Fermi Liquid Parameters Research Articles

Observation of suppressed viscosity in the normal state of 3He due to superfluid fluctuations

Evidence of fluctuations in transport have long been predicted in 3He. They are expected to contribute only within 100μK of Tc and play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid 3He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk 3He, finding data collapse consistent with the predicted theoretical behavior.

Dipole representation of half-filled Landau level

We introduce a variant of a dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under an exchange of particles and holes. This is implemented by a special constraint on a composite fermion and a composite hole degree of freedom (of an enlarged space), which makes the resulting composite particle (dipole) a symmetric object. We study an effective Hamiltonian that commutes with the constraint on the physical space and fulfills the requirement for boost invariance on the Fermi level. The calculated Fermi liquid parameter ${F}_{2}$ is in good agreement with numerical investigations in Phys. Rev. Lett. 121, 147601 (2018).

Gifts from anomalies: Exact results for Landau phase transitions in metals

Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, \mathbf{q}=0𝐪=0, is a constant independent of frequency, and the real part of the optical conductivity, \sigma(\omega)σ(ω), is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

Nonlinear Fermi liquid transport through a quantum dot in asymmetric tunnel junctions

We study the nonlinear conductance through a quantum dot, specifically its dependence on the asymmetries in the tunnel couplings and bias voltages $V$, at low energies. Extending the microscopic Fermi liquid theory for the Anderson impurity model, we obtain an exact formula for the steady current $I$ up to terms of order ${V}^{3}$ in the presence of these asymmetries. The coefficients for the nonlinear terms are described in terms of a set of the Fermi liquid parameters: the phase shift, static susceptibilities, and three-body correlation functions of electrons in the quantum dots, defined with respect to the equilibrium ground state. We calculate these correlation functions, using the numerical renormalization group approach (NRG), over a wide range of impurity-electron filling that can be controlled by a gate voltage in real systems. The NRG results show that the order ${V}^{2}$ nonlinear current is enhanced significantly in the valence fluctuation regime. It is caused by the order $V$ energy shift of the impurity level, induced in the presence of the tunneling or bias asymmetry. Furthermore, in the valence fluctuation regime, we also find that the order ${V}^{3}$ nonlinear current exhibits a shoulder structure, for which the three-body correlations that evolve for large asymmetries play an essential role.

Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computers

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chemistry and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced density matrices. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and efficient optimization of this subspace. We show that with a simple error mitigation strategy and optimization of compact tensor product bases to minimize the number of terms to sample, these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware. Furthermore, we demonstrate the use of these density matrices for the sampling of non-energetic properties, including dipole moments and Fermi liquid parameters in condensed phase systems, achieving a reliable accuracy with sparse sampling. It appears that uncertainties derived from the iterative optimization of these subspaces is smaller than variances in the energy for a single subspace optimization with current quantum hardware. This boosts the prospect for routine self-consistency to improve the choice of correlated subspaces in hybrid quantum-classical approaches to electronic structure for large systems in this multiscale fashion.

Rise and fall of Landau\u2019s quasiparticles while approaching the Mott transition

Landau suggested that the low-temperature properties of metals can be understood in terms of long-lived quasiparticles with all complex interactions included in Fermi-liquid parameters, such as the effective mass m⋆. Despite its wide applicability, electronic transport in bad or strange metals and unconventional superconductors is controversially discussed towards a possible collapse of the quasiparticle concept. Here we explore the electrodynamic response of correlated metals at half filling for varying correlation strength upon approaching a Mott insulator. We reveal persistent Fermi-liquid behavior with pronounced quadratic dependences of the optical scattering rate on temperature and frequency, along with a puzzling elastic contribution to relaxation. The strong increase of the resistivity beyond the Ioffe–Regel–Mott limit is accompanied by a ‘displaced Drude peak’ in the optical conductivity. Our results, supported by a theoretical model for the optical response, demonstrate the emergence of a bad metal from resilient quasiparticles that are subject to dynamical localization and dissolve near the Mott transition.

