How bad metals turn good: spectroscopic signatures of resilient quasiparticles

Disorder- and Interaction-Driven Quantum Criticality in WSe2

Quantum fluctuations resulting from strong Coulomb interactions or strong disorders lead to quantum phase transitions (QPTs) in 2D materials. However, understanding of disorder- and interaction-driven QPTs remains a fundamental challenge in 2D materials owing to the presence of strong disorder and strong Coulomb interactions. Here, we study the systematic interplay of strong disorder and strong Coulomb interactions by controlling the thickness of WSe2 to elucidate the disorder- and interaction-driven metal-insulator QPTs. An observation of metal-insulator transitions (MITs) with a conductivity of ∼e2/h in thin-WSe2 agrees with the Mott-Ioffe-Regel limit, excluding bad-metal behavior; conversely, MITs with a conductivity of Collapse

Key Words

• Coulomb interactions
• WSe2
• bad-metal behavior
• disorder
• metallic glass phase
• quantum criticality
• quantum fluctuations

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MESH Headings Collapse

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Affiliation(s)

Nasir Ali SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Fida Ali Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
Hyungyu Choi SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea Department of Nano Science and Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Sobia Waheed SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Youqiang Huang Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
Fedor Nigmatulin Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
Zhenping Wang Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06510, United States
Hyokwang Park SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea Department of Nano Science and Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Hoseong Shin SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea Department of Nano Science and Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Kwangro Lee SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Faisal Ahmed Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
Boseok Kang SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea Department of Nano Science and Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea Department of Nano Engineering and Department of Semiconductor Convergence Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea
Zhipei Sun Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
Won Jong Yoo SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Korea

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Enhanced Strange Metallicity due to Hubbard-U Coulomb Repulsion

We solve a model of electrons with Hubbard-U Coulomb repulsion and a random Yukawa coupling to a two-dimensional bosonic bath, using an extended dynamical mean field theory scheme. Our model exhibits a quantum critical point, at which the repulsive component of the electron interactions strongly enhances the effects of the quantum critical bosonic fluctuations on the electrons, leading to a breakdown of Fermi liquid physics and the formation of a strange metal with "Planckian" [O(k_{B}T/ℏ)] quasiparticle decay rates at low temperatures T→0. Furthermore, the eventual Mott transition that occurs as the repulsion is increased seemingly bounds the maximum decay rate in the strange metal. Our results provide insight into low-temperature strange metallicity observed in proximity to a Mott transition, as is observed, for instance, in recent experiments on certain moiré materials.

Local correlations necessitate waterfalls as a connection between quasiparticle band and developing Hubbard bands

Waterfalls are anomalies in the angle-resolved photoemission spectrum where the energy-momentum dispersion is almost vertical, and the spectrum strongly smeared out. These anomalies are observed at relatively high energies, among others, in superconducting cuprates and nickelates. The prevalent understanding is that they originate from the coupling to some boson, with spin fluctuations and phonons being the usual suspects. Here, we show that waterfalls occur naturally in the process where a Hubbard band develops and splits off from the quasiparticle band. Our results for the Hubbard model with ab initio determined parameters well agree with waterfalls in cuprates and nickelates, providing a natural explanation for these spectral anomalies observed in correlated materials.

Dispersion kinks from electronic correlations in an unconventional iron-based superconductor

The attractive interaction in conventional BCS superconductors is provided by a bosonic mode. However, the pairing glue of most unconventional superconductors is unknown. The effect of electron-boson coupling is therefore extensively studied in these materials. A key signature is dispersion kinks that can be observed in the spectral function as abrupt changes in velocity and lifetime of quasiparticles. Here, we show the existence of two kinks in the unconventional iron-based superconductor RbFe2As2 using angle-resolved photoemission spectroscopy (ARPES) and dynamical mean field theory (DMFT). In addition, we observe the formation of a Hubbard band multiplet due to the combination of Coulomb interaction and Hund's rule coupling in this multiorbital system. We demonstrate that the two dispersion kinks are a consequence of these strong many-body interactions. This interpretation is in line with a growing number of theoretical predictions for kinks in various general models of correlated materials. Our results provide a unifying link between iron-based superconductors and different classes of correlated, unconventional superconductors such as cuprates and heavy-fermion materials.

