Fermi Liquid Metal Research Articles

Superconductivity and Mott Physics in Organic Charge Transfer Materials.

The phase diagrams of quasi two-dimensional organic superconductors display a plethora of fundamental phenomena associated with strong electron correlations, such as unconventional superconductivity, metal-insulator transitions, frustrated magnetism and spin liquid behavior. We analyze a minimal model for these compounds, the Hubbard model on an anisotropic triangular lattice, using cutting-edge quantum embedding methods respecting the lattice symmetry. We demonstrate the existence of unconventional superconductivity by directly entering the symmetry-broken phase. We show that the crossover from the Fermi liquid metal to the Mott insulator is associated with the formation of a pseudogap. The predicted momentum-selective destruction of the Fermi surface into hot and cold regions provides motivation for further spectroscopic studies. Our theoretical results agree with experimental phase diagrams of κ-BEDT organics.

Prevailing Charge Order in Overdoped La_{2-x}Sr_{x}CuO_{4} beyond the Superconducting Dome.

The extremely overdoped cuprates are generally considered to be Fermi liquid metals without exotic orders, whereas the underdoped cuprates harbor intertwined states. Contrary to this conventional wisdom, using Cu L_{3}-edge and O K-edge resonant x-ray scattering, we reveal a charge order (CO) correlation in overdoped La_{2-x}Sr_{x}CuO_{4} (0.35≤x≤0.6) beyond the superconducting dome. This CO has a periodicity of ∼6 lattice units with correlation lengths of ∼20 lattice units. It shows similar in-plane momentum and polarization dependence and dispersive excitations as the CO of underdoped cuprates, but its maximum intensity differs along the c direction and persists up to 300K. This CO correlation cannot be explained by the Fermi surface instability and its origin remains to be understood. Our results suggest that CO is prevailing in the overdoped metallic regime and requires a reassessment of the picture of overdoped cuprates as weakly correlated Fermi liquids.

Coulomb Drag and Heat Transfer in Strange Metals.

We address Coulomb drag and near-field heat transfer in a double-layer system of incoherent metals. Each layer is modeled by an array of tunnel-coupled SYK dots with random interlayer interactions. Depending on the strength of intradot interactions and interdot tunneling, this model captures the crossover from the Fermi liquid to a strange metal phase. The absence of quasiparticles in the strange metal leads to temperature-independent drag resistivity, which is in strong contrast with the quadratic temperature dependence in the Fermi liquid regime. We show that all the parameters can be independently measured in near-field heat transfer experiments, performed in Fermi liquid and strange metal regimes.

Jamming and unusual charge density fluctuations of strange metals

The strange metallic regime across a number of high-temperature superconducting materials presents numerous challenges to the classic theory of Fermi liquid metals. Recent measurements of the dynamical charge response of strange metals, including optimally doped cuprates, have revealed a broad, featureless continuum of excitations, extending over much of the Brillouin zone. The collective density oscillations of this strange metal decay into the continuum in a manner that is at odds with the expectations of Fermi liquid theory. Inspired by these observations, we investigate the phenomenology of bosonic collective modes and the particle-hole excitations in a class of strange metals by making an analogy to the phonons of classical lattices falling apart across an unconventional jamming-like transition associated with the onset of rigidity. By making comparisons to the experimentally measured dynamical response functions, we reproduce many of the qualitative features using the above framework. We conjecture that the dynamics of electronic charge density over an intermediate range of energy scales in a class of strongly correlated metals can be at the brink of a jamming-like transition.

Fermi-Liquid Nonadiabatic Highly Compressed Cesium Iodide Superconductor

The experimental discovery that compressed sulfur hydride exhibits superconducting transition temperature of Tc=203 K by Drozdov et al. (Nature 2015, 525, 73–76) sparked studies of compressed hydrides. This discovery was not a straightforward experimental examination of a theoretically predicted phase, but instead it was a nearly five-decade-long experimental quest for superconductivity in highly compressed matters, varying from pure elements (hydrogen, oxygen, sulfur), hydrides (SiH4, AlH3) to semiconductors and ionic salts. One of these salts was cesium iodide, CsI, which exhibits the transition temperature of Tc≅1.5 K at P=206 GPa (Eremets et al., Science 1998, 281, 1333–1335). Detailed first principles calculations (Xu et al., Phys Rev B 2009, 79, 144110) showed that CsI should exhibit Tc~0.03 K (P=180 GPa). In an attempt to understand the nature of this discrepancy between the theory and the experiment, we analyzed the temperature-dependent resistance in compressed CsI and found that this compound is a perfect Fermi liquid metal which exhibits an extremely high ratio of Debye energy to Fermi energy, ℏωDkBTF≅17. This implies that direct use of the Migdal–Eliashberg theory of superconductivity to calculate the transition temperature in CsI is incorrect, because the theory is valid for ℏωDkBTF≪1. We also showed that CsI falls into the unconventional superconductors band in the Uemura plot.

