Mott Metal-insulator Transition Research Articles

Transition of a pristine Mott insulator to a correlated Fermi liquid: Pressure-dependent optical investigations of a quantum spin liquid

Systematic pressure- and temperature-dependent infrared studies on the two-dimensional organic quantum spin-liquid $\beta^{\prime}$-EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ disclose the electronic and lattice evolution across the Mott insulator-metal transition. Increasing hydrostatic pressure continuously suppresses the insulating ground state; for $p>0.6$~GPa, a Drude-like component develops indicating the appearance of coherent quasiparticles at the Fermi level. In the vicinity of the Mott transition, not only the electronic state changes rapidly, but also the vibration modes exhibit a jump both in frequency and Fano constant, underlining the strong coupling between lattice and electrons. The anisotropy of the in-plane optical response becomes inverted above 0.6~GPa. The findings are discussed in detail and summarized in a phase diagram comprising different experimental approaches.

Frustrated Magnetism in Mott Insulating (V1−xCrx)2O3

V2O3 famously features all four combinations of paramagnetic vs antiferromagnetic, and metallic vs insulating states of matter in response to %-level doping, pressure in the GPa range, and temperature below 300 K. Using time-of-flight neutron spectroscopy combined with density functional theory calculations of magnetic interactions, we have mapped and analyzed the inelastic magnetic neutron scattering cross section over a wide range of energy and momentum transfer in the chromium stabilized antiferromagnetic and paramagnetic insulating phases (AFI & PI). Our results reveal an important magnetic frustration and degeneracy of the PI phase which is relieved by the rhombohedral to monoclinic transition at $T_N=185$ K due to a significant magneto-elastic coupling. This leads to the recognition that magnetic frustration is an inherent property of the paramagnetic phase in $\rm (V_{1-x}Cr_x)_2O_3$ and plays a key role in suppressing the magnetic long range ordering temperature and exposing a large phase space for the paramagnetic Mott metal-insulator transition to occur.

Manifestation of electron correlation effect in 5f states of uranium compounds revealed by 4d–5f resonant photoelectron spectroscopy

We have elucidated the nature of the electron correlation effect in uranium compounds by imaging the partial $\mathrm{U}~5f$ density of states (pDOS) of typical itinerant, localized, and heavy fermion uranium compounds by using the $\mathrm{U}~4d-5f$ resonant photoemission spectroscopy. Obtained $\mathrm{U}~5f$ pDOS exhibit a systematic trend depending on the physical properties of compounds. The coherent peak at the Fermi level can be described by the band-structure calculation, but an incoherent peak emerges on the higher binding energy side ($\lesssim 1~\mathrm{eV}$) in the \Uf pDOS of localized and heavy fermion compounds. As the $\mathrm{U}~5f$ state is more localized, the intensity of the incoherent peak is enhanced and its energy position is shifted to higher binding energy. These behaviors are consistent with the prediction of the Mott metal-insulator transition, suggesting that the Hubbard-$U$ type mechanism takes an essential role in the $5f$ electronic structure of actinide materials.

Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling

We formulate a finite-temperature scheme of the variational cluster approximation (VCA) particularly suitable for an exact-diagonalization cluster solver. Based on the analytical properties of the single-particle Green's function matrices, we explicitly show the branch-cut structure of logarithm of the complex determinant functions appearing in the self-energy-functional theory (SFT) and whereby construct an efficient scheme for the finite-temperature VCA. We first apply the method to explore the antiferromagnetic order in a half-filled Hubbard model by calculating the entropy, specific heat, and single-particle excitation spectrum for different values of on-site Coulomb repulsion $U$ and temperature $T$. We also calculate the $T$ dependence of the single-particle excitation spectrum in the strong coupling region, and discuss the overall similarities to and the fine differences from the spectrum obtained by the spin-density-wave mean-field theory at low temperatures and the Hubbard-I approximation at high temperatures. On the basis of the thermodynamic properties, we obtain a crossover diagram in the $(U,T)$-plane which separates a Slater-type insulator and a Mott-type insulator. Next, we demonstrate the finite-temperature scheme in the cluster-dynamical-impurity approximation (CDIA) and study the paramagnetic Mott metal-insulator transition in the half-filled Hubbard model. Formulating the finite-temperature CDIA, we first address a subtle issue regarding the treatment of the artificially introduced bath degrees of freedom which are absent in the originally considered Hubbard model. We then apply the finite-temperature CDIA to calculate the finite-temperature phase diagram in the $(U,T)$-plane. We find that the Mott transition at low temperatures is discontinuous, and the coexistence region of the metallic and insulating states persists down to zero temperature.