Fully algebraic and self-consistent effective dynamics in a static quantum embedding

Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The `energy-weighted' density matrix embedding theory (EwDMET) was established recently as a way to systematically control the resolution of the fragment-environment coupling, and allow for true quantum fluctuations over this boundary to be self-consistently optimized within a fully static framework. In this work, we reformulate the algorithm to ensure that EwDMET can be considered equivalent to an optimal and rigorous truncation of the self-consistent dynamics of dynamical mean-field theory (DMFT). A practical limitation of these quantum embedding approaches is often a numerical fitting of a self-consistent object defining the quantum effects. However, we show here that in this formulation, all numerical fitting steps can be entirely circumvented, via an effective Dyson equation in the space of truncated dynamics. This provides a robust and analytic self-consistency for the method, and an ability to systematically and rigorously converge to DMFT from a static, wave function perspective. We demonstrate that this improved approach can solve the correlated dynamics and phase transitions of the Bethe lattice Hubbard model in infinite dimensions, as well as one- and two-dimensional Hubbard models where we clearly show the benefits of this rapidly convergent basis for correlation-driven fluctuations. This systematically truncated description of the effective dynamics of the problem also allows access to quantities such as Fermi liquid parameters and renormalized dynamics, and demonstrates a numerically efficient, systematic convergence to the zero-temperature dynamical mean-field theory limit.

Crossover between ballistic and diffusive regime in 2D SiGe quantum well

In this manuscript, we report a theoretical investigation of the magneto-conductivity (σ(B,T)) in the metallic side (where dσ/dt<0) of a low densities 2D hole system in SiGe at very low temperature (below 2K). We have reanalyzed the experimental data already prepared and published by Drichko et al. in [23]. The purpose of this study is to determine the dominant electronic transport regime by confronting the experience with current theories. Based on the Fermi-liquid approach and the ZNA theory, we have able to determine the régimes of electronic transport in 2D p-SiGe quantum well. Indeed, the careful analysis of the results shows the coexistence of the two electronic transport regimes: ballistic and diffusive and, above all, a transition from one regime to the other. At low magnetic field (less than 6T), the Fermi liquid parameter values are found negative and positive for the highest values of the parallel magnetic field. The results are consistent with recent works on graphene sample and other similar samples.

Electron-electron interactions in the two-dimensional semiconductor InSe

Electron-electron interactions (EEIs) in 2D van der Waals structures is one of the topics with high current interest in physics. We report the observation of a negative parabolic magnetoresistance (MR) in multilayer 2D semiconductor InSe beyond the low-field weak localization/antilocalization regime, and provide evidence for the EEI origin of this MR behavior. Further, we analyze this negative parabolic MR and other observed quantum transport signatures of EEIs (temperature dependent conductance and Hall coefficient) within the framework of Fermi liquid theory and extract the gate voltage tunable Fermi liquid parameter $F_0^\sigma$ which quantifies the electron spin-exchange interaction strength.

Nuclear saturation energy in effective chiral model within Fermi liquid theory approach

We calculate the relativistic Fermi liquid parameters (RFLPs) for the description of the nuclear saturation energy using a chiral effective Lagrangian. Analytical expressions of Fermi liquid parameters (FLPs) are presented both for the direct and exchange contributions by retaining the meson masses. We present a comparative study of perturbative calculation with mean field results. The FLPs, so determined, are then used to calculate the chemical potential, energy densities, and binding energy for dense nuclear matter interacting via the exchange of σ, ω, and π mesons. In addition, we also estimate bulk quantities like incompressibility and first sound velocity in terms of RFLPs for dense nuclear matter.

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application to the Hubbard model on the triangular lattice at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid to the static fermion-boson response function. In the charge sector the limits of small transferred momentum and frequency of this response function commute at the Mott transition.