Doping-driven resistive collapse of the Mott insulator in a minimal model for VO2

We study the resistive collapse of the Mott insulator state in the dimer Hubbard model. This minimal model has been used to describe the physics of ${\mathrm{VO}}_{2}$, and should be relevant to other strongly correlated materials. It incorporates the physics of correlated dimers and the explicit competition between on-site Coulomb repulsion and magnetic exchange interactions. Our results unveil that between the Mott insulator at half filling and the Fermi liquid metal at high doping there is an intermediate bad metallic phase with exotic features such as a pseudogap, orbital selectivity, and a first-order metal-metal transition. The model is solved within dynamical mean field theory by means of quantum Monte Carlo, which provides the numerically exact solution of the model in the limit of large lattice dimensionality. This model can be considered as a minimal one that captures exotic phenomena associated to the physics of a doped Mott insulator, shading light on their basic physical mechanism.

Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal

We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality. We discuss physical implications of effective one-dimensional spin dynamics and extremely overdamped gauge dynamics at the Mott quantum criticality.

Orbital-selective nature of the 3d electronic structure of the ThFeAsN superconductor

Based on local-density approximation plus dynamical mean-field theory ($\mathrm{LDA}+\mathrm{DMFT}$) calculations, we perform a comprehensive analysis of electronic structure reconstruction of the ThFeAsN superconductor, showing how the normal and $s$ wave superconducting spectra are reshaped by many-particle electron-electron interactions. Here, the ThFeAsN parent compound is described as an orbital-selective marginal Fermi liquid metal, with coexisting Fermi liquid quasiparticles and pseudogapped electronic states. Upon electron doping, an additional Kondo insulating state is predicted to exist in this system. Furthermore, we show how dynamical correlations strongly renormalize the bare Bogoliubov quasiparticles in the $s$ wave superconducting state into totally correlated lineshapes. These findings contribute to the microscopic understanding of the role played by dynamical multiorbital electronic correlations in the low energy spectrum relevant to unconventional Fe-based superconductors.

Noncommutative field theory and composite Fermi liquids in some quantum Hall systems

Composite Fermi liquid metals arise at certain special filling fractions in the quantum Hall regime and play an important role as parent states of gapped states with quantized Hall response. They have been successfully described by the Halperin-Lee-Read (HLR) theory of a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with a Chern-Simons term. However, the validity of the HLR description when the microscopic system is restricted to a single Landau has not been clear. Here for the specific case of bosons at filling $\nu = 1$, we build on earlier work from the 1990s to formulate a low energy description that takes the form of a {\em non-commutative} field theory. This theory has a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with no Chern-Simons term but with the feature that all fields are defined in a non-commutative spacetime. An approximate mapping of the long wavelength, small amplitude gauge fluctuations yields a commutative effective field theory which, remarkably, takes the HLR form but with microscopic parameters correctly determined by the interaction strength. Extensions to some other composite fermi liquids, and to other related states of matter are discussed.

Deconfined metal-insulator transitions in quantum Hall bilayers

We propose that quantum Hall bilayers in the presence of a periodic potential at the scale of the magnetic length can host examples of a Deconfined Metal-Insulator Transition (DMIT), where a Fermi liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or, an insulator with Goldstone modes) through a continuous quantum phase transition. The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework. At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL). The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different. The FL-gCFL quantum critical point hosts a sharply defined Fermi surface without long-lived electronic quasiparticles. Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase. We discuss the topological properties of the insulator and various observable signatures associated with the DMIT.