Persistent flat band splitting and strong selective band renormalization in a kagome magnet thin film

Magnetic kagome materials provide a fascinating playground for exploring the interplay of magnetism, correlation and topology. Many magnetic kagome systems have been reported including the binary FemXn (X = Sn, Ge; m:n = 3:1, 3:2, 1:1) family and the rare earth RMn6Sn6 (R = rare earth) family, where their kagome flat bands are calculated to be near the Fermi level in the paramagnetic phase. While partially filling a kagome flat band is predicted to give rise to a Stoner-type ferromagnetism, experimental visualization of the magnetic splitting across the ordering temperature has not been reported for any of these systems due to the high ordering temperatures, hence leaving the nature of magnetism in kagome magnets an open question. Here, we probe the electronic structure with angle-resolved photoemission spectroscopy in a kagome magnet thin film FeSn synthesized using molecular beam epitaxy. We identify the exchange-split kagome flat bands, whose splitting persists above the magnetic ordering temperature, indicative of a local moment picture. Such local moments in the presence of the topological flat band are consistent with the compact molecular orbitals predicted in theory. We further observe a large spin-orbital selective band renormalization in the Fed x y + d x 2 - y 2 spin majority channel reminiscent of the orbital selective correlation effects in the iron-based superconductors. Our discovery of the coexistence of local moments with topological flat bands in a kagome system echoes similar findings in magic-angle twisted bilayer graphene, and provides a basis for theoretical effort towards modeling correlation effects in magnetic flat band systems.

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.

Transient Localization from the Interaction with Quantum Bosons

We carefully revisit the electron-boson scattering problem, going beyond weak-coupling expansions and popular semiclassical treatments. By providing numerically exact results valid at finite temperatures, we demonstrate the existence of a broad regime of electron-boson scattering where quantum localization processes become relevant despite the absence of extrinsic disorder. Localization in the Anderson sense is caused by the dynamical randomness resulting from a large thermal boson population, being, however, effective only at transient times before diffusion can set in. Compelling evidence of this transient localization phenomenon is provided by the observation of a distinctive displaced Drude peak in the optical absorption and the ensuing suppression of conductivity. Our findings identify a general route for anomalous metallic behavior that can broadly apply in interacting quantum matter.

Quantum critical phase of FeO spans conditions of Earth's lower mantle

Seismic and mineralogical studies have suggested regions at Earth's core-mantle boundary may be highly enriched in FeO, reported to exhibit metallic behavior at extreme pressure-temperature (P-T) conditions. However, underlying electronic processes in FeO remain poorly understood. Here we explore the electronic structure of B1-FeO at extreme conditions with large-scale theoretical modeling using state-of-the-art embedded dynamical mean field theory (eDMFT). Fine sampling of the phase diagram reveals that, instead of sharp metallization, compression of FeO at high temperatures induces a gradual orbitally selective insulator-metal transition. Specifically, at P-T conditions of the lower mantle, FeO exists in an intermediate quantum critical state, characteristic of strongly correlated electronic matter. Transport in this regime, distinct from insulating or metallic behavior, is marked by incoherent diffusion of electrons in the conducting t2g orbital and a band gap in the eg orbital, resulting in moderate electrical conductivity (~105 S/m) with modest P-T dependence as observed in experiments. Enrichment of solid FeO can thus provide a unifying explanation for independent observations of low seismic velocities and elevated electrical conductivities in heterogeneities at Earth's mantle base.

Magnetotransport and Fermi surface segmentation in Pauli limited superconductors

We report the first theoretical investigation of the spectroscopic, electrical and optical transport signatures ofd-wave Pauli limited superconductors, based on a non perturbative numerical approach. We demonstrate that the high magnetic field low temperature regime of these materials host a finite momentum paired superconducting phase. Multi-branched dispersion spectra with finite energy superconducting gaps, anisotropic segmentation of the Fermi surface and spatial modulations of the superconducting order characterizes this finite momentum paired phase and should be readily accessible through angle resolved photo emission spectroscopy, quasiparticle interference and differential conductance measurements. Based on the electrical and optical transport properties we capture the non Fermi liquid behavior of these systems at high temperatures, dominated by local superconducting correlations and characterized by resilient quasiparticles which survive the breakdown of the Fermi liquid description. We map out the generic thermal phase diagram of thed-wave Pauli limited superconductors and provide for the first time the accurate estimates of the thermal scales corresponding to the: (a) loss of (quasi) long range superconducting phase coherence (Tc), (b) loss of local pair correlations (Tpg), (c) breakdown of the Fermi liquid theory (Tmax) and cross-over from the non Fermi liquid to the bad metallic phase (TBR). Our thermal phase diagram mapped out on the basis of the spectroscopic and transport properties are found to be in qualitative agreement with the experimental observations on CeCoIn5andκ-BEDT, in terms of the thermodynamic phases and the phase transitions. The results presented in this paper are expected to initiate important transport and spectroscopic experiments on the Pauli limitedd-wave superconductors, providing sharp signatures of the finite momentum Cooper paired state in these materials.

