Landau Fermi Liquid Research Articles

Hidden transport phenomena in an ultraclean correlated metal

Advancements in materials synthesis have been key to unveil the quantum nature of electronic properties in solids by providing experimental reference points for a correct theoretical description. Here, we report hidden transport phenomena emerging in the ultraclean limit of the archetypical correlated electron system SrVO3. The low temperature, low magnetic field transport was found to be dominated by anisotropic scattering, whereas, at high temperature, we find a yet undiscovered phase that exhibits clear deviations from the expected Landau Fermi liquid, which is reminiscent of strange-metal physics in materials on the verge of a Mott transition. Further, the high sample purity enabled accessing the high magnetic field transport regime at low temperature, which revealed an anomalously high Hall coefficient. Taken with the strong anisotropic scattering, this presents a more complex picture of SrVO3 that deviates from a simple Landau Fermi liquid. These hidden transport anomalies observed in the ultraclean limit prompt a theoretical reexamination of this canonical correlated electron system beyond the Landau Fermi liquid paradigm, and more generally serves as an experimental basis to refine theoretical methods to capture such nontrivial experimental consequences emerging in correlated electron systems.

Anomalous properties in normal and superconducting states of Sc2Ir4-xSix due to flat band effect driven by spin-orbit coupling

Correlation effect may be induced by the flat band(s) near the Fermi energy, as demonstrated in twisted graphene, Kagome materials, and heavy Fermion materials. Unconventional superconductivity may arise from this correlation effect and show deviation from the phonon-mediated pairing as well as the Landau Fermi liquid in the normal state. Here, we report the anomalous properties in normal and superconducting states in the Laves phase superconductor Sc2Ir4-xSix with a kagome lattice and silicon doping. By doping silicon to the iridium sites, a phase diagram with nonmonotonic and two-dome-like doping dependence of the superconducting transition temperature Tc was observed. The samples in the region of the second dome, including Sc2Ir3.5Si0.5 with the optimal Tc, exhibit non-Fermi liquid behavior at low temperatures after superconductivity is suppressed, as evidenced by the divergence of the specific heat coefficient and the semiconducting-like resistivity, together with a strong superconducting fluctuation in the optimally doped samples. Combined with first-principles calculations, we attribute the anomalous properties in normal and superconducting states to the correlation effect, which is intimately induced by the flat band effect when considering the strong spin-orbit coupling.

Topological order and fractionalized excitations in quantum many-body systems

The Landau Fermi liquid theory and the Ginzburg-Landau phase transition theory stand as two pivotal cornerstones in traditional condensed matter physics, achieving significant success in addressing crucial physical phenomena such as BCS superconductors and liquid helium superfluids. However, marked by the discoveries of the quantum Hall effect and high-temperature superconductivity in the 1980s, it gradually became evident that for a broad class of novel quantum states, such as fractional quantum Hall states and quantum spin liquids, their properties transcend the Landau Fermi liquid theory and Ginzburg-Landau phase transition theory. Topological order and its related concepts of long-range many-body quantum entanglement and fractionalized excitation have become the key concepts to understand these exotic quantum states. Designing and identifying topologically ordered states of matter in quantum materials and quantum simulation systems, and probing and manipulating their fractionalized excitations, are important research directions in modern condensed matter physics. In recent years, great progress has been made in the quantum simulation and manipulation of topological order on highly controllable quantum simulation platforms, such as Rydberg atomic systems, superconducting quantum processors, and two-dimensional moiré superlattices. This article provides a brief overview of recent research advances and challenges in the study of topological order in traditional condensed matter systems and quantum simulation experimental platforms. It also provides prospects for the future developments of this field.

Friedel oscillation in non-Fermi liquid: lesson from exactly solvable Hatsugai–Kohmoto model

When non-magnetic impurity immerses in Fermi sea, a regular modulation of charge density around impurity will appear and such phenomena is called Friedel oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is still largely unknown. Here, we show that FO indeed exists in NFL state of an exactly solvable model, i.e. the Hatsugai–Kohmoto model which has been intensively explored in recent years. Combining T-matrix approximation and linear-response-theory, an interesting picture emerges, if two interaction-induced quasi-particles bands in NFL are partially occupied, FO in this situation is determined by a novel structure in momentum space, i.e. the ‘average Fermi surface’ (average over two quasi-particle Fermi surface), which highlights the inter-band particle-hole excitation. We hope our study here provides a counterintuitive example in which FO with Fermi surface coexists with NFL quasi-particle, and it may be useful to detect hidden ‘average Fermi surface’ structure in other correlated electron systems.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids.