Resistivity phase diagram of cuprates revisited

The phase diagram of the cuprate superconductors has posed a formidable scientific challenge for more than three decades. This challenge is perhaps best exemplified by the need to understand the normal-state charge transport as the system evolves from Mott insulator to Fermi-liquid metal with doping. Here we report a detailed analysis of the temperature (T) and doping (p) dependence of the planar resistivity of simple-tetragonal HgBa$_2$CuO$_{4+\delta}$ (Hg1201), the single-CuO$_2$-layer cuprate with the highest optimal $T_c$. The data allow us to test a recently proposed phenomenological model for the cuprate phase diagram that combines a universal transport scattering rate with spatially inhomogeneous (de)localization of the Mott-localized hole. We find that the model provides an excellent description of the data. We then extend this analysis to prior transport results for several other cuprates, including the Hall number in the overdoped part of the phase diagram, and find little compound-to-compound variation in (de)localization gap scale. The results point to a robust, universal structural origin of the inherent gap inhomogeneity that is unrelated to doping-related disorder. They are inconsistent with the notion that much of the phase diagram is controlled by a quantum critical point, and instead indicate that the unusual electronic properties exhibited by the cuprates are fundamentally related to strong nonlinearities associated with subtle nanoscale inhomogeneity.

Deconfined metallic quantum criticality: A U(2) gauge-theoretic approach

We discuss a new class of quantum phase transitions -- Deconfined Mott Transition (DMT) -- that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and an electrical insulator without Fermi surfaces of emergent neutral excitations. We construct a unified $U(2)$ gauge theory to describe a variety of metallic and insulating phases, which include Fermi liquids, fractionalized Fermi liquids (FL*), conventional insulators and quantum spin liquids, as well as the quantum phase transitions between them. Using the DMT as a basic building block, we propose a distinct quantum phase transition -- Deconfined Metal-Metal Transition (DM$^2$T) -- that describes a continuous transition between two metallic phases, accompanied by a jump in the size of their electronic Fermi surfaces (also dubbed a 'Fermi transition'). We study these new classes of deconfined metallic quantum critical points using a renormalization group framework at the leading nontrivial order in a controlled expansion, and comment on the various interesting scenarios that can emerge going beyond this leading order calculation. We also study a $U(1)\times U(1)$ gauge theory that shares a number of similarities with the $U(2)$ gauge theory and sheds important light on many phenomena related to DMT, DM$^2$T and quantum spin liquids.

Intrinsic superconducting instabilities of a solvable model for an incoherent metal

We construct a family of translationally invariant lattice models with a large number ($N$) of orbitals at every site coupled together via single electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, that have a modified Sachdev-Ye-Kitaev (SYK) form, we demonstrate a number of unusual features at strong coupling and in the large$-N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi liquid metal, and, (ii) an instability of an incipient heavy Fermi liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong-coupling, these solvable models display pairing instabilities that are not driven by any special "nesting" properties associated with an underlying Fermi surface.

Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene.

We develop a proposal to realize a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings ν=±3+1/2 and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band structure of bilayer graphene and includes the fluctuations between the n=0 and n=1 cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of n=0/1 orbits.

Bridging Hubbard model physics and quantum Hall physics in trilayer graphene/h−BN moiré superlattice

The moir\'e superlattice formed by ABC stacked trilayer graphene aligned with a hexagonal boron nitride substrate (TG/h-BN) provides an interesting system where both the bandwidth and the topology can be tuned by an applied perpendicular electric field $D$ . Thus the TG/h-BN system can simulate both Hubbard model physics and nearly flat Chern band physics within one sample. We derive lattice models for both signs of $D$ (which controls the band topology) separately through explicit Wannier orbital construction and mapping of Coulomb interaction. When the bands are topologically trivial, we discuss possible candidates for Mott insulators at integer number of holes per site (labeled as $\nu_T$). These include both broken symmetry states and quantum spin liquid insulators which may be particularly favorable in the vicinity of the Mott transition. We propose feasible experiments to study carefully the bandwidth tuned and the doping tuned Mott metal-insulator transition at both $\nu_T=1$ and $\nu_T=2$. We discuss the interesting possibility of probing experimentally a bandwidth (or doping) controlled continuous Mott transition between a Fermi liquid metal and a quantum spin liquid insulator. Finally we also show that the system has a large valley Zeeman coupling to a small out-of-plane magnetic field, which can be used to control the valley degree of freedom.

