Fermi Liquid State Research Articles

Mn-induced spin glass behavior in metallic Ir3Sn7−x Mn x

Transition metal stannides are usually semiconductors with a narrow band gap. We report experimental investigation on metallic Ir3Sn7–x Mn x (x = 0 and 0.56). Single crystal x-ray diffraction refinement indicates that Ir3Sn7–x Mn x crystals form a cubic structure (space group Im m) with the lattice parameter a = 9.362(4) Å for x = 0 and 9.328(6) Å for x = 0.56. The electrical resistivity shows metallic behavior between 2 K and 300 K with T 2 dependence at T < 30 K for x = 0, reflecting the Fermi-liquid ground state. While Ir3Sn7 exhibits weak diamagnetism, partial substitution of Sn by Mn results in spin glass behavior in Ir3Sn7−x Mn x below T g ∼ 13 K for x = 0.56. Remarkably, an upturn in the resistivity is observed in x = 0.56 below ∼2T g, suggesting strong spin fluctuation. This fluctuation is suppressed by the application of magnetic field, which is reflected in the observation of negative magnetoresistance. The unusual properties that emerge due to Mn doping are discussed.

Enhancement of electron correlations and spin density wave fluctuations of the organic superconductor λ−(BETS)2GaCl4 under pressure proved by C13 NMR

We performed $^{13}\mathrm{C}$ NMR measurements on an organic superconductor $\ensuremath{\lambda}\text{\ensuremath{-}}{(\mathrm{B}\mathrm{E}\mathrm{T}\mathrm{S})}_{2}\mathrm{Ga}{\mathrm{Cl}}_{4}$ [BETS: bis(ethylenedithio)tetraselenafulvalene] to investigate the pressure effect on the spin density wave (SDW) fluctuations at low temperatures, which were observed at ambient pressure. We found that the spin-lattice relaxation rate divided by temperature $(1/{T}_{1}T)$ is significantly enhanced at low temperatures at 3 kbar, implying enhancement of the SDW fluctuation. When further pressure is applied, increase in $1/{T}_{1}T$ at low temperatures is suppressed and $1/{T}_{1}T$ becomes temperature independent, indicating the Fermi liquid state. Moreover, we revealed that the Korringa factor under pressure becomes double compared to its value at ambient pressure, suggesting a significant change in electron correlation. We discuss the effect of the SDW fluctuation and the electron correlation on the unconventional superconductivity.

Orbitally selective breakdown of the Fermi liquid and simultaneous enhancement of metallic and insulating states in correlated multiband systems with spin-orbit coupling

We show that spin-orbit coupling (SOC) plays Janus-faced roles on the orbitally-selective Mott transitions in a three-orbital Hubbard model with crystal field splitting at a specific filling of $2/3$, which is a minimal Hamiltonian for ruthenates. While the SOC favors metallic state due to enhancement of orbital hybridization at smaller on-site Coulomb repulsions, it stabilizes the Mott insulating state ascribed to lifting of orbital degeneracies and enhancement of band polarizations at larger electronic interaction. Moreover, an orbitally-selective non-Fermi liquid (OSnFL), where breakdown and retention of the Fermi liquid coexist in different orbitals, emerges between the orbitally-selective Mott phase and the Fermi-liquid state. This novel state can be used to account for the exotic metallic behavior observed in 4$d$ materials, such as Ca$_{1.8}$Sr$_{0.2}$RuO$_4$, Ba$_2$RuO$_4$ under strain and Sr$_2$RuO$_4$ under uniaxial pressure. We propose that orbitally-selective Kondo breakdown may account for the OSnFL.

Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

We present a new method for calculating Renyi entanglement entropies for fermionic field-theories originating from microscopic Hamiltonians. The method builds on an operator identity which we discover for the first time. The identity leads to the representation of traces of operator products, and thus Renyi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out-of-equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well known expressions for entanglement entropy in terms of the correlation matrix for non-interacting fermions. We demonstrate the effectiveness of the method by explicitly formulating the field theory for Renyi entropy in a few zero and higher-dimensional large-$N$ interacting models based on the Sachdev-Ye-Kitaev (SYK) model, and for the Hubbard model within dynamical mean-field theory (DMFT) approximation. We use the formulation to compute Renyi entanglement entropy of interacting Fermi liquid (FL) and non-Fermi liquid (NFL) states in the large-$N$ models and compare successfully with the results obtained via exact diagonalization for finite $N$. We elucidate the connection between entanglement entropy and residual entropy of the NFL ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to FL transition. Furthermore, we employ the method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal described by a chain of SYK dots.