Precise simulation of strongly correlated quantum impurity systems

In recent years, nano-sized systems involving local charge or spin states have received wide interests because of their potential application in emerging fields such as quantum information and quantum computation. For instance, organometallic molecular complexes may serve as building blocks of quantum storage devices, because the spin-unpaired d or f electrons at transition metal centers may be employed to construct spin qubits. Moreover, if the system contains strong electron-electron interaction, the involving local quantum states are subject to prominent electron correlation effects (such as the Kondo effect). Theoretically, spatially confined nano-systems are often described by quantum impurity models. Thus the accurate prediction of the intrinsic properties of quantum impurity systems and the deep understanding on the response and evolution of local quantum states under external fields or in dissipative environment are fundamentally important for the design and fabrication of quantum devices. The accurate characterization of quantum coherence, correlation, and entanglement in quantum impurity systems remains a great challenge. Enormous efforts have been made to achieve this goal. A variety of theoretical methods have been developed, including the numerical renormalization group method, the quantum Monte Carlo method, and many others. However, all the existing methods are subject to certain limitations regarding accuracy or efficiency. Therefore, we choose to view this problem from a new perspective—the perspective of open quantum systems. Over the past decade, we have developed a formally exact quantum dissipation theory, the hierarchical equations of motion (HEOM) theory, for fermionic open systems. The HEOM theory captures the combined effects of system-environment dissipation, many-body interaction, and non-Markovian memory in a nonperturbative manner. It is capable of addressing static and dynamic responses of system observables in both equilibrium and nonequilibrium situations. We have implemented the HEOM method in our self-designed computer program HEOM-QUICK. We have also devised a series of advanced algorithms which substantially enhance the numerical efficiency of HEOM. The HEOM-QUICK program thus provides an accurate, efficient, and versatile theoretical tool for the investigation of strongly correlated quantum impurity systems. We have applied the HEOM method to study a variety of problems associated with quantum impurity systems. These include the intrinsic properties of quantum impurity models and lattice models, the transient current response of quantum dots to ac voltages, the thermopower and local heating effect in nonequilibrium quantum dots, and the tuning of local spin states in adsorbed molecular magnets. In particular, the HEOM method has been combined with density functional theory (DFT) method, and thus allows for first-principles-based simulation on the precise tuning of local spin states in adsorbed magnetic molecules. Numerical simulations have discovered or reproduced many important quantum phenomena that are essential for relevant experiments, including the Kondo effect, Mott metal-insulator transition, quantum memristive effect, etc. This paper gives a brief overview of our development of the HEOM method for fermionic open systems, as well as its applications to various strongly correlated quantum impurity systems.

Pressure-Induced Site-Selective Mott Insulator-Metal Transition inFe2O3

We provide experimental and theoretical evidence for a pressure-induced Mott insulator-metal transition in Fe2O3 characterized by site-selective delocalization of the electrons. Density functional plus dynamical mean-field theory (DFT+DMFT) calculations, along with Mössbauer spectroscopy, x-ray diffraction, and electrical transport measurements on Fe2O3 up to 100 GPa, reveal this site-selective Mott transition between 50 and 68 GPa, such that the metallization can be described by (Fe3+HSVI)2O3 [R3¯c structure]→50 GPa(Fe3+HSVIII FeVIM)O3 [P21/n structure]→68 GPa(FeMVI)2O3[Aba2/PPv structure]. Within the P21/n crystal structure, characterized by two distinct coordination sites (VI and VIII), we observe equal abundances of ferric ions (Fe3+) and ions having delocalized electrons (FeM), and only at higher pressures is a fully metallic high-pressure structure obtained, all at room temperature. Thereby, the transition is characterized by delocalization/metallization of the 3d electrons on half the Fe sites, with a site-dependent collapse of local moments. Above approximately 50 GPa, Fe2O3 is a strongly correlated metal with reduced electron mobility (large band renormalizations) of m*/m∼4 and 6 near the Fermi level. Importantly, upon decompression, we observe a site-selective (metallic) to conventional Mott insulator phase transition (Fe3+HSVIII FeVIM)O3→50 GPa(Fe3+HSVIII FeVI3+HS)O3 within the same P21/n structure, indicating a decoupling of the electronic and lattice degrees of freedom. Our results offer a model for understanding insulator-metal transitions in correlated electron materials, showing that the interplay of electronic correlations and crystal structure may result in rather complex behavior of the electronic and magnetic states of such compounds.3 MoreReceived 15 December 2017Revised 1 June 2018DOI:https://doi.org/10.1103/PhysRevX.8.031059Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBand gapDensity of statesElectrical conductivityInsulatorsMagnetic phase transitionsMetal-insulator transitionMetalsPhase transitionsPressure effectsSolid-solid transformationsPhysical SystemsCrystal structuresMott insulatorsPolycrystalline materialsStrongly correlated systemsTechniquesBand structure methodsCryogenicsDensity functional theoryDynamical mean field theoryLiquid helium coolingLiquid nitrogen coolingMössbauer spectroscopyTransport techniquesX-ray diffractionX-ray powder diffractionCondensed Matter, Materials & Applied Physics