Fate of Quasiparticles at High Temperature in the Correlated Metal Sr_{2}RuO_{4}

We study the temperature evolution of quasiparticles in the correlated metal Sr_{2}RuO_{4}. Our angle resolved photoemission data show that quasiparticles persist up to temperatures above 200 K, far beyond the Fermi liquid regime. Extracting the quasiparticle self-energy, we demonstrate that the quasiparticle residue Z increases with increasing temperature. Quasiparticles eventually disappear on approaching the bad metal state of Sr_{2}RuO_{4} not by losing weight but via excessive broadening from super-Planckian scattering. We further show that the Fermi surface of Sr_{2}RuO_{4}-defined as the loci where the spectral function peaks-deflates with increasing temperature. These findings are in semiquantitative agreement with dynamical mean field theory calculations.

Chemical Modulation of Metal-Insulator Transition toward Multifunctional Applications in Vanadium Dioxide Nanostructures

The metal-insulator transition (MIT) of vanadium dioxide (VO2 ) has been of great interest in materials science for both fundamental understanding of strongly correlated physics and a wide range of applications in optics, thermotics, spintronics, and electronics. Due to the merits of chemical interaction with accessibility, versatility, and tunability, chemical modification provides a new perspective to regulate the MIT of VO2 , endowing VO2 with exciting properties and improved functionalities. In the past few years, plenty of efforts have been devoted to exploring innovative chemical approaches for the synthesis and MIT modulation of VO2 nanostructures, greatly contributing to the understanding of electronic correlations and development of MIT-driven functionalities. Here, this comprehensive review summarizes the recent achievements in chemical synthesis of VO2 and its MIT modulation involving hydrogen incorporation, composition engineering, surface modification, and electrochemical gating. The newly appearing phenomena, mechanism of electronic correlation, and structural instability are discussed. Furthermore, progresses related to MIT-driven applications are presented, such as the smart window, optoelectronic detector, thermal microactuator, thermal radiation coating, spintronic device, memristive, and neuromorphic device. Finally, the challenges and prospects in future research of chemical modulation and functional applications of VO2 MIT are also provided.

A stability bound on the [Formula: see text]-linear resistivity of conventional metals

Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/τtr = 2πλT, where λ is a dimensionless strength of the electron-phonon coupling. The fact that measured values satisfy λ ≲ 1 has been noted in the context of a possible "Planckian" bound on transport. However, since the electron-phonon scattering is quasielastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on λ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

How to Recognize the Universal Aspects of Mott Criticality?

In this paper we critically discuss several examples of two-dimensional electronic systems displaying interaction-driven metal-insulator transitions of the Mott (or Wigner–Mott) type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers. Remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at the transition. We compare the available experimental data on these systems to three existing theoretical scenarios: spinon theory, Dynamical Mean Field Theory (DMFT) and percolation theory. We show that the DMFT and percolation pictures for Mott criticality can be distinguished by studying the origins of the resistivity maxima using an analysis of the dielectric response.

Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two-dimensional Hubbard model

SignificanceMost metals display an electron-scattering rate [Formula: see text] that follows [Formula: see text] at low temperatures, as prescribed by Fermi liquid theory. But there are important exceptions. One of the most prominent examples is the "strange" metal regime in overdoped cuprate supercondcutors, which exhibits a linear T dependence of the scattering rate [Formula: see text] that reaches a putative Planckian limit. Here, using cutting-edge computational approaches, we show that T-linear scattering rate can emerge from the overdoped Hubbard model at low temperatures. Our results agree with cuprate experiments in various aspects but challenge the Planckian limit. Finally, by identifying antiferromagnetic fluctuations as the physical origin of the T-linear scattering rate, we discover the microscopic mechanism of strange metallicity in cuprates.