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

Violation of Luttinger's theorem in the simplest doped Mott insulator: Falicov-Kimball model in the strong-correlation limit

The Luttinger's theorem has long been taken as the key feature of Landau's Fermi liquid, which signals the presence of quasiparticles. Here, by the unbiased Monte Carlo method, violation of Luttinger's theorem is clearly revealed in the Falicov-Kimball (FK) model, indicating the robust correlation-driven non-Fermi liquid characteristic under any electron density. Introducing hole carriers to the half-filled FK leads to Mott insulator-metal transition, where the Mott quantum criticality manifests unconventional scaling behavior in transport properties. Further insight on the violation of the Luttinger's theorem is examined by combining Hubbard-I approximation with a composite fermion picture, which emphasizes the importance of a mixed excitation of the itinerant electron and the composite fermion. Interestingly, when compared FK model with a binary disorder system, it suggests that the two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is underlying the violation of Luttinger's theorem.

Nonlinear bosonization of Fermi surfaces: The method of coadjoint orbits

We develop a method for bosonizing the Fermi surface based on the formalism of the coadjoint orbits. This allows one to parametrize the Fermi surface by a bosonic field that depends on the spacetime coordinates and on the position on the Fermi surface. The Wess-Zumino-Witten term in the effective action, governing the adiabatic phase acquired when the Fermi surface changes its shape, is completely fixed. As an effective field theory the action also involves a Hamiltonian, which contains, beside the kinetic energy and the Landau interaction, terms with arbitrary number of derivatives and fields. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau's Fermi liquid theory. The approach can be extended to incorporate spin degrees of freedom and the charge-2 fields corresponding to the BCS order parameter.

Zero sound and plasmon modes for non-Fermi liquids

We derive the quantum Boltzmann equation (QBE) by using generalized Landau-interaction parameters, obtained through the nonequilibrium Green's function technique. This is a generalization of the usual QBE formalism to non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles. We apply this framework to a controlled low-energy effective field theory for the Ising-nematic quantum critical point, in order to find the collective excitations of the critical Fermi surface in the collisionless regime. We also compute the nature of the dispersion after the addition of weak Coulomb interactions. The zero angular momentum longitudinal vibrations of the Fermi surface show a linear-in-wavenumber dispersion, which corresponds to the zero sound of Landau's Fermi liquid theory. The Coulomb interaction modifies it to a plasmon mode in the long-wavelength limit, which disperses as the square-root of the wavenumber. Remarkably, our results show that the zero sound and plasmon modes exhibit the same behaviour as in a Fermi liquid, although an NFL is fundamentally different from the former.

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.

Strongly Correlated Quantum Spin Liquids versus Heavy Fermion Metals: A Review.

This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in and quasi-one dimensional (1D) quantum spin liquid in both and with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal , with , and on its sister compounds and , carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of and in its sister compounds and emerge, as well as establish connection of these (HF) metals with insulators , and . We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields.

Ultraviolet-Infrared Mixing in Marginal Fermi Liquids.

When Fermi surfaces (FSs) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this Letter, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the FS enters as a relevant scale. The UV-IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a (2+1)-dimensional MFL shrinks to a measure-zero set in the low-energy limit. This UV-IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.

Transport coefficients of magnetized neutron star cores

We review the calculations of the kinetic coefficients (thermal conductivity, shear viscosity, momentum transfer rates) of the neutron star core matter within the framework of the Landau Fermi-liquid theory. We restrict ourselves to the case of normal (i.e. non-superfluid) matter. As an example we consider simplest $npe\mu$ composition of neutron star core matter. Utilizing the CompOSE database of dense matter equations of state and several microscopic interactions we analyze the uncertainties in calculations of the kinetic coefficients that result from the insufficient knowledge of the properties of the dense nuclear matter and suggest possible approximate treatment. In our study we also take into account non-quantizing magnetic field. The presence of magnetic field makes transport anisotropic leading to the tensor structure of kinetic coefficients. We find that the moderate ($B\lesssim 10^{12}$ G) magnetic field do not affect considerably thermal conductivity of neutron star core matter, since the latter is mainly governed by the electrically neutral neutrons. In contrast, shear viscosity is affected even by the moderate $B\sim 10^8 - 10^{10}$ G. Based on the in-vacuum nucleon interactions we provide practical expressions for calculation of transport coefficients for any equation of state of dense matter.

Quantitative theory of composite fermions in Bose-Fermi mixtures at ν=1

Composite fermions provide a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor $\nu=1$ has been formulated by Dong and Senthil. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor $\nu=1$. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, $\nu_b = 1 -\nu_f$. This tunability enables us to study the dilute limit $\nu_b\ll 1$, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of $\nu_f\ll 1$, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.

Doping a Mott insulator in an Ising-Kondo lattice: Strange metal and Mott criticality

Metallic quantum states coined strange metal (SM), with robust linear-$T$ resistivity, have been widely observed in many quantum materials under strong electron correlations, ranging from high-${T}_{c}$ cuprate superconductors and organic superconductors to twisted multilayer graphene and ${\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}$ superlattices. Despite decades of intensive studies, the mystery of SM still defies any sensible theoretical explanation and has been a key puzzle in modern condensed matter physics. Here, we solve a doped Mott insulator model called an Ising-Kondo lattice, which includes static spin fluctuation. With Monte Carlo simulation, the Ising-Kondo lattice unambiguously exhibits SM phenomena accompanied with quantum critical scaling in observables, e.g., resistivity, susceptibility, and specific heat. A closer look at SM reveals the breakdown of Landau's Fermi liquid theory without any symmetry breaking, i.e., the violation of Luttinger theorem. Our paper reveals that the long-overlooked static fluctuations in literature may play an essential role in non-Fermi liquid behaviors in correlated electron systems.