Signatures of multiple charge excitations in resonant inelastic x-ray scattering spectra of metals

We study how multiple charge excitations appear in the resonant inelastic x-ray scattering (RIXS) spectra of metals. The single excitations in the problem are the plasmons and electron-hole pairs, and multi-excitation processes are usually neglected. However, at small momentum transfer the multi-excitation contributions may dominate the signal and one needs to understand how to interpret the data. In particular, we demonstrate how to "decode" the total multi-excitation intensity and extract the plasmon dispersion. While our calculations are based on the random phase approximation, which does not allow to obtain quantitatively precise results in the entire region of parameters, we expect them to capture semi-qualitatively all features expected for charged Fermi-liquid states, including universal and singular properties of the RIXS spectra.

Scrambling versus relaxation in Fermi and non-Fermi liquids

We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $N$, allows us to clarify the relations between the quasi-particle relaxation rate $1/\tau$ and the Lyapunov exponent $\lambda_L$ characterizing scrambling. In the Fermi liquid states we find that the quasi-particle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/\tau \gg T$, we find that $\lambda_L$ is always $T$-linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. $\lambda_L$ approaches the general upper bound $2\pi T$ at the transition to a fast scrambling state. Finally in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a non analytic function $\sim g \ln (1/g)$ of the coupling constant $g$.

Unconventional free charge in the correlated semimetal Nd2Ir2O7

Nd2Ir2O7 is a correlated semimetal with the pyrochlore structure, in which competing spin-orbit coupling and electron-electron interactions are believed to induce a time-reversal symmetry broken Weyl semimetal phase characterized by pairs of topologically protected Dirac points at the Fermi energy. However, the emergent properties in these materials are far from clear, and exotic new states of matter have been conjectured. Here we demonstrate optically that at low temperatures the free carrier spectral weight is proportional to T^2 where T is the temperature, as expected for massless Dirac electrons. However, we do {\em not} observe the corresponding T^3 term in the specific heat. That the system is not in a Fermi liquid state is further corroborated by the "Planckian" T-linear temperature dependence of the momentum relaxation rate and the progressive opening of a correlation-induced gap at low temperatures. These observations can not be reconciled within the framework of band theory of electron-like quasiparticles and point toward the effective decoupling of the charge transport from the single particle sector.

Thermoelectric response and entropy of fractional quantum Hall systems

We study thermoelectric transport properties of fractional quantum Hall systems based on exact diagonalization calculation. Based on the relation between thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity $\alpha_{xy}$ has powerlaw scaling $\alpha_{xy} \propto T^{\eta}$ for gapless composite Fermi-liquid states at filling number $\nu=1/2$ and $1/4$ at low temperature ($T$), with exponent $\eta \sim 0.5$ distinctly different from Fermi liquids. The powerlaw scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior at low $T$. In contrast, for $1/3$ fractional quantum Hall state, $\alpha_{xy}$ vanishes at low $T$ with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish a new manifestation of the non-Fermi-liquid nature of quantum Hall fluids at finite temperature.

Lifshitz transition in triangular lattice Kondo-Heisenberg model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11704166, and 11834005), the Fundamental Research Funds for the Central Universities, China, and PCSIRT, China (Grant No. IRT-16R35).