Optical Properties of the Infinite-Layer La_{1-x}Sr_{x}NiO_{2} and Hidden Hund's Physics

We investigate the optical properties of the normal state of the infinite-layer La_{1-x}Sr_{x}NiO_{2} using density functional theory plus dynamical mean-field theory. We find a correlated metal which exhibits substantial transfer of spectral weight to high energies relative to the density functional theory. The correlations are not due to Mott physics, which would suppress the charge fluctuations and the integrated optical spectral weight as we approach a putative insulating state. Instead, we find the unusual situation, that the integrated optical spectral weight decreases with doping and increases with increasing temperature. We contrast this with the coherent component of the optical conductivity, which decreases with increasing temperature as a result of a coherence-incoherence crossover. Our studies reveal that the effective crystal field splitting is dynamical and increases strongly at low frequency. This leads to a picture of a Hund's metallic state, where dynamical orbital fluctuations are visible at intermediate energies, while at low energies a Fermi surface with primarily d_{x^{2}-y^{2}} character emerges. The infinite-layer nickelates are thus in an intermediate position between the iron based high temperature superconductors where multiorbital Hund's physics dominates and a one-band system such as the cuprates. To capture this physics we propose a low-energy two-band model with atom centered e_{g} states.

Rise and fall of Landau's 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.

Charge transport in strongly correlated electron systems is not fully understood. Here, the authors show that resilient quasiparticles at finite frequency persist into the bad-metal regime near a Mott insulator, where dynamical localization results in a ‘displaced Drude peak’ and strongly enhanced dc resistivity.

Possible observation of the signature of the bad metal phase and its crossover to a Fermi liquid in κ-(BEDT-TTF)2Cu(NCS)2 bulk and nanoparticles by Raman scattering

κ-(BEDT-TTF)2Cu(NCS)2 has been investigated by Raman scattering in both bulk and nanoparticle compounds. Phonon modes from 20 to 1600 cm-1 have been assigned. Focusing on the unexplored low frequency phonons, a plateau in frequencies is observed in the bulk phonons between 50 and 100 K and assigned to the signature of the bad metal phase. Nanoparticles of κ-(BEDT-TTF)2Cu(NCS)2 exhibit anomalies at 50 K associated to the crossover from a bad metal to a Fermi liquid whose origins are discussed.

Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions

"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

Heteroepitaxial vertical perovskite hot-electron transistors down to the monolayer limit

Two-dimensional heterostructures combined with vertical geometries are candidates to probe and utilize the physical properties of atomically-thin materials. The vertical configuration enables a unique form of hot-carrier spectroscopy as well as atomic-scale devices. Here, we present the room-temperature evolution of heteroepitaxial perovskite hot-electron transistors using a SrRuO₃ base down to the monolayer limit (∼4 Å). As a fundamental electronic probe, we observe an abrupt transition in the hot-electron mean free path as a function of base thickness, coinciding with the thickness-dependent resistive transition. As a path towards devices, we demonstrate the integrated synthesis of perovskite one-dimensional electrical edge contacts using water-soluble and growth-compatible Sr₃Al₂O₆ hard masks. Edge-contacted monolayer-base transistors exhibit on/off ratios reaching ∼10⁸, complete electrostatic screening by the base manifesting pure hot-electron injection, and excellent scaling of the output current density with device dimensions. These results open new avenues for incorporating emergent phenomena at oxide interfaces and in heterostructures.

Two-dimensional heterostructures combined with vertical geometries trigger superior functionalities in fundamental studies and applications. Here, the authors report vertical perovskite hot-electron transistors integrated with perovskite one-dimensional edge contacts down to the monolayer limit.

Strange metallicity in the doped Hubbard model

Strange or bad metallic transport, defined by incompatibility with the conventional quasiparticle picture, is a theme common to many strongly correlated materials, including high-temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 of the noninteracting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.

