Fermi Liquid Corrections Research Articles

Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi liquid corrections in quantum dots and magnetic alloys

Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi liquid corrections in quantum dots and magnetic alloys

Tilt-induced many-body corrections to optical conductivity of tilted Dirac cone materials

Katsnelson has shown that, within the Fermi-liquid approach, the optical conductivity of Dirac electrons in graphene is not affected by many-body interactions [M. I. Katsnelson, Eur. Phys. Lett. 84, 37001 (2008)]. We show that, when the Dirac cone is tilted, the Fermi-liquid corrections arise in the optical conductivity in a manner that the correction depends on the angle between the electric field of the incident light and the tilt direction. Therefore the mapping of the optical conductivity for various directions of the incident light enables a determination of the many-body effect in the optical conductivity spectrum of the two-dimensional tilted Dirac cone materials.

Half-quantum vortex pair in the polar-distorted B phase of superfluid He3 in aerogels

Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connected by a Kibble-Lazarides-Shafi wall in superfluid $^{3}\mathrm{He}$ in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur in the polar-distorted $B$ (PdB) phase of superfluid $^{3}\mathrm{He}$. First, the ``impurity''-scattering model used in a previous study is extended to a form interpolating the weakly and strongly anisotropic cases, and it is found that, within the Ginzburg-Landau (GL) approach, Anderson's theorem is satisfied in the strongly anisotropic case. By taking account of the Fermi-liquid (FL) corrected gradient terms and solving numerically the resulting GL free energy, the anisotropy dependence of the vortex structure minimizing the free energy is examined within the weak-coupling approximation. It is found that, close to the transition between the polar and PdB phases, an interplay of the strong anisotropy and the FL correction makes possible the emergence of a large HQV pair in the PdB phase, and that, nevertheless, such a large pair easily shrinks upon deeply entering the PdB phase, indicating that a pinning effect due to the aerogel structure is necessary in order to keep a large pair size there. The obtained result indicates the validity of the London limit for describing the vortex structure, and a consistency with the picture based on the NMR measurement is discussed.

Erratum: Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport [Phys. Rev. B 97 , 035435 (2018)

Received 8 August 2018DOI:https://doi.org/10.1103/PhysRevB.98.079905©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasKondo effectCondensed Matter, Materials & Applied Physics

Erratum: Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport [Phys. Rev. B 97, 035435 (2018)

Erratum: Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport [Phys. Rev. B 97, 035435 (2018)

Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling.

We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017)PRBMDO2469-995010.1103/PhysRevB.95.165404]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex Γ_{σσ^{'};σ^{'}σ}(ω,ω^{'};ω^{'},ω), which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies ω and ω^{'} using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

Quasiclassical Theory of Spin Dynamics in Superfluid $$^3$$ 3 He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States

We develop a theory based on the formalism of quasiclassical Green's functions to study the spin dynamics in superfluid $^3$He. First, we derive kinetic equations for the spin-dependent distribution function in the bulk superfluid reproducing the results obtained earlier without quasiclassical approximation. Then we consider a spin dynamics near the surface of fully gapped $^3$He-B phase taking into account spin relaxation due to the transitions in the spectrum of localized fermionic states. The lifetime of longitudinal and transverse spin waves is calculate taking into account the Fermi-liquid corrections which lead to the crucial modification of fermionic spectrum and spin responses.

Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport

We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys. Rev. B 64, 153305 (2001)] to explore nonequilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the analytic and antisymmetric properties of the vertex function, the spin-dependent Fermi-liquid corrections of order ${T}^{2}$ and ${(eV)}^{2}$ are determined at low temperatures $T$ and low bias voltages $eV$. Away from half filling, these corrections can be expressed in terms of the linear and nonlinear static susceptibilities which represent the two-body and three-body fluctuations, respectively. We calculate the nonlinear susceptibilities using the numerical renormalization group, to explore the differential conductance $dI/dV$ through a quantum dot. We find that the two-body fluctuations dominate the corrections in the Kondo regime at zero magnetic field. The contribution of the three-body fluctuations becomes significant far away from half filling, especially in the valence-fluctuation regime and empty-orbital regimes. In finite magnetic fields, the three-body contributions become comparable to the two-body contributions, and play an essential role in the splitting of the zero-bias conductance peak occurring at a magnetic field of the order of the Kondo energy scale. We also apply our microscopic formulation to the magnetoresistance and thermal conductivity of dilute magnetic alloys away from half filling.