Uncovering the Mechanism of the Impurity-Selective Mott Transition in Paramagnetic V_{2}O_{3}.

While the phase diagrams of the one- and multiorbital Hubbard model have been well studied, the physics of real Mott insulators is often much richer, material dependent, and poorly understood. In the prototype Mott insulator V_{2}O_{3}, chemical pressure was initially believed to explain why the paramagnetic-metal to antiferromagnetic-insulator transition temperature is lowered by Ti doping while Cr doping strengthens correlations, eventually rendering the high-temperature phase paramagnetic insulating. However, this scenario has been recently shown both experimentally and theoretically to be untenable. Based on full structural optimization, we demonstrate via the charge self-consistent combination of density functional theory and dynamical mean-field theory that changes in the V_{2}O_{3} phase diagram are driven by defect-induced local symmetry breakings resulting from dramatically different couplings of Cr and Ti dopants to the host system. This finding emphasizes the high sensitivity of the Mott metal-insulator transition to the local environment and the importance of accurately accounting for the one-electron Hamiltonian, since correlations crucially respond to it.

Lattice Energetics and Correlation-Driven Metal-Insulator Transitions: The Case of Ca_{2}RuO_{4}.

This Letter uses density functional, dynamical mean field, and Landau-theory methods to elucidate the interplay of electronic and structural energetics in the Mott metal-insulator transition. A Landau-theory free energy is presented that incorporates the electronic energetics, the coupling of the electronic state to local distortions and the coupling of local distortions to long-wavelength strains. The theory is applied to Ca_{2}RuO_{4}. The change in lattice energy across the metal-insulator transition is comparable to the change in electronic energy. Important consequences are a strongly first order transition, a sensitive dependence of the phase boundary on pressure and that the geometrical constraints on in-plane lattice parameter associated with epitaxial growth on a substrate typically change the lattice energetics enough to eliminate the metal-insulator transition entirely.

First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction

While the Hubbard model is the standard model to study Mott metal-insulator transitions, it is still unclear to which extent it can describe metal-insulator transitions in real solids, where non-local Coulomb interactions are always present. By using a variational principle, we clarify this issue for short- and long-ranged non-local Coulomb interactions for half-filled systems on bipartite lattices. We find that repulsive non-local interactions generally stabilize the Fermi-liquid regime. The metal-insulator phase boundary is shifted to larger interaction strengths to leading order linearly with non-local interactions. Importantly, non-local interactions can raise the order of the metal-insulator transition. We present a detailed analysis of how the dimension and geometry of the lattice as well as the temperature determine the critical non-local interaction leading to a first-order transition: for systems in more than two dimensions with non-zero density of states at the Fermi energy the critical non-local interaction is arbitrarily small; otherwise it is finite.

Low-Frequency Dynamics of Strongly Correlated Electrons in (BEDT-TTF)2X Studied by Fluctuation Spectroscopy

Fluctuation spectroscopy measurements of quasi-two-dimensional organic charge-transfer salts (BEDT-TTF) 2 X are reviewed. In the past decade, the method has served as a new approach for studying the low-frequency dynamics of strongly correlated charge carriers in these materials. We review some basic aspects of electronic fluctuations in solids, and give an overview of selected problems where the analysis of 1 / f -type fluctuations and the corresponding slow dynamics provide a better understanding of the underlying physics. These examples are related to (1) an inhomogeneous current distribution due to phase separation and/or a percolative transition; (2) slow dynamics due to a glassy freezing either of structural degrees of freedom coupling to the electronic properties or (3) of the electrons themselves, e.g., when residing on a highly-frustrated crystal lattice, where slow and heterogeneous dynamics are key experimental properties for the vitrification process of a supercooled charge-liquid. Another example is (4), the near divergence and critical slowing down of charge carrier fluctuations at the finite-temperature critical endpoint of the Mott metal-insulator transition. Here also indications for a glassy freezing and temporal and spatial correlated dynamics are found. Mapping out the region of ergodicity breaking and understanding the influence of disorder on the temporal and spatial correlated fluctuations will be an important realm of future studies, as well as the fluctuation properties deep in the Mott or charge-ordered insulating states providing a connection to relaxor or ordered ferroelectric states studied by dielectric spectroscopy.