Renormalizations in unconventional superconducting states of Ce1−xYbxCoIn5

We have measured the superconducting penetration depth~$\Lambda(T)$ in the heavy-fermion/intermediate-valent superconducting alloy series~Ce$_{1-x}$Yb$_x$CoIn$_5$ using transverse-field muon spin relaxation, to study the effect of intermediate-valent Yb doping on Fermi-liquid renormalization. From $\Lambda(T)$ we determine the superfluid density $\rho_s(T)$, and find that it decreases continuously with increasing nominal Yb concentration~$x$, i.e., with increasing intermediate valence. The temperature-dependent renormalization of the "normal" fluid density~$\rho_N(T) = \rho_s(0) - \rho_s(T)$ in both the heavy-fermion and intermediate valence limits is proportional to the temperature-dependent renormalization of the specific heat. This indicates that the temperature-dependent Fermi-liquid Landau parameters of the superconducting quasiparticles entering the two different physical quantities are the same. These results represent an important advance in understanding of both intermediate valence and heavy-fermion phenomena in superconductors.

Pomeranchuk Instability of Composite Fermi Liquids.

Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F_{ℓ}≤-1 in the angular momentum ℓ=2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational MonteCarlo technique, Fermi liquid parameters F_{ℓ} of the composite fermion Fermi liquid with a finite layer width. We consider F_{ℓ} in different Landau levels n=0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η_{c} is higher for the n=2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n=2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.

Generation of pure superconducting spin current in magnetic heterostructures via nonlocally induced magnetism due to Landau Fermi liquid effects

We propose a mechanism for the generation of pure superconducting spin-current carried by equal-spin triplet Cooper pairs in a superconductor (S) sandwiched between a ferromagnet (F) and a normal metal (N$_{\rm so}$) with intrinsic spin-orbit coupling. We show that in the presence of Landau Fermi-liquid interactions the superconducting proximity effect can induce non-locally a ferromagnetic exchange field in the normal layer, which disappears above the superconducting transition temperature of the structure. The internal Landau Fermi-liquid exchange field leads to the onset of a spin supercurrent associated with the generation of long-range spin-triplet superconducting correlations in the trilayer. We demonstrate that the magnitude of the spin supercurrent as well as the induced magnetic order in the N$_{\rm so}$ layer depends critically on the superconducting proximity effect between the S layer and the F and N$_{\rm so}$ layers and the magnitude of the relevant Landau Fermi-liquid interaction parameter. We investigate the effect of spin flip processes on this mechanism. Our results demonstrate the crucial role of Landau Fermi-liquid interaction in combination with spin-orbit coupling for the creation of spin supercurrent in superconducting spintronics, and give a possible explanation of a recent experiment utilizing spin-pumping via ferromagnetic resonance [Jeon $\it{ et}$ $\it{al.}$, Nat. Mat. ${\bf 17}$, 499 (2018)].

Screening and antiscreening of the pairing interaction in low-density neutron matter

We study pairing in low-density neutron matter including the screening interaction due to the exchange of particle-hole and RPA excitations. As bare force we employ the effective low-momentum interaction $V_{low\,k}$, while the Fermi-liquid parameters are taken from a phenomenological energy density functional (SLy4) which correctly reproduces the equation of state of neutron matter. At low density, we find screening, i.e., pairing is reduced, while at higher densities, we find anti-screening, i.e., pairing is enhanced. This enhancement is mostly due to the strongly attractive Landau parameter $f_0$. We discuss in detail the critical temperature $T_c$ in the limit of low densities and show that the suppression of $T_c$ predicted by Gor'kov and Melik-Barkhudarov can only be reproduced if the cutoff of the $V_{low\,k}$ interaction is scaled with the Fermi momentum. We also discuss the effect of non-condensed pairs on the density dependence of $T_c$ in the framework of the Nozi\`eres-Schmitt-Rink theory.

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.