Superconductivity in three-dimensional spin-orbit coupled semimetals

Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, projecting them to the Fermi surface and deriving the corresponding Eliashberg theory. Applying our method to a generic density-density interaction in YPtBi we establish the following results: (i) The pairing strength in each channel uniquely encodes the j=3/2 nature of the Fermi surface band structure--a manifestation of the fundamental difference with ordinary metals. In particular, this implies that Anderson's theorem, which addresses the effect of spin-orbit coupling and disorder on pairing states of spin-1/2 electrons, cannot be applied in this case. (ii) The leading pairing instabilities are different for electron and hole doping. This implies that superconductivity depends on carrier type. (iii) In the case of hole doping--relevant to YPtBi, we find two odd-parity channels in close competition with s-wave pairing. One of these two channels is a multicomponent pairing channel, allowing for the possibility of time-reversal symmetry breaking. (iv) In the case of Coulomb interactions mediated by the long-ranged electric polarization of optical phonon modes, a significant coupling strength is generated in spite of the extremely low density of carriers. Furthermore, non-linear response and Fermi liquid corrections can favor non-s-wave pairing and potentially account for the experimentally-observed Tc.

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG ({\epsilon}FRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in {\epsilon}FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the {\epsilon}FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of {\epsilon}FRG to the spinless disordered Hubbard model we calculate its phase-boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S = 1/2 is also given.

Anomalous Local Fermi Liquid in f2-Singlet Configuration: Impurity Model for Heavy-Electron System UPt3

It is shown by the Wilson numerical renormalization group method that a strongly correlated impurity with a crystalline-electric-field singlet ground state in the f^2-configuration exhibits an anomalous local Fermi liquid state in which the static magnetic susceptibility remains an uncorrelated value while the NMR relaxation rate is enhanced in proportion to the square of the mass enhancement factor. Namely, the Korringa-Shiba relation is apparently broken. This feature closely matches the anomalous behaviors observed in UPt_3, i.e., the coexistence of an unenhanced value of the Knight shift due to quasiparticles contribution (the decrease across the superconducting transition) and the enhanced relaxation rate of NMR. Such an anomalous Fermi liquid behavior suggests that the Fermi liquid corrections for the susceptibility are highly anisotropic.

Superfluid3He in a restricted geometry with a perpendicular magnetic field

We theoretically investigate the role of surface Andreev bound states (SABSs) on the phase diagram and spin susceptibilities of superfluid 3He confined to a restricted geometry. We first explicitly derive the dispersion of the SABS in 3He-B in the presence of a magnetic field, where the Majorana Ising spin and the spin susceptibility contributed from the SABS are associated with the SO(3) order parameter manifold. Subsequently, based on the quasiclassical Eilenberger theory with Fermi liquid corrections, we discuss the nonlinear effect of a magnetic field on the SABS, where the magnetic field is perpendicular to the specular surface. It is directly demonstrated that a gapped SABS strongly enhances the magnetization density and spin susceptibility at the surface, compared with that in the normal 3He. To capture the characteristics of the SABS, we show the field- and temperature-dependences of the spatially averaged susceptibility which is detectable through NMR experiments. It turns out that the contribution of the SABS leads to nonmonotonic temperature-dependence of the spin susceptibility. Furthermore, we present the superfluid phase diagram, where the B-phase undergoes a first-order (second-order) phase transition to A-phase or planar phase at low (high) temperatures.

Current-current Fermi-liquid corrections to the superconducting fluctuations on conductivity and diamagnetism

We analyze the behavior of the superconducting-fluctuations contribution to diamagnetism and conductivity in a model system having current-current interactions. We show that in proximity to a Mott-insulating phase, one recovers an overall suppression of the fluctuating contribution to the conductivity with respect to diamagnetism, in close analogy with recent experiments on the underdoped phase of cuprate superconductors.