Fermions and bosons in nonsymmorphic PdSb2 with sixfold degeneracy

PdSb2 is a candidate for hosting 6-fold-degenerate exotic fermions (beyond Dirac and Weyl fermions).The nontrivial band crossing protected by the nonsymmorphic symmetry plays a crucial role in physical properties. We have grown high-quality single crystals of PdSb2 and characterized their physical properties under several stimuli (temperature, magnetic field, and pressure). While it is a diamagnetic Fermi-liquid metal under ambient pressure, PdSb2 exhibits a large magnetoresistance with continuous increase up to 14 T, which follows the Kohler's scaling law at all temperatures. This implies one-band electrical transport, although multiple bands are predicted by first principles calculations. By applying magnetic field along the [111] direction, de Haas-van Alphen oscillations are observed with frequency of 102 T. The effective mass is nearly zero (0.045m0) with the Berry phase close to {\pi}, confirming that the band close to the R point has a nontrivial character. Under quasihydrostatic pressure (p), evidence for superconductivity is observed in the resistivity below the critical temperature Tc. The dome-shaped Tc versus p is obtained with maximum Tc~2.9 K. We argue that the formation of Cooper pairs (bosons) is the consequence of the redistribution of the 6-fold-degenerate fermions under pressure.

Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid.

We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.

Quantum critical local spin dynamics near the Mott metal-insulator transition in infinite dimensions

Finding microscopic models for metallic states that exhibit quantum critical properties such as $\omega/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $\chi(T,\omega)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $\omega/T$ scaling where $T$ is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity and are relevant to experiments on organic charge transfer salts.

Unconventional high-Tc superconductivity in fullerides.

A3C60 molecular superconductors share a common electronic phase diagram with unconventional high-temperature superconductors such as the cuprates: superconductivity emerges from an antiferromagnetic strongly correlated Mott-insulating state upon tuning a parameter such as pressure (bandwidth control) accompanied by a dome-shaped dependence of the critical temperature, Tc However, unlike atom-based superconductors, the parent state from which superconductivity emerges solely by changing an electronic parameter-the overlap between the outer wave functions of the constituent molecules-is controlled by the C60 (3-) molecular electronic structure via the on-molecule Jahn-Teller effect influence of molecular geometry and spin state. Destruction of the parent Mott-Jahn-Teller state through chemical or physical pressurization yields an unconventional Jahn-Teller metal, where quasi-localized and itinerant electron behaviours coexist. Localized features gradually disappear with lattice contraction and conventional Fermi liquid behaviour is recovered. The nature of the underlying (correlated versus weak-coupling Bardeen-Cooper-Schrieffer theory) s-wave superconducting states mirrors the unconventional/conventional metal dichotomy: the highest superconducting critical temperature occurs at the crossover between Jahn-Teller and Fermi liquid metal when the Jahn-Teller distortion melts.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.

Conductance of molecularly linked gold nanoparticle films across an insulator-to-metal transition: From hopping to strong Coulomb electron-electron interactions and correlations

We study the influence of Coulomb effects on conductance $(g)$ of 1,4-butanedithiol-linked gold nanoparticle (NP) films near a percolation insulator-to-metal transition. On the insulating side, $g\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}{({T}_{\ensuremath{\circ}}/T)}^{1/2}]$, where $T$ is absolute temperature, a behavior predicted by Efros-Shklovskii's theory for charges optimizing pathways that accommodate Coulomb charging barriers. On the metallic side below $\ensuremath{\sim}20$ K, $g$ varies linearly with ${T}^{1/2}$. Such a correction to $g(T=0)$ is predicted by Altshuler-Aronov's theory for Fermi liquid metals when disorder mediates electron-electron $(e\text{\ensuremath{-}}e)$ Coulomb interactions. Remarkably, in the present system, the ${T}^{1/2}$ component of $g$ is significant compared to $g(T=0)$, and fitting to Boltzmann's transport theory yields elastic scattering lengths that are anomalously small---much smaller than the distance between atoms (Ioffe-Regel limit required for metals). Previous studies of materials such as fullerites, layered organic salts, and transition metal compounds have also reported such anomalously small scattering lengths and large ${T}^{1/2}$ components and attributed them to strong Coulomb mediated $e\text{\ensuremath{-}}e$ correlations, which we believe is likely the case in the present system as well. This study highlights a potential opportunity to use molecularly linked nanoparticle films as a platform to study strongly correlated electrons in a controlled fashion.