctuations are strong enough, they can induce triplet pairing involving the quasiparticles of the cold regions of the Fermi surface. Overall, the opposing effects of energy and spin fluctuations lead to a suppression of $T_{c}$.

cond-mat.supr-con↗

arXiv2016

Strong coupling theory of heavy fermion criticality II

We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal governed by $d$-dimensional fluctuations at a quantum critical point, where the electron quasiparticle effective mass diverges. We determine how the critical bosonic order parameter fluctuations are affected by the effective mass divergence. The coupled system of fermions and bosons is found to be governed by two stable fixed points: the conventional weak-coupling fixed point and a new strong-coupling fixed point, provided the boson-boson interaction is irrelevant. The latter fixed point supports hyperscaling, characterized by fractional exponents. The theory is applied to the antiferromagnetic critical point in certain heavy fermion compounds, in which the strong-coupling regime is reached.

cond-mat.str-el↗

arXiv2016

High Temperature Superconductivity in Iron Pnictides and Chalcogenides

Superconductivity develops in metals upon the formation of a coherent macroscopic quantum state of electron pairs. Iron pnictides and chalcogenides are materials that have high superconducting transition temperatures. In this Review, we describe the advances in the field that have led to higher superconducting transition temperatures in iron-based superconductors and the wide range of materials that form them. We summarize both the essential aspects of the normal state and the mechanism for superconductivity. We emphasize the degree of electron-electron correlations and their manifestation in properties of the normal state. We examine the nature of magnetism, analyse its role in driving the electronic nematicity, and discuss quantum criticality at the border of magnetism in the phase diagram. Finally, we review the amplitude and structure of the superconducting pairing, and survey the potential settings for optimizing superconductivity.

cond-mat.supr-con↗

arXiv2016

Magnetic and Ising quantum phase transitions in a model for isoelectronically tuned iron pnictides

Considerations of the bad-metal behavior led to an early proposal for a quantum critical point under a P for As doping in the iron pnictides, which has since been experimentally observed. We study here an effective model for the isoelectronically tuned pnictides using a large-$N$ approach. The model contains antiferromagnetic and Ising-nematic order parameters appropriate for $J_1$-$J_2$ exchange-coupled local moments on an Fe square lattice, and a damping caused by coherent itinerant electrons. The zero-temperature magnetic and Ising transitions are concurrent and essentially continuous. The order-parameter jumps are very small, and are further reduced by the inter-plane coupling; quantum criticality hence occurs over a wide dynamical range. Our results provide the basis for further studies on the quantum critical properties in the P-doped iron arsenides.

cond-mat.str-el↗

arXiv2015

Vertex functions at finite momentum: Application to antiferromagnetic quantum criticality

We analyze the three-point vertex function that describes the coupling of fermionic particle-hole pairs in a metal to spin or charge fluctuations at non-zero momentum. We consider Ward identities, which connect two-particle vertex functions to the self energy, in the framework of a Hubbard model. These are derived using conservation laws following from local symmetries. The generators considered are the spin density and particle density. It is shown that at certain antiferromagnetic critical points, where the quasiparticle effective mass is diverging, the vertex function describing the coupling of particle-hole pairs to the spin density Fourier component at the antiferromagnetic wavevector is also divergent. Then we give an explicit calculation of the irreducible vertex function for the case of three-dimensional antiferromagnetic fluctuations, and show that it is proportional to the diverging quasiparticle effective mass .

cond-mat.str-el↗

arXiv2015

Spin-flip scattering of critical quasiparticles and the phase diagram of YbRh2Si2

Several observed transport and thermodynamic properties of the heavy-fermion compound YbRh2Si2 in the quantum critical regime are unusual and suggest that the fermionic quasiparticles are critical, characterized by a scale-dependent diverging effective mass. A theory based on the concept of critical quasiparticles (CQP) scattering off antiferromagnetic spin fluctuations in a strong-coupling regime has been shown to successfully explain the unusual existing data and to predict a number of so far unobserved properties. In this paper, we point out a new feature of a magnetic field-tuned quantum critical point of a heavy-fermion metal: anomalies in the transport and thermodynamic properties caused by the freezing out of spin-flip scattering of critical quasiparticles and the scattering off collective spin excitations. We show that a step-like behavior as a function of magnetic field of e.g. the Hall coefficient and magnetoresistivity results, which accounts quantitatively for the observed behavior of these quantities. That behavior has been described as a crossover line T*(H) in the T - H phase diagram of YbRh2Si2. Whereas some authors have interpreted this observation as signaling the breakdown of Kondo screening and an associated abrupt change of the Fermi surface, our results suggest that the T* line may be quantitatively understood within the picture of robust critical quasiparticles.