Theory of nonequilibrium transport in theSU(N)Kondo regime

Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an $\text{SU}(N)$ Kondo model, focusing on the case $N=4$ relevant to carbon nanotube dots. We show that for general $N$, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.

Long-wavelength correlations and transport in a marginal Fermi liquid

Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi surface is proportional to the energy measured from the chemical potential, ${\ensuremath{\tau}}_{i}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\epsilon}$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional Fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.

Temperature dependence of superfluid density in YBa2Cu3O7−δ and Y0.7Ca0.3Ba2Cu3O7−δ thin films: A doping dependence study of the linear slope

By using a microstrip ring resonator to measure the temperature dependence of the in-plane magnetic penetration depth λ(T) in YBa2Cu3O7−δ (YBCO) and Y0.7Ca0.3Ba2Cu3O7−δ (Ca-YBCO) epitaxially grown thin films, the linear temperature dependence of the superfluid density ρs/m∗≡1/λ2(T) was observed from the under- to the overdoped regime at the temperatures below TTc≈0.3. For the underdoped regime of YBCO and Ca-YBCO thin films, the magnitude of the slope d(1/λ2(T))/dT is insensitive to doping, and it can be treated in the framework of projected d-density-wave model. Combining these slope values with the thermal conductivity measurements, the Fermi-liquid correction factor α2 from the Fermi-liquid model, suggested by Wen and Lee, was revealed here with various doping levels.

Concentration dependence of the attenuation of first sound in supersaturated superfluid He3–4He solutions under pressure

The concentration dependence of the attenuation coefficient of first sound in superfluid He3–4He solutions in the saturation and supersaturation regions is investigated experimentally at pressures of 0–10 atm. An original technique of continuous variation of the concentration in situ by variation of the osmotic and thermomechanical pressures is used, permitting measurements to be made in the long-lived metastable phase of the superfluid solutions. It is shown that the data obtained are described well in terms of the theory of sound propagation in a gas of Fermi excitations without taking the Fermi-liquid corrections into account. The corresponding values of the effective mass and relaxation time of He3 quasiparticles are taken from an analysis of the existing experimental data. Within the experimental error, no excess sound attenuation was found in the region of supersaturated solutions.

Magnetic Susceptibility of the Balian-Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of 3He impregnated into high-porosity (98%) silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian–Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure 3He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid 3He in aerogel within the framework of the Fermi-liquid theory of superfluid 3He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of 3He-aerogel compared to pure3He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid 3He.

Impurity-induced quasiparticle transport and universal-limit Wiedemann-Franz violation ind-wave superconductors

Due to the node structure of the gap in a d-wave superconductor, the presence of impurities generates a finite density of quasiparticle excitations at zero temperature. Since these impurity-induced quasiparticles are both generated and scattered by impurities, prior calculations indicate a universal limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}0,$ $\stackrel{\ensuremath{\rightarrow}}{T}0)$ where the transport coefficients obtain scattering-independent values, depending only on the velocity anisotropy ${v}_{f}{/v}_{2}.$ We improve upon prior results, including the contributions of vertex corrections and Fermi-liquid corrections in our calculations of universal-limit electrical, thermal, and spin conductivity. We find that while vertex corrections modify electrical conductivity and Fermi-liquid corrections renormalize both electrical and spin conductivity, only thermal conductivity maintains its universal value, independent of impurity scattering or Fermi-liquid interactions. Hence, low-temperature thermal conductivity measurements provide the most direct means of obtaining the velocity anisotropy for high-${T}_{c}$ cuprate superconductors.

Effects of orbital correlation on Drude weight in ferromagnetic metallic phase of La 1− xSr xMnO 3

It is argued that a large discrepancy between the Drude weight and the specific heat coefficient observed in ferromagnetic metallic phase of La 1− x Sr x MnO 3 can be understood as a result of a Fermi-liquid correction F 1 s due to backward scattering of quasi-particles mediated by antiferro-orbital fluctuations. The Ward identity requires that the single-particle spectral weight at the Fermi level vanishes when F 1 s→−3.