Theory of angle-dependent marginal Fermi liquid self-energy and its existence at all dopings in cuprates

Various angle-dependent measurements in hole-doped cuprates suggested that non-Fermi liquid (NFL) and Fermi-liquid (FL) self-energies coexist in the Brillouin zone. Moreover, it is also found that NFL self-energies survive up to the overdoped region where the resistivity features a global FL-behavior. To address this problem, we compute the momentum dependent self-energy from a single band Hubbard model. The self-energy is calculated self-consistently by using a momentum-dependent density-fluctuation (MRDF) method. One of our main results is that the computed self-energy exhibits a marginal-FL (MFL)-like frequency dependence only in the antinodal region, and FL-like behavior elsewhere at all dopings. The MFL self-energy stems from the fluctuations between the itinerant and localized densities-a result that appears when self-energy is calculated self-consistently and features an intermediate coupling behavior of cuprates. We also calculate the DC conductivity by including the full momentum dependent self-energy. We find that the resistivity-temperature exponent n becomes 1 near the optimal doping, while the MFL self-energy occupies largest momentum-space volume. Surprisingly, even in the NFL state near the optimal doping, the nodal region contains FL-like self-energies; while in the under- and over-dopings ([Formula: see text]), the antinodal region remains NFL-like. These results highlight the non-local correlation physics in cuprates and in other similar intermediately correlated materials, where a direct link between the microscopic single-particle spectral properties and the macroscopic transport behavior can not be well established.

Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results, and the question of the exact solution for the conductivity in the Hubbard model remained open. In this Letter, we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity and identify the best available result to be compared to experiment. We find that, at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4×4, and the corresponding Lanczos diagonalization result is, therefore, close to the exact result in the thermodynamic limit.

Signatures of Mottness and Hundness in archetypal correlated metals

Physical properties of multi-orbital materials depend not only on the strength of the effective interactions among the valence electrons but also on their type. Strong correlations are caused by either Mott physics that captures the Coulomb repulsion among charges, or Hund physics that aligns the spins in different orbitals. We identify four energy scales marking the onset and the completion of screening in orbital and spin channels. The differences in these scales, which are manifest in the temperature dependence of the local spectrum and of the charge, spin and orbital susceptibilities, provide clear signatures distinguishing Mott and Hund physics. We illustrate these concepts with realistic studies of two archetypal strongly correlated materials, and corroborate the generality of our conclusions with a model Hamiltonian study.

Bad Metallic Transport in a Modified Hubbard Model

Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.

Bad-metal relaxation dynamics in a Fermi lattice gas

Electrical current in conventional metals is carried by electrons that retain their individual character. Bad metals, such as the normal state of some high-temperature superconductors, violate this scenario, and the complete picture for their behavior remains unresolved. Here, we report phenomena consistent with bad-metal behaviour in an optical-lattice Hubbard model by measuring the transport lifetime for a mass current excited by stimulated Raman transitions. We demonstrate incompatibility with weak-scattering theory and key characteristics of bad metals: anomalous resistivity scaling consistent with T-linear behavior, the onset of incoherent transport, and the approach to the Mott–Ioffe–Regel limit. Our work demonstrates a direct method for determining the transport lifetime, which is critical to theory but difficult to measure in materials, and exposes minimal ingredients for bad-metal behavior.

The origin of bad-metal resistivity is a long-standing problem for condensed matter physics. Here the authors show anomalous resistivity, transport lifetime, and relaxation dynamics consistent with bad-metal behavior over a wide range of temperature for fermionic potassium atoms in optical lattices.

Band-Edge Quasiparticles from Electron-Phonon Coupling and Resistivity Saturation

We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion U≤D and to first order in (dimensionless) electron-phonon coupling strength λ≤0.5, where D is the half bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasiparticles as a positive slope in the frequency dependence of the real part of the electron self-energy. In the presence of phonons, the self-energy grows linearly with the temperature at high T, causing the resistivity to saturate. As U is increased, the saturation temperature is pushed to higher values, offering a mechanism by which electron correlations destroy saturation.

Bad metallic transport in a cold atom Fermi-Hubbard system

Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold lithium-6 in a two-dimensional optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity by using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we developed in this study may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.