cond-mat.str-el↗

arXiv2014

Strong coupling theory of heavy fermion criticality

We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal at an antiferromagnetic critical point. We show how the critical spin fluctuations at the AFM wavevector q=Q induce energy fluctuations at small q, giving rise to a diverging quasiparticle effective mass over the whole Fermi surface. The coupling of the fermionic and bosonic degrees of freedom leads to a self-consistent relation for the effective mass, which has a strong coupling solution in addition to the well-known weak-coupling, spin-density-wave solution. We thereby use the recently-introduced concept of critical quasiparticles, employing a scale-dependent effective mass ratio m*/m and quasiparticle weight factor Z. As a consequence of the diverging effective mass the Landau Fermi liquid interaction is found to diverge in all channels except the critical one, causing important vertex corrections. The ensuing spin fluctuation spectrum obeys omega/T scaling. Our results are in good agreement with experimental data on the heavy fermion compounds YbRh2Si2$ and CeCu(6-x)Au(x) assuming 3D and 2D spin fluctuations, respectively.

cond-mat.str-el↗

arXiv2013

Evidence for a Kondo destroying quantum critical point in YbRh2Si2

The heavy-fermion metal YbRh$_{2}$Si$_{2}$ is a weak antiferromagnet below $T_{N} = 0.07$ K. Application of a low magnetic field $B_{c} = 0.06$ T ($\perp c$) is sufficient to continuously suppress the antiferromagnetic (AF) order. Below $T \approx 10$ K, the Sommerfeld coefficient of the electronic specific heat $γ(T)$ exhibits a logarithmic divergence. At $T < 0.3$ K, $γ(T) \sim T^{-ε}$ ($ε: 0.3 - 0.4$), while the electrical resistivity $ρ(T) = ρ_{0} + aT$ ($ρ_{0}$: residual resistivity). Upon extrapolating finite-$T$ data of transport and thermodynamic quantities to $T = 0$, one observes (i) a vanishing of the "Fermi surface crossover" scale $T^{*}(B)$, (ii) an abrupt jump of the initial Hall coefficient $R_{H}(B)$ and (iii) a violation of the Wiedemann Franz law at $B = B_{c}$, the field-induced quantum critical point (QCP). These observations are interpreted as evidence of a critical destruction of the heavy quasiparticles, i.e., propagating Kondo singlets, at the QCP of this material.

cond-mat.str-el↗

arXiv2012

Electron Correlation and Spin Dynamics in Iron Pnictides and Chalcogenides

Superconductivity in the iron pnictides and chalcogenides is closely connected to a bad-metal normal state and a nearby antiferromagnetic order. Therefore, considerable attention has been focused on the role of electron correlations and spin dynamics. In this article, we summarize some key experiments that quite directly imply strong electron correlations in these materials, and discuss aspects of the recent theoretical studies on these issues. In particular, we outline a $w$-expansion, which treats the correlation effects using the Mott transition as the reference point. For the parent systems, it gives rise to an effective J1-J2 model that is coupled to the itinerant electrons in the vicinity of the Fermi energy; this model yields an isoelectronically-tuned quantum critical point, and allows a study of the distribution of the spin spectral weight in the energy and momentum space in the paramagnetic phase. Within the same framework, we demonstrate the Mott insulating phase in the iron oxychalcogenides as well as the alkaline iron selenides; for the latter system, we also consider the role of an orbital-selective Mott phase. Finally, we discuss the singlet superconducting pairing driven by the short-range J1-J2 interactions. Our considerations highlight the iron pnictides and chalcogenides as exemplifying strongly-correlated electron systems at the boundary of electronic localization and itinerancy.