Continuous Mott transition in semiconductor moiré superlattices.

The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics1-6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids4-7, exciton condensates8 and unconventional superconductivity1. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice9-22, providing a unique opportunity to drive a metal-insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe2/WSe2 moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is approached from the insulating side, and a diverging quasiparticle effective mass from the metallic side. We also observe a smooth evolution of the magnetic susceptibility across the MIT and no evidence of long-range magnetic order down to ~5% of the Curie-Weiss temperature. This signals an abundance of low-energy spinful excitations on the insulating side that is further corroborated by the Pomeranchuk effect observed on the metallic side. Our results are consistent with the universal critical theory of a continuous Mott transition in two dimensions4,23.

Fragile versus stable two-dimensional fermionic quasiparticles

We provide a comprehensive theoretical investigation of the Fermi liquid quasiparticle description in two-dimensional electron gas interacting via the long-range Coulomb interaction by calculating the electron self-energy within the leading-order approximation, which is exact in the high-density limit. We find that the quasiparticle energy is larger than the imaginary part of the self-energy up to very high energies, implying that the basic Landau quasiparticle picture is robust up to far above the Fermi energy. We find, however, that the quasiparticle picture becomes fragile in a small discrete region around a critical wave vector where the quasiparticle spectral function strongly deviates from the expected quasiparticle Lorentzian line shape with a vanishing renormalization factor. We show that such a non-Fermi liquid behavior arises due to the coupling of quasiparticles with the collective plasmon mode. This situation is somewhat intermediate between the one-dimensional interacting electron gas (i.e., Luttinger liquid), where the Landau Fermi liquid theory completely breaks down since only bosonic collective excitations exist, and three-dimensional electron gas, where quasiparticles are well-defined and more stable against interactions than in one and two dimensions. We use a number of complementary definitions for a quasiparticle to examine the interacting spectral function, contrasting two-dimensional and three-dimensional situations critically.

Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum MonteCarlo.

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion MonteCarlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.

Fermi arcs and pseudogap in a lattice model of a doped orthogonal metal

Since the discovery of the pseudogap and Fermi arc states in underdoped cuprates, the understanding of such non-Fermi-liquid states and the associated violation of Luttinger's theorem have been the central theme in correlated electron systems. However, still lacking is a well-accepted theoretical framework to unambiguously explain these metallic states that are clearly beyond Landau's Fermi liquid and Luttinger's theorem of a Fermi surface and electron filling. Here, we design a lattice model of orthogonal metals with fermion and Ising matter fields coupled to topological order and, by solving the model via unbiased quantum Monte Carlo simulation at generic electron fillings, find that the system gives birth to phenomena of the Fermi arc and pseudogap in the single-particle spectrum that go beyond the Luttinger sum rule with broken Fermi surface but no symmetry breaking. The pseudogap and Fermi arcs coexist with a background of a deconfined Z2 gauge field, and we further find that the confinement transition of the gauge field triggers a superconductivity instability and that the hopping of the gauge-neutral fermions brings the "large" Fermi surface back from the Fermi arc state. Our unbiased numerical results provide a concrete model realization and theoretical framework for the coupling between gauge field and fermions and, in the process, generate the rich phenomena of the pseudogap, the Fermi arc, and superconductivity in generic correlated electron systems.

Anomalous plasmon mode in strained Weyl semimetals

An exotic anomalous plasmon mode is found in strained Weyl semimetals utilizing the topological Landau Fermi liquid and chiral kinetic theories, in which quasiparticle interactions are modeled by long-range Coulomb and residual short-range interactions. The gapped collective mode is derived from the dynamical charge pumping between the bulk and the surface and behaves like $k_{\rm F}^{-1}$. The charge oscillations are accurately determined by the coupling between the induced electric field and the background pseudofields. This novel mode unidirectionally disperses along the pseudomagnetic field and manifests itself in an unusual thermal conductivity in apparent violation of the Wiedemann-Franz law. The excitation can be achieved experimentally by mechanical vibrations of the crystal lattice in the THz regime.

Landau-Fermi liquids without quasiparticles

Landau-Fermi liquid theory is conventionally believed to hold whenever the interacting single-particle density of states develops a $\delta$-like component at the Fermi surface, which is associated with quasiparticles. Here we show that a microscopic justification can be actually achieved under more general circumstances, even in case coherent quasiparticles are totally missing and the interacting single-particle density of states vanishes at the chemical potential as consequence of a pole singularity in the self-energy.