Motivated by recent experimental progress on triangular lattice heavy-fermion compounds, we investigate possible Lifshitz transitions and the scanning tunnel microscope (STM) spectra of the Kondo–Heisenberg model on the triangular lattice. In the heavy Fermi liquid state, the introduced Heisenberg antiferromagnetic interaction (JH) results in the twice Lifshitz transition at the case of the nearest-neighbour electron hopping but with next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole hopping but with next-nearest-neighbour electron hopping, respectively. Driven by JH, the Lifshitz transitions on triangular lattice are all continuous in contrast to the case on square lattice. Furthermore, the STM spectra shows rich line-shape which is influenced by the Kondo coupling JK, the Heisenberg antiferromagnetic interaction JH, and the ratio of the tunneling amplitude of f-electron tf versus conduction electron tc. Our work provides a possible scenario to understand the Fermi surface topology and the quantum critical point in heavy-fermion compounds.

Particle-Hole Duality, Emergent Fermi Liquids, and Fractional Chern Insulators in Moiré Flatbands

Moiré flatbands, occurring, e.g., in twisted bilayer graphene at magic angles, have attracted ample interest due to their high degree of experimental tunability and the intriguing possibility of generating novel strongly interacting phases. Here we consider the core problem of Coulomb interactions within fractionally filled spin and valley polarized Moiré flatbands and demonstrate that the dual description in terms of holes, which acquire a nontrivial hole dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. In experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent interaction-driven Fermi liquid states at electronic filling fractions down to around 1/3 and 2/3, respectively. At even lower filling fractions, the electron density still faithfully tracks the single-hole dispersion while exhibiting distinct non-Fermi liquid behavior. Most saliently, we provide microscopic evidence that high temperature fractional Chern insulators can form in twisted bilayer graphene aligned with hexagonal boron nitride.

Local lattice distortions and dynamics in extremely overdoped superconducting YSr2Cu2.75Mo0.25O7.54

A common characteristic of many "overdoped" cuprates prepared with high-pressure oxygen is Tc values ≥ 50 K that often exceed that of optimally doped parent compounds, despite O stoichiometries that place the materials at the edge or outside of the conventional boundary between superconducting and normal Fermi liquid states. X-ray absorption fine-structure (XAFS) measurements at 52 K on samples of high-pressure oxygen (HPO) YSr2Cu2.75Mo0.25O7.54, Tc = 84 K show that the Mo is in the (VI) valence in an unusually undistorted octahedral geometry with predominantly Mo neighbors that is consistent with its assigned substitution for Cu in the chain sites of the structure. Perturbations of the Cu environments are minimal, although the Cu X-ray absorption near-edge structure (XANES) differs from that in other cuprates. The primary deviation from the crystal structure is therefore nanophase separation into Mo- and Cu-enriched domains. There are, however, indications that the dynamical attributes of the structure are altered relative to YBa2Cu3O7, including a shift of the Cu-apical O two-site distribution from the chain to the plane Cu sites. Another effect that would influence Tc is the possibility of multiple bands at the Fermi surface caused by the presence of the second phase and the lowering of the Fermi level.

Strongly Correlated Materials from a Numerical Renormalization Group Perspective: How the Fermi-Liquid State of Sr_{2}RuO_{4} Emerges.

The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr_{2}RuO_{4}. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and Fermi-liquid behavior, concomitant with spin coherence, below a temperature of 25K. By computing real-frequency correlation functions, we directly observe this spin-orbital scale separation and show that the van Hove singularity drives strong orbital differentiation. We extract quasiparticle interaction parameters from the low-energy spectrum and find an effective attraction in the spin-triplet sector.

Scaling theory of magnetism in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering and quantum-disordered state being investigated. The calculations taking into account magnon and incoherent spin dynamics are performed. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach. Possibility of a non-Fermi-liquid behavior is treated.

Magnetic field-tuned Fermi liquid in a Kondo insulator

Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the electron spin, yet the required strength of the magnetic field–typically of order 100 T–means that very little is known about this insulator-metal transition. Here we show that Ce{}_{3}Bi{}_{4}Pd{}_{3}, owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A metallic Fermi liquid state is established above a critical magnetic field of only {B}_{{rm{c}}}approx 11 T. A peak in the strength of electronic correlations near {B}_{{rm{c}}}, which is evident in transport and susceptibility measurements, suggests that Ce{}_{3}Bi{}_{4}Pd{}_{3} may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

On the scaling theory of antiferromagnetic ordering in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering being investigated. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach.

Quantum Criticality and Formation of a Singular Fermi Liquid in the Attractive SU(N>2) Anderson Model.