Splitting of electrons and violation of the Luttinger sum rule

We obtain a controlled description of a strongly correlated regime of electronic behaviour. We begin by arguing that there are two ways to characterise the electronic degree of freedom, either by the canonical fermion algebra or the graded Lie algebra su(2|2). The first underlies the Fermi liquid description of correlated matter, and we identify a novel regime governed by the latter. We exploit an exceptional central extension of su(2|2) to employ a perturbative scheme recently developed by Shastry, and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.

Realization of a scenario with two relaxation rates in the Hubbard Falicov-Kimball model

A single transport relaxation rate governs the decay of both longitudinal and Hall currents in Landau Fermi liquids (FL). Breakdown of this fundamental feature, first observed in two-dimensional cuprates and subsequently in other three-dimensional correlated systems close to the Mott metal-insulator transition, played a pivotal role in emergence of a non-FL (NFL) paradigm in higher dimensions $D(>1)$. Motivated hereby, we explore the emergence of this ``two relaxation rates'' scenario in the Hubbard Falicov-Kimball model (HFKM) using the dynamical mean-field theory (DMFT). Specializing to $D=3$, we find, beyond a critical Falicov-Kimball (FK) interaction, that two distinct relaxation rates governing distinct temperature $(T)$ dependence of the longitudinal and Hall currents naturally emerges in the NFL metal. Our results show good accord with the experiment in ${\mathrm{V}}_{2\ensuremath{-}y}{\mathrm{O}}_{3}$ near the metal-to-insulator transition (MIT). We rationalize this surprising finding by an analytical analysis of the structure of charge and spin Hamiltonians in the underlying impurity problem, specifically through a bosonization method applied to the Wolff model and connecting it to the x-ray edge problem.

Correlation-Driven Lifshitz Transition at the Emergence of the Pseudogap Phase in the Two-Dimensional Hubbard Model.

We study the relationship between the pseudogap and Fermi-surface topology in the two-dimensional Hubbard model by means of the cellular dynamical mean-field theory. We find two possible mean-field metallic solutions on a broad range of interactions, doping, and frustration: a conventional renormalized metal and an unconventional pseudogap metal. At half filling, the conventional metal is more stable and displays an interaction-driven Mott metal-insulator transition. However, for large interactions and small doping, a region that is relevant for cuprates, the pseudogap phase becomes the ground state. By increasing doping, we show that a first-order transition from the pseudogap to the conventional metal is tied to a change of the Fermi surface from hole- to electronlike, unveiling a correlation-driven mechanism for a Lifshitz transition. This explains the puzzling link between the pseudogap phase and Fermi surface topology that has been pointed out in recent experiments.

Quasi-continuous transition from a Fermi liquid to a spin liquid in \u03ba-(ET)2Cu2(CN)3

The Mott metal-insulator transition—a manifestation of Coulomb interactions among electrons—is known as a discontinuous transition. Recent theoretical studies, however, suggest that the transition is continuous if the Mott insulator carries a spin liquid with a spinon Fermi surface. Here, we demonstrate the case of a quasi-continuous Mott transition from a Fermi liquid to a spin liquid in an organic triangular-lattice system κ-(ET)2Cu2(CN)3. Transport experiments performed under fine pressure tuning have found that as the Mott transition is approached, the Fermi liquid coherence temperature continuously falls to the scale of kelvins, with a divergent quasi-particle decay rate on the metal side, and the charge gap continuously closes on the insulator side. A Clausius-Clapeyron analysis provides thermodynamic evidence for the extremely weak first-order nature of the transition. These results provide additional support for the existence of a spinon Fermi surface, which becomes an electron Fermi surface when charges are delocalized.