Non-Fermi liquids in oxide heterostructures

Understanding the anomalous transport properties of strongly correlated materials is one of the most formidable challenges in condensed matter physics. For example, one encounters metal-insulator transitions, deviations from Landau Fermi liquid behavior, longitudinal and Hall scattering rate separation, a pseudogap phase, and bad metal behavior. These properties have been studied extensively in bulk materials, such as the unconventional superconductors and heavy fermion systems. Oxide heterostructures have recently emerged as new platforms to probe, control, and understand strong correlation phenomena. This article focuses on unconventional transport phenomena in oxide thin film systems. We use specific systems as examples, namely charge carriers in SrTiO₃ layers and interfaces with SrTiO₃, and strained rare earth nickelate thin films. While doped SrTiO₃ layers appear to be a well behaved, though complex, electron gas or Fermi liquid, the rare earth nickelates are a highly correlated electron system that may be classified as a non-Fermi liquid. We discuss insights into the underlying physics that can be gained from studying the emergence of non-Fermi liquid behavior as a function of the heterostructure parameters. We also discuss the role of lattice symmetry and disorder in phenomena such as metal-insulator transitions in strongly correlated heterostructures.

Spin-Orbit Coupling and Electronic Correlations in Sr_{2}RuO_{4}

We investigate the interplay of spin-orbit coupling (SOC) and electronic correlations in Sr_{2}RuO_{4} using dynamical mean-field theory. We find that SOC does not affect the correlation-induced renormalizations, which validates Hund's metal picture of ruthenates even in the presence of the sizable SOC relevant to these materials. Nonetheless, SOC is found to change significantly the electronic structure at k points where a degeneracy applies in its absence. We explain why these two observations are consistent with one another and calculate the effects of SOC on the correlated electronic structure. The magnitude of these effects is found to depend on the energy of the quasiparticle state under consideration, leading us to introduce the notion of an energy-dependent quasiparticle spin-orbit coupling λ^{*}(ω). This notion is generally applicable to all materials in which both the spin-orbit coupling and electronic correlations are sizable.

Quasiparticles in condensed matter systems

Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.

Coherent band excitations in CePd3: A comparison of neutron scattering and ab initio theory

In common with many strongly correlated electron systems, intermediate valence compounds are believed to display a crossover from a high-temperature regime of incoherently fluctuating local moments to a low-temperature regime of coherent hybridized bands. We show that inelastic neutron scattering measurements of the dynamic magnetic susceptibility of CePd₃ provides a benchmark for ab initio calculations based on dynamical mean field theory. The magnetic response is strongly momentum dependent thanks to the formation of coherent f-electron bands at low temperature, with an amplitude that is strongly enhanced by local particle-hole interactions. The agreement between experiment and theory shows that we have a robust first-principles understanding of the temperature dependence of f-electron coherence.

Finite Temperature Green's Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state, correlation, and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W, and improves on the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regimes, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small; also the spectral function broadens and damping increases with temperature, blurring the usual quasiparticle picture. These effects are evident, e.g., in Compton scattering which exhibits many-body corrections that persist at normal densities and intermediate T. The approach also yields exchange-correlation energies and potentials in good agreement with existing methods.

Orbital dependent coherence temperature and optical anisotropy of V2O3 quasiparticles

We report on an orbital and temperature dependent study of the onset of coherent quasiparticles in V₂O₃ single crystal. By using polarized infrared spectroscopy we demonstrate that the electronic coherence temperature is strongly orbital dependent, being about 400 K for [Formula: see text] orbitals and 500 K for the [Formula: see text]. This suggests that V₂O₃ low energy electrodynamics can be described in terms of two electron liquids differently renormalized by electronic correlations.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T^{α} for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic change with U and V of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.

Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x

The thermal diffusivity in the [Formula: see text] plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25-300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron-phonon "soup" picture characterized by a diffusion constant [Formula: see text], where [Formula: see text] is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time [Formula: see text].

Slowdown of the Electronic Relaxation Close to the Mott Transition

We investigate the time-dependent reformation of the quasiparticle peak in a correlated metal near the Mott transition, after the system is quenched into a hot electron state and equilibrates with an environment which is colder than the Fermi-liquid crossover temperature. Close to the transition, we identify a purely electronic bottleneck time scale, which depends on the spectral weight around the Fermi energy in the bad metallic phase in a nonlinear way. This time scale can be orders of magnitude larger than the bare and renormalized electronic hopping time, so that a separation of electronic and lattice time scales may break down. The results are obtained using nonequilibrium dynamical mean-field theory and a slave-rotor representation of the Anderson impurity model.