Momentum distribution in two-orbital Hubbard model: Quantum Monte Carlo approach

The two-dimensional two-orbital Hubbard model is studied with the use of worldline quantum Monte Carlo algorithm. Spectral functions and the density of states for various parameters of the model are obtained in both the undoped and low-doped regimes. The invariance of the Fermi surface with respect to the strength of the interaction is testified. Fermi-liquid parameters of the model are derived.

Weak-coupling analysis of quasiparticle excitations in Sr2RuO4 along the Γ−M cut

We examine normal-state quasiparticle excitations along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}M$ cut in momentum space for the putative $p$-wave superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ on the basis of fluctuation exchange approximation calculations. We take as input first-principles derived parameters for the band structure and spin-orbit and electron-electron interactions. The numerical results are in excellent agreement with data from photoemission experiments and provide insight into the underlying quasiparticle properties. We find that, despite the correlation-induced effective mass increase near the Fermi surface, the full $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ bandwidths are, if anything, increased by correlations. Furthermore, for the $\ensuremath{\gamma}$ band we find anomalous lifetime broadening and a significant temperature of variation of unoccupied state quasiparticle energies for temperatures between 25 and 100 K, both of which are accounted for by the momentum dependence of the electron self-energy. In addition to aiding our understanding of experimental data, these results point to the challenge of assigning appropriate Fermi-liquid parameters or momentum-independent self-energies for schemes that require such approximations in order to model ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$.

Momentum distribution and non-Fermi-liquid behavior in low-doped two-orbital model: Finite-size cluster quantum Monte Carlo approach

The two-dimensional two-orbital Hubbard model is studied with the use of finite-size cluster worldline quantum Monte Carlo algorithm. This model is widely used for simulation of the band structure of FeAs clusters, which are structure elements of Fe-based high-temperature superconductors. The choice of a special basis set of hyper-sites allowed to take into account four-fermion operator terms and to overcome partly the sign problem. Spectral functions and the density of states for various parameters of the model are obtained in the undoped and low-doped regimes. The correlated distortion of the spectral density with the change of doping is observed, and the applicability of the "hard-band" approximation in the doped regime is demonstrated. Profiles of the momentum distribution are obtained for the first Brillouin zone; they have pronounced jump near the Fermi level, which decreases with the growth of the strength of the interaction. The invariance of the Fermi surface with respect to the strength of the interaction is testified. Nesting is found in the case of electron and hole doping. Fermi-liquid parameters of the model are derived. Z-factor grows sharply with the increasing the level of doping, and monotonously decreases with the growth of the strength of the interaction. Moreover, electron-hole doping asymmetry of the Z-factor is revealed. The non-Fermi liquid behaviour and the deviation from Luttinger theorem are observed.

Effective mass in bilayer graphene at low carrier densities: The role of potential disorder and electron-electron interaction

In a two-dimensional electron gas, the electron-electron interaction generally becomes stronger at lower carrier densities and renormalizes the Fermi-liquid parameters, such as the effective mass of carriers. We combine experiment and theory to study the effective masses of electrons and holes ${m}_{e}^{*}$ and ${m}_{h}^{*}$ in bilayer graphene in the low carrier density regime on the order of $1\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{11}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$. Measurements use temperature-dependent low-field Shubnikov--de Haas oscillations observed in high-mobility hexagonal boron nitride supported samples. We find that while ${m}_{e}^{*}$ follows a tight-binding description in the whole density range, ${m}_{h}^{*}$ starts to drop rapidly below the tight-binding description at a carrier density of $n=\phantom{\rule{0.16em}{0ex}}6\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{11}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ and exhibits a strong suppression of 30% when $n$ reaches $2\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{11}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$. Contributions from the electron-electron interaction alone, evaluated using several different approximations, cannot explain the experimental trend. Instead, the effect of the potential fluctuation and the resulting electron-hole puddles play a crucial role. Calculations including both the electron-electron interaction and disorder effects explain the experimental data qualitatively and quantitatively. This Rapid Communication reveals an unusual disorder effect unique to two-dimensional semimetallic systems.