Effects of Disorder on the Pressure-Induced Mott Transition in κ-(BEDT-TTF)2Cu[N(CN)2]Cl

We present a study of the influence of disorder on the Mott metal-insulator transition for the organic charge-transfer salt κ -(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl. To this end, disorder was introduced into the system in a controlled way by exposing the single crystals to X-ray irradiation. The crystals were then fine-tuned across the Mott transition by the application of continuously controllable He-gas pressure at low temperatures. Measurements of the thermal expansion and resistance show that the first-order character of the Mott transition prevails for low irradiation doses achieved by irradiation times up to 100 h. For these crystals with a moderate degree of disorder, we find a first-order transition line which ends in a second-order critical endpoint, akin to the pristine crystals. Compared to the latter, however, we observe a significant reduction of both, the critical pressure p c and the critical temperature T c . This result is consistent with the theoretically-predicted formation of a soft Coulomb gap in the presence of strong correlations and small disorder. Furthermore, we demonstrate, similar to the observation for the pristine sample, that the Mott transition after 50 h of irradiation is accompanied by sizable lattice effects, the critical behavior of which can be well described by mean-field theory. Our results demonstrate that the character of the Mott transition remains essentially unchanged at a low disorder level. However, after an irradiation time of 150 h, no clear signatures of a discontinuous metal-insulator transition could be revealed anymore. These results suggest that, above a certain disorder level, the metal-insulator transition becomes a smeared first-order transition with some residual hysteresis.

Pressure-induced Mott-insulator–metal crossover at ambient temperature in an overexpanded fulleride

The Mott-insulator–metal transition in A3C60 fullerides is traversed at ambient temperature through the application of external pressure.

Hydrothermal Synthesis and Phase Transition Properties of Uniform Free-standing Vanadium Dioxide Nanowires

Vanadium dioxide (VO 2 ) undergoes a Mott metal-insulator transition (MIT) close to room temperature, and has been suggested as a candidate for use in smart window and adaptive infrared camouflage. Here we report the synthesis of uniform free-standing VO 2 nanowires using a novel hydrothermal method. The synthetic nanowires have typical diameters of 150±30 nm and lengths of tens of micrometer. These VO 2 nanowires exhibit high crystallinity and a pure monoclinic phase, which were characterized by X-ray diffraction, X-ray photoelectron spectroscopy, high resolution transmission electron microscopy and selected area electron diffraction. Moreover, reversible phase transition properties of VO 2 nanowires are monitored via differential scanning calorimetry, variable temperature X-ray diffraction and temperature-dependent Raman spectroscopy. The results show VO 2 nanowires obtained exhibit a reversible phase transition with an endothermic phase transition at 65.2 °C and a narrow hysteresis width of 6.5 °C. These VO 2 nanowires should be promising materials for fundamental investigations of nanoscale metal-insulator transitions.

Response of the Lattice across the Filling-Controlled Mott Metal-Insulator Transition of a Rare Earth Titanate.

The lattice response of a prototype Mott insulator, SmTiO_{3}, to hole doping is investigated with atomic-scale spatial resolution. SmTiO_{3} films are doped with Sr on the Sm site with concentrations that span the insulating and metallic sides of the filling-controlled Mott metal-insulator transition (MIT). The GdFeO_{3}-type distortions are investigated using an atomic resolution scanning transmission electron microscopy technique that can resolve small lattice distortions with picometer precision. We show that these distortions are gradually and uniformly reduced as the Sr concentration is increased without any phase separation. Significant distortions persist into the metallic state. The results present a new picture of the physics of this prototype filling-controlled MIT, which is discussed.

Physical origins of current and temperature controlled negative differential resistances in NbO2

Negative differential resistance behavior in oxide memristors, especially those using NbO2, is gaining renewed interest because of its potential utility in neuromorphic computing. However, there has been a decade-long controversy over whether the negative differential resistance is caused by a relatively low-temperature non-linear transport mechanism or a high-temperature Mott transition. Resolving this issue will enable consistent and robust predictive modeling of this phenomenon for different applications. Here we examine NbO2 memristors that exhibit both a current-controlled and a temperature-controlled negative differential resistance. Through thermal and chemical spectromicroscopy and numerical simulations, we confirm that the former is caused by a ~400 K non-linear-transport-driven instability and the latter is caused by the ~1000 K Mott metal-insulator transition, for which the thermal conductance counter-intuitively decreases in the metallic state relative to the insulating state.

Mott metal-insulator transition in the doped Hubbard-Holstein model

Motivated by the current interest in the understanding of the Mott insulators away from half