cond-mat.str-el↗

arXiv2012

Spin Dynamics of a J1-J2-K Model for the Paramagnetic Phase of Iron Pnictides

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic J_1-J_2 Heisenberg model on a square lattice with a biquadratic coupling $-K (S_i \cdot S_j)^2$ between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this J_1-J_2-K model where the ground state is a (π,0) collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition, and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor S(q,ω) is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary, and gradually split into two parts, forming a pattern around (π,π). Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra on BaFe_2As_2 and SrFe_2As_2.

cond-mat.str-el↗

arXiv2012

Critical quasiparticle theory: Scaling, thermodynamic and transport properties

We use the recently developed critical quasiparticle theory to derive the scaling behavior associated with a quantum critical point (QCP) in a correlated metal. This is applied to the magnetic-field induced QCP observed in YbRh$_2$Si$_2$ (YRS), for which we also derive the critical behavior of the specific heat, resistivity, Gr{\" u}neisen coefficient, and the thermopower. The theory accounts very well for the experimental results

cond-mat.str-el↗

arXiv2011

Spin Dynamics of a $J_1-J_2$ Antiferromagnet and its Implications for Iron Pnictides

Motivated by the recent observation of antiferromagnetic correlations in the paramagnetic phase of iron pnictides, we study the finite-temperature spin dynamics of a two-dimensional $J_1-J_2$ antiferromagnet. We consider the paramagnetic phase in the $J_2>J_1$ regime of a $(π,0)$ collinear ground state, using the modified spin wave theory. Below the mean-field Ising transition temperature, we identify short-range anisotropic antiferromagnetic correlations. We show that the dynamical structure factor $\mathcal{S}(\mathbf{q},ω)$ contains elliptic features in the momentum space, and determine its variation with temperature and energy. Implications for the spin-dynamical experiments in the iron pnictides are discussed.

cond-mat.str-el↗

arXiv2011

Anisotropic in-plane resistivity in the nematic phase of the iron pnictides

We show that the interference between scattering by impurities and by critical spin fluctuations gives rise to anisotropic transport in the Ising-nematic state of the iron pnictides. The effect is closely related to the non-Fermi liquid behavior of the resistivity near an antiferromagnetic quantum critical point. Our theory not only explains the observed sign of the resistivity anisotropy $Δρ$ in electron doped systems, but also predicts a sign change of $Δρ$ upon sufficient hole doping. Furthermore, our model naturally addresses the changes in $Δρ$ upon sample annealing and alkaline-earth substitution.

cond-mat.str-el↗

arXiv2011

Quasiparticles beyond the Fermi liquid and heavy fermion criticality

We give a self-consistent theory of the scale dependent effective mass enhancement m*/m of quasiparticles by 3D antiferromagnetic (AFM) spin fluctuations in the presence of disorder at an AFM quantum critical point. The coupling of fermionic and bosonic degrees of freedom in the critical regime is described in terms of a critical quasiparticle theory. Using the fact that even in the "non-Fermi liquid" regime the quasiparticle width does not exceed the quasiparticle energy, we adopt relations from Fermi liquid theory to determine the dependence of the spin fluctuation spectrum on m*/m, from which the self energy and hence m*/m may be calculated. The self-consistent equation for m*/m has a strong coupling solution provided the initial value is sufficiently large. We argue that in YbRh2Si2, quasi-2D Gaussian fluctuations existing over a wide range drive the system into the 3D strongly coupled fluctuation regime. We find critical exponents of the temperature dependence of the specific heat coefficient γ\propto T^{-1/4} and of the resistivity ρ(T)=ρ(0)+ A T^{3/4} in good agreement with experiments on YbRh2Si2 in the temperature range T < 0.3K.

cond-mat.str-el↗

arXiv2011

Quantum criticality in the iron pnictides and chalcogenides

Superconductivity in the iron pnictides and chalcogenides arises at the border of antiferromagnetism, which raises the question of the role of quantum criticality. In this topical review, we describe the theoretical work that led to the prediction for a magnetic quantum critical point arising out of a competition between electronic localization and itinerancy, and the proposal for accessing it by using isoelectronic P substitution for As in the undoped iron pnictides. We go on to compile the emerging experimental evidence in support of the existence of such a quantum critical point in isoelectronically-tuned iron pnictides. We close by discussing the implications of these results for the physics of the iron pnictides and chalcogenides.

cond-mat.supr-con↗