Landau Fermi Liquid Theory Research Articles

Magnetic Spin Susceptibility of quasi-particles in metals using the Landau Fermi Liquid Theory

    38  In this work, the magnetic spin susceptibility of quasi-particles in metals were computed for some metals based on the modified Landau Fermi Liquids Theory using the electron density parameter. The results showed that for each metal, the Landau magnetic spin susceptibility of quasi-particles is higher than the computed magnetic spin susceptibility of quasi-particles and experimental values. This may be due to the fact that the Landau parameter must have been over estimated in its application. The computed magnetic spin susceptibility of quasi-particles is in good agreement with the experimental values of metals available with a remarkable agreement at. The better estimation of the magnetic spin susceptibility of quasi-particles using the modified Landau Fermi Liquid theory were compared with available experimental values. This show that the introduction of the electron density parameter in the Landau Fermi Liquid theory is promising in predicting the contribution of quasi-particles to the bulk properties of metals. The magnetic spin susceptibility of quasi-particles for transition metals is higher than most of the magnetic spin susceptibility of quasi-particles for alkali metals. This suggests that the magnetic spin susceptibility is considerably higher for most transition metals due to the incomplete inner electronic shells as more quasi-particles can be excited which enhances their susceptibility than the alkali metals.

Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale.

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Modulating electrical transport properties of SnSe crystal to improve the thermoelectric power factor by adjusting growth method

The SnSe crystal is a promising candidate in the field of thermoelectric materials. In order to elucidate basic physics in the SnSe system, here we report the heavily hole doping SnSe single crystals by the flux method (using alkali halide as solvent). Compared to bad-metal behavior of SnSe grown by the Bridgeman method, the flux-grown SnSe crystals show the metallic conductive behavior consistent with the Landau Fermi liquid (resistivity ρ ∼ T2) with temperatures ranging from 2 to 300 K. Combined angle-resolved photoemission spectroscopy and empirical Landau Fermi liquid theory, screening lengths λ of Coulomb electron–electron interaction U of SnSe grown by the flux method are 6.6 Å and 6.1 eV, which are much higher than those of normal metals. Remarkably, the excellent electrical conductivity (870 S/cm) of the SnSe crystal grown by the flux method at room temperature is attributed to the higher hole concentration (∼3.8 × 1019 cm−3) and large mobility (152.2 cm2 V−1 s−1). Meanwhile, these SnSe crystals still have large Seebeck coefficients (∼190 μV/K). Thus, the SnSe crystals grown by the flux method have an ultrahigh power factor [∼31.5 μW/(cm K2)] at room temperature, which is ten times larger than that of SnSe crystals grown by the Bridgeman method and as best as currently reported results. Our work shows a method for growing heavily hole-doped SnSe crystals, which provides a platform for understanding the electrical properties and improving its thermoelectric performance.

Flat bands and strongly correlated Fermi systems

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which Landau Fermi-liquid (LFL) theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle-hole (C) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity dI/dV, where I is the current and V the bias voltage, is a symmetric function of V. Thus, it has been predicted that the conductivity becomes asymmetric for HF metals such as CeCoIn5 and . In these systems, the background electron liquid is considered to undergo a transformation that renders a portion of its excitation spectrum dispersionless, giving rise to so-called flat bands. The presence of a flat band indicates that the system is close to a special quantum critical point, namely a topological fermion-condensation quantum phase transition. An essential aspect of the behavior of a system hosting a flat band is that application of a magnetic field can restore its normal Fermi-liquid properties, including T- and C-invariance, with the differential conductivity again becoming a symmetric function of V. This behavior has been observed in recent measurements of tunneling conductivity in both and graphene. Also within the FC framework, we describe and explain recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that the observed scaling is explained by the emergence of flat bands formed by fermion condensation.

Proto-neutron stars in the Thomas-Fermi theory

The structure and composition of proto-neutron stars (PNSs) are studied by the equation of state (EOS) of hot baryonic matter in β−equilibrium. On the basis of the Landau Fermi-liquid theory (LFT), the Thomas-Fermi (TF) approximation is used in a semi-classical mean-field (MF) model to present an isentropic description of PNS matter including hyperons. Our findings for the PNS structure indicate that higher values of the proton abundance may exist at higher baryonic densities. In addition, the maximum mass of PNSs is increased by the effects of neutrino trapping and, therefore, rising of the lepton number, since the EOS of PNS matter becomes stiffer. However, this maximum value is slightly affected by the changes in the entropy per baryon.