Mixed valent metals

We review the theory of mixed-valent metals and make comparison with experiments. A single-impurity description of the mixed-valent state is discussed alongside the description of the nearly-integer valent or Kondo limit. The degeneracy N of the f-shell plays an important role in the description of the low-temperature Fermi-liquid state. In particular, for large N, there is a rapid cross-over between the mixed-valent and the Kondo limit when the number of f electrons is changed. We discuss the limitations on the application of the single-impurity description to concentrated compounds such as those caused by the saturation of the Kondo effect and those due to the presence of magnetic interactions between the impurities. This discussion is followed by a description of a periodic lattice of mixed-valent ions, including the role of the degeneracy N. The article concludes with a comparison of theory and experiment. Topics covered include the single-impurity Anderson model, Luttinger's theorem, the Friedel sum rule, the Schrieffer-Wolff transformation, the single-impurity Kondo model, Kondo screening, the Wilson ratio, local Fermi-liquids, Fermi-liquid sum rules, the Noziéres exhaustion principle, Doniach's diagram, the Anderson lattice model, the Slave-Boson method, etc.

Thermopower and Entropy: Lessons from Sr_{2}RuO_{4}

We calculate the in-plane Seebeck coefficient of Sr_{2}RuO_{4} within a framework combining electronic structure and dynamical mean-field theory. We show that its temperature dependence can be interpreted using entropic considerations based on the Kelvin formula and that it provides a meaningful probe of the crossover out of the Fermi liquid regime into an incoherent metal. This crossover proceeds in two stages: The entropy of spin degrees of freedom is released around room temperature, while orbital degrees of freedom remain quenched up to much higher temperatures. This is confirmed by a direct calculation of the corresponding susceptibilities and is a hallmark of "Hund's metals." We also calculate the c-axis thermopower and predict that it exceeds substantially the in-plane one at high temperature, a peculiar behavior which originates from an interlayer "hole-filtering" mechanism.

Transport Properties of Metallic Ruthenates: A DFT+DMFT Investigation

We present a systematical theoretical study on the transport properties of an archetypal family of Hund's metals, Sr_{2}RuO_{4}, Sr_{3}Ru_{2}O_{7}, SrRuO_{3}, and CaRuO_{3}, within the combination of first principles density functional theory and dynamical mean field theory. The agreement between theory and experiments for optical conductivity and resistivity is good, which indicates that electron-electron scattering dominates the transport of ruthenates. We demonstrate that in the single-site dynamical mean field approach the transport properties of Hund's metals fall into the scenario of "resilient quasiparticles." We explain why the single layered compound Sr_{2}RuO_{4} has a relative weak correlation with respect to its siblings, which corroborates its good metallicity.

Self-energy behavior away from the Fermi surface in doped Mott insulators

We analyze self-energies of electrons away from the Fermi surface in doped Mott insulators using the dynamical cluster approximation to the Hubbard model. For large onsite repulsion, U, and hole doping, the magnitude of the self-energy for imaginary frequencies at the top of the band ([Formula: see text]) is enhanced with respect to the self-energy magnitude at the bottom of the band ([Formula: see text]). The self-energy behavior at these two [Formula: see text]-points is switched for electron doping. Although the hybridization is much larger for (0, 0) than for [Formula: see text], we demonstrate that this is not the origin of this difference. Isolated clusters under a downward shift of the chemical potential, [Formula: see text], at half-filling reproduce the overall self-energy behavior at (0, 0) and [Formula: see text] found in low hole doped embedded clusters. This happens although there is no change in the electronic structure of the isolated clusters. Our analysis shows that a downward shift of the chemical potential which weakly hole dopes the Mott insulator can lead to a large enhancement of the [Formula: see text] self-energy for imaginary frequencies which is not associated with electronic correlation effects, even in embedded clusters. Interpretations of the strength of electronic correlations based on self-energies for imaginary frequencies are, in general, misleading for states away from the Fermi surface.

Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model

The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.