While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N>2. Beyond a critical value of attractive interaction, an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.

Characteristics of Very High Q Nb Superconducting Resonators for Microwave Kinetic Inductance Detectors

We have prepared superconducting resonators using high-quality Nb thin films with RRR = 48 and studied their resonance characteristics in detail. It was observed that the measured internal quality factor Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> reached as high as 4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> , which might be the highest value obtained among the Nb thin film superconducting resonators ever reported. It is demonstrated that the temperature dependence of the internal quality factors can be well explained by considering the temperature dependence of the residual resistance due to phonon scattering, electron-electron scattering, and the Kondo effect of the residual quasiparticle in addition to the extended Mattis-Bardeen theory. It is also found that the change of the resonance frequency of the Nb thin film resonator with respect to temperature can be well explained by considering the temperature dependence of both the Kondo effect and the kinetic inductance of the residual quasiparticles. These results strongly indicate that a finite number of quasiparticles are present in the superconducting gap of the high-quality Nb film even at a sufficiently low temperature of T/T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <; 0.15 and form a Fermi liquid state.

Effect of Anisotropic Hybridization in YbAlB_{4} Probed by Linear Dichroism in Core-Level Hard X-Ray Photoemission Spectroscopy.

We have probed the crystalline electric-field ground states of pure |J=7/2,J_{z}=±5/2⟩ as well as the anisotropic c-f hybridization in both valence fluctuating systems α- and β-YbAlB_{4} by linear polarization dependence of angle-resolved core level photoemission spectroscopy. Interestingly, the small but distinct difference between α- and β-YbAlB_{4} was found in the polar angle dependence of linear dichroism, indicating the difference in the anisotropy of c-f hybridization, which may be a key to understanding a heavy Fermi liquid state in α-YbAlB_{4} and a quantum critical state in β-YbAlB_{4}.

Fermi-liquid ground state of interacting Dirac fermions in two dimensions

An unbiased zero-temperature auxiliary-field quantum Monte Carlo method is employed to analyze the nature of the semimetallic phase of the two-dimensional Hubbard model on the honeycomb lattice at half filling. It is shown that the quasiparticle weight $Z$ of the massless Dirac fermions at the Fermi level, which characterizes the coherence of zero-energy single-particle excitations, can be evaluated in terms of the long-distance equal-time single-particle Green's function. If this quantity remains finite in the thermodynamic limit, the low-energy single-particle excitations of the correlated semimetallic phase are described by a Fermi-liquid-type single-particle Green's function. Based on the unprecedentedly large-scale numerical simulations on finite-size clusters containing more than ten thousands sites, we show that the quasiparticle weight remains finite in the semimetallic phase below a critical interaction strength. This is also supported by the long-distance algebraic behavior ($\sim r^{-2}$, where $r$ is distance) of the equal-time single-particle Green's function that is expected for the Fermi liquid. Our result thus provides a numerical confirmation of Fermi-liquid theory in two-dimensional correlated metals.

Highly anisotropic strain dependencies in PrIr2Zn20

We report thermal expansion and magnetostriction of the cubic non-Kramers system PrIr$_2$Zn$_{20}$ with a non-magnetic $\varGamma_{3}$ ground state doublet. In previous experiments, antiferroquadrupolar order at \hbox{$T_{\mathrm{Q}}=0.11$\,K} and a Fermi liquid state around $B_{\mathrm{c}}\approx5$\,T for \hbox{$\boldsymbol{B}\parallel[001]$}, indicative of possible ferrohastatic order, were discovered. For magnetic fields \hbox{$\boldsymbol{B}\parallel[001]$}, the low temperature longitudinal and transverse thermal expansion and magnetostriction are highly anisotropic. The resulting volume strain is very small, indicating that the Pr valence remains nearly constant as a function of magnetic field. We conclude that the Fermi liquid state around $B_{\mathrm{c}}$ forms through a very little change in c-f hybridization. This result is in sharp contrast to Ce- and Yb-based Kramers Kondo lattices which show significantly larger volume strains due to the high sensitivity of the Kondo temperature to hydrostatic pressure.