Shear sound of two-dimensional Fermi liquids

We study the appearance of a sharp collective mode which features transverse current fluctuations within the bosonization approach to interacting two-dimensional Fermi liquids. This mode is analogous to the shear sound modes in elastic media, and, unlike the conventional zero sound mode, it is damped in weakly interacting Fermi liquids and only separates away from the particle-hole continuum when the quasiparticle mass becomes twice the transport mass $m^* \gtrsim 2 m$. The shear sound should be present in a large class of interacting charged and neutral Fermi liquids especially those proximate to critical points where the quasiparticle mass diverges. In metals this mode remains linearly dispersing in the presence of the long-ranged Coulomb force, unlike the conventional zero sound mode which becomes the plasma mode. We also detail a quick path between bosonization and classical Landau's Fermi liquid theory by constructing a mapping between the solutions of the classical kinetic equation and the quantized bosonic eigenmodes. By further mapping the kinetic equation into a 1D tight-binding model we solve for the entire spectrum of collective and incoherent particle-hole excitations of Fermi liquids with non-zero $F_0$ and $F_1$ Landau parameters.

Beyond-mean-field effective masses in the nuclear Fermi liquid from axial breathing modes

Axial breathing modes are studied within the nuclear energy--density--functional theory to discuss the modification of the nucleon effective mass produced beyond the mean--field approximation. This analysis is peformed with the subtracted second random--phase--approximation (SSRPA) model applied to two nuclei, $^{48}$Ca and $^{90}$Zr. Analyzing the centroid energies of axial breathing modes obtained with the mean--field--based random--phase approximation and with the beyond--mean--field SSRPA model, we estimate the modification (enhancement) of the effective mass which is induced beyond the mean field. This is done by employing a relation, obtained with the Landau's Fermi liquid theory, between the excitation frequency of axial modes to $\sqrt{m/m^*}$, where $m$ ($m^*$) is the bare (effective) mass. Such an enhancement of the effective mass is discussed in connection with the renormalization of single--particle excitation energies generated by the energy--dependent SSRPA self-energy correction. We find that the effective beyond--mean--field compression of the single--particle spectrum produced by the self--energy correction is coherent with the increase of the effective mass estimated from the analysis of axial breathing modes.

Collective dynamics of Fermi surface fluctuations in an interacting Weyl metal phase

Instabilities in a Landau's Fermi-liquid state occur, increasing the strength of interaction parameters in the Landau's Fermi-liquid theory. Introducing both the Berry curvature and chiral anomaly into this theoretical framework, we investigate collective dynamics of Fermi surface fluctuations and reveal their instabilities in an interacting Weyl metal phase with broken time reversal symmetry. Recently, a topological Fermi-liquid theory has been proposed to describe this interacting Weyl metal phase, where not only the Berry curvature but also the chiral anomaly is introduced into the Landau's Fermi-liquid theory [Phys. Rev. B 95, 205113 (2017)]. Based on the Boltzmann-equation framework, we find criteria for the stability of the topological Fermi-liquid state as a function of forward-scattering Landau's interaction parameters and the distance of a pair of Weyl points given by an external magnetic field. In addition to these instability criteria for general angular momentum channels, we investigate the dispersion relation of the zero-sound mode as the simplest example of such Fermi surface fluctuations. Zero-sound modes are well-defined collective excitations in a Landau's Fermi-liquid state, given by the collective dynamics of Fermi surface deformations in the spin-singlet channel with zero angular momentum, where their instability is related with phase separation. We find that the role of the Berry curvature changes the instability criteria of the Landau's Fermi-liquid state. Even if the zero-sound mode is stable in the region of the forward-scattering amplitude, the Berry curvature gives rise to Landau damping beyond the Landau's Fermi-liquid theory. Based on the instability criterion of the zero-sound mode, we propose a phase diagram for a topological Fermi-liquid state against the phase separation in the plane of Landau's interaction parameter and effective Berry curvature, which generalizes the one-dimensional phase diagram of the Landau's Fermi-liquid theory.

Low-temperature resistance in metals without inversion center

The well known quadratic low-temperature dependence of resistance in ordinary metals habitually serves as the criterium of applicability of the Landau Fermi liquid theory to the description of electron liquid in concrete material. Such a type of behavior is determined by momentum relaxation due to the electron-electron scattering.Here I consider this problem in the metals without inversion center. It is shown that the corresponding scattering time at temperatures much smaller than the spin-orbit coupling is practically temperature independent.

Thomas–Fermi approximation for β-stable nuclear matter in the Landau Fermi-liquid theory

An isentropic description of the equation of state (EOS) for β-stable nuclear matter (BSNM) is presented in a semi-classical mean-field model. Within the Thomas–Fermi (TF) approximation, the Landau Fermi-liquid theory (LFT) is used in a self-consistent approach. Accordingly, isentropic thermodynamics of BSNM is investigated for the neutrino-free and neutrino-trapped cases. We find that the EOS for neutrino-trapped matter is stiffer than the one for neutrino-free matter. Our findings can set the stage for profound studies about the structure and composition of proto-neutron stars (PNSs).