Searching for new thermoelectric materials: some examples among oxides, sulfides and selenides

Different families of thermoelectric materials have been investigated since the discovery of thermoelectric effects in the mid-19th century, materials mostly belonging to the family of degenerate semi-conductors. In the last 20 years, new thermoelectric materials have been investigated following different theoretical proposals, showing that nanostructuration, electronic correlations and complex crystallographic structures (low dimensional structures, large number of atoms per lattice, presence of 'rattlers'…) could enhance the thermoelectric properties by enhancing the Seebeck coefficient and/or reducing the thermal conductivity. In this review, the different strategies used to optimize the thermoelectric properties of oxides and chalcogenides will be presented, starting with a review on thermoelectric oxides. The thermoelectric properties of sulfides and selenides will then be discussed, focusing on layered materials and low dimensional structures (TiS2 and pseudo-hollandites). Some sulfides with promising ZT values will also be presented (tetrahedrites and chalcopyrites).

Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal

We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

Observation of the Leggett-Rice effect in a unitary Fermi gas

We observe that the diffusive spin current in a strongly interacting degenerate Fermi gas of (40)K precesses about the local magnetization. As predicted by Leggett and Rice, precession is observed both in the Ramsey phase of a spin-echo sequence, and in the nonlinearity of the magnetization decay. At unitarity, we measure a Leggett-Rice parameter γ=1.08(9) and a bare transverse spin diffusivity D(0)(⊥)=2.3(4)ℏ/m for a normal-state gas initialized with full polarization and at one-fifth of the Fermi temperature, where m is the atomic mass. One might expect γ=0 at unitarity, where two-body scattering is purely dissipative. We observe γ→0 as temperature is increased towards the Fermi temperature, consistent with calculations that show the degenerate Fermi sea restores a nonzero γ. Tuning the scattering length a, we find that a sign change in γ occurs in the range 0<(k(F)a)(-1)≲1.3, where k(F) is the Fermi momentum. We discuss how γ reveals the effective interaction strength of the gas, such that the sign change in γ indicates a switching of branch between a repulsive and an attractive Fermi gas.

Shining light on transition-metal oxides: unveiling the hidden Fermi liquid

We use low energy optical spectroscopy and first principles local density approximation plus dynamical mean field theory calculations to test the hypothesis that the anomalous transport properties of strongly correlated metals originate in the strong temperature dependence of their underlying resilient quasiparticles. We express the resistivity in terms of an effective plasma frequency ω(p)* and an effective scattering rate 1/τ(tr)*. We show that in the archetypal correlated material V₂O₃, ω(p)* increases with increasing temperature, while the plasma frequency from the partial sum rule exhibits the opposite trend. 1/τ(tr)* has a more pronounced temperature dependence than the scattering rate obtained from the extended Drude analysis. The theoretical calculations of these quantities are in quantitative agreement with experiment. We conjecture that these are robust properties of all strongly correlated metals, and test the conjecture by carrying out a similar analysis on thin film NdNiO₃ on a LaAlO₃ substrate.

Optical response of Sr2RuO4 reveals universal fermi-liquid scaling and quasiparticles beyond Landau theory

We report optical measurements demonstrating that the low-energy relaxation rate (1/τ) of the conduction electrons in Sr(2)RuO(4) obeys scaling relations for its frequency (ω) and temperature (T) dependence in accordance with Fermi-liquid theory. In the thermal relaxation regime, 1/τ ∝ (ħω)(2)+(pπk(B)T)(2) with p = 2, and ω/T scaling applies. Many-body electronic structure calculations using dynamical mean-field theory confirm the low-energy Fermi-liquid scaling and provide quantitative understanding of the deviations from Fermi-liquid behavior at higher energy and temperature. The excess optical spectral weight in this regime provides evidence for strongly dispersing "resilient" quasiparticle excitations above the Fermi energy.

Normal-state charge dynamics in doped BaFe₂As₂: roles of doping and necessary ingredients for superconductivity

In high-transition-temperature superconducting cuprates and iron arsenides, chemical doping plays an important role in inducing superconductivity. Whereas in the cuprate case, the dominant role of doping is to inject charge carriers, the role for the iron arsenides is complex owing to carrier multiplicity and the diversity of doping. Here, we present a comparative study of the in-plane resistivity and the optical spectrum of doped BaFe₂As₂, which allows for separation of coherent (itinerant) and incoherent (highly dissipative) charge dynamics. The coherence of the system is controlled by doping, and the doping evolution of the charge dynamics exhibits a distinct difference between electron and hole doping. It is found in common with any type of doping that superconductivity with high transition temperature emerges when the normal-state charge dynamics maintains incoherence and when the resistivity associated with the coherent channel exhibits dominant temperature-linear dependence.