Asymmetric Tunneling Conductance and the Non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.

Fermi liquid, clustering, and structure factor in dilute warm nuclear matter

Properties of nuclear systems at subsaturation densities can be obtained from different approaches. We demonstrate the use of the density autocorrelation function which is related to the isothermal compressibility and, after integration, to the equation of state. This way we connect the Landau Fermi liquid theory well elaborated in nuclear physics with the approaches to dilute nuclear matter describing cluster formation. A quantum statistical approach is presented, based on the cluster decomposition of the polarization function. The fundamental quantity to be calculated is the dynamic structure factor. Comparing with the Landau Fermi liquid theory which is reproduced in lowest approximation, the account of bound state formation and continuum correlations gives the correct low-density result as described by the second virial coefficient and by the mass action law (nuclear statistical equilibrium). Going to higher densities, the inclusion of medium effects is more involved compared with other quantum statistical approaches, but the relation to the Landau Fermi liquid theory gives a promising approach to describe not only thermodynamic but also collective excitations and non-equilibrium properties of nuclear systems in a wide region of the phase diagram.

Breakdown of Landau Fermi liquid theory: Restrictions on the degrees of freedom of quantum electrons

One challenge in contemporary condensed matter physics is to understand unconventional electronic physics beyond the paradigm of Landau Fermi-liquid theory. Here, we present a perspective that posits that most such examples of unconventional electronic physics stem from restrictions on the degrees of freedom of quantum electrons in Landau Fermi liquids. Since the degrees of freedom are deeply connected to the system's symmetries and topology, these restrictions can thus be realized by external constraints or by interaction-driven processes via the following mechanisms: (i) symmetry breaking, (ii) new emergent symmetries, and (iii) nontrivial topology. Various examples of unconventional electronic physics beyond the reach of traditional Landau Fermi liquid theory are extensively investigated from this point of view. Our perspective yields basic pathways to study the breakdown of Landau Fermi liquids and also provides a guiding principle in the search for novel electronic systems and devices.

Renormalized Landau quasiparticle dispersion revealed by photoluminescence spectra from a two-dimensional Fermi liquid at the MgZnO/ZnO heterointerface

We analyze the low-temperature photoluminescence spectra from two-dimensional electron systems (2DESs) confined at ${\mathrm{Mg}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}\mathrm{O}$/ZnO heterojunctions as the electron density is decreased from $2.3\ifmmode\times\else\texttimes\fi{}{10}^{12}$ to $3.5\ifmmode\times\else\texttimes\fi{}{10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}2}$. The value of the quasiparticle optical density-of-states mass is directly extracted from the width of the 2DES photoluminescence band and is shown to renormalize and double from the value close to that of bulk ZnO material, $0.3{m}_{0}$ (${m}_{0}$ is the bare electron mass), to $0.6{m}_{0}$ due to electron-electron interactions as the interaction parameter ${r}_{s}$ increases from 2.4 to 6.5. The experimentally probed quasiparticle energies far exceed the limits of Landau's Fermi-liquid theory.

Violation of Ohm's law in a Weyl metal.

Ohm's law is a fundamental paradigm in the electrical transport of metals. Any transport signatures violating Ohm's law would give an indisputable fingerprint for a novel metallic state. Here, we uncover the breakdown of Ohm's law owing to a topological structure of the chiral anomaly in the Weyl metal phase. We observe nonlinear I-V characteristics in Bi0.96Sb0.04 single crystals in the diffusive limit, which occurs only for a magnetic-field-aligned electric field (E∥B). The Boltzmann transport theory with the charge pumping effect reveals the topological-in-origin nonlinear conductivity, and it leads to a universal scaling function of the longitudinal magnetoconductivity, which completely describes our experimental results. As a hallmark of Weyl metals, the nonlinear conductivity provides a venue for nonlinear electronics, optical applications, and the development of a topological Fermi-liquid theory beyond the Landau Fermi-liquid theory.

Thomas–Fermi approximation for the equation of state of nuclear matter: A semi-classical approach from the Landau Fermi-Liquid theory

The equation of state (EOS) of nuclear matter is investigated in a semi-classical mean-field (MF) approach. Starting from the phase-space NN-interaction of Myers and Swiatecki [Nucl. Phys. A 601 (1996) 141], the EOS of nuclear matter by the Thomas–Fermi approximation is derived. A self-consistent semi-classical approach is presented by employing the Landau Fermi-Liquid theory (LFT). In our statistical approach, the phase-space occupation number can be expressed in terms of an extended effective mass which is affected by both temperature and nucleonic density. Accordingly, an explicit expression of the nucleonic chemical potential inside the nucleonic occupation number can be obtained. Special attention is also devoted to the density dependence of the nuclear symmetry free energy at different temperatures. The results of this model are compared with other theoretical predictions.

Topological Fermi-liquid theory for interacting Weyl metals with time reversal symmetry breaking

Introducing both Berry curvature and chiral anomaly into Landau's Fermi-liquid theory, we construct a topological Fermi-liquid theory, applicable to interacting Weyl metals in the absence of time reversal symmetry. Following the Landau's Fermi-liquid theory, we obtain an effective free-energy functional in terms of the density field of chiral fermions. The density field of chiral fermions is determined by a self-consistent equation, minimizing the effective free-energy functional with respect to the order-parameter field. Beyond these thermodynamic properties, we construct Boltzmann transport theory to encode both the Berry curvature and the chiral anomaly in the presence of forward scattering of a Fermi-liquid state, essential for understanding dynamic correlations in interacting Weyl metals. This generalizes the Boltzmann transport theory for the Landau's Fermi-liquid state in the respect of incorporating the topological structure and extends that for noninteracting Weyl metals in the sense of introducing the forward scattering. Finally, we justify this topological Fermi-liquid theory, generalizing the first-quantization description for noninteracting Weyl metals into the second-quantization representation for interacting Weyl metals. First, we derive a topological Fermi-gas theory, integrating over high-energy electronic degrees of freedom deep inside a pair of chiral Fermi surfaces. As a result, we reproduce a topological Drude model with both the Berry curvature and the chiral anomaly. Second, we take into account interactions between such low-energy chiral fermions on the pair of chiral Fermi surfaces. We perform the renormalization group analysis, and find that only forward scattering turns out to be marginal above possible superconducting transition temperatures, justifying the topological Fermi-liquid theory of interacting Weyl metals with time reversal symmetry breaking.

Irreversible thermodynamics of uniform ferromagnets with spin accumulation: Bulk and interface dynamics

Using ideas from Landau's Fermi-liquid theory, we apply irreversible thermodynamics to conducting and insulating ferromagnets with magnetic variables $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ for the quantization axis and for the spin accumulation $\stackrel{P\vec}{m}$ of the nonequilibrium excitations; thus the total magnetization is taken to be $\stackrel{P\vec}{\mathcal{M}}=\stackrel{P\vec}{M}+\stackrel{P\vec}{m}$. The resulting theory closely corresponds to the theory of Silsbee et al. [Silsbee, Janossy, and Monod, Phys. Rev. B 19, 4382 (1979)]. For the bulk, in addition to confirming the usual Landau-Lifshitz equation for $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ and a Bloch-like equation for $\stackrel{P\vec}{m}$ (with a nonuniform precession term), there are two related cross-relaxation terms between the transverse parts of the nonequilibrium $\stackrel{P\vec}{m}$ and $\stackrel{P\vec}{M}$. Unlike the s-d model, where in a field $\stackrel{P\vec}{H}$ the equilibrium magnetizations ${\stackrel{P\vec}{M}}_{s}$ and ${\stackrel{P\vec}{M}}_{d}$ are both nonzero, for this m-M model in a field $\stackrel{P\vec}{H}$, only the equilibrium magnetization $\stackrel{P\vec}{M}$ is nonzero. For the interface, the boundary condition for $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ is given by micromagnetics, and that for $\stackrel{P\vec}{m}$ is given by irreversible thermodynamics, where the current of transverse spins crossing the interface is proportional to the discontinuity in the transverse part of the vector spin chemical potential. $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}, \stackrel{P\vec}{m}$, and $\stackrel{P\vec}{H}$ are coupled; in the decoupled approximation, we find the wave vectors for the modes of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ and the transverse $\stackrel{P\vec}{m}$. We discuss reciprocity between spin pumping ($\stackrel{P\vec}{\mathcal{M}}$ driven out of the ferromagnet) and spin transfer torque ($\stackrel{P\vec}{\mathcal{M}}$ driven into the ferromagnet).

Berry Fermi liquid theory

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory.

Fermi liquid theory applied to a film on an oscillating substrate

We have studied the transmission of transverse oscillations through a thin Fermi liquid film, using Landau's Fermi liquid theory. Fermi liquid theory describes the dynamics of interacting, degenerate fermion systems, for example non-superfluid, i.e.\ normal state \textsuperscript{3}He at millikelvin temperatures. The response of a Fermi liquid to the transverse oscillations of a planar substrate has previously been calculated for a fluid layer of infinite thickness. We have modified these calculations for application to a film of finite thickness, either with a free surface, or as confined between two parallel substrates. The equations take into account contributions to the acoustic impedance from both the collective transverse zero sound mode, as well as the incoherent single-quasiparticle excitations and are solved using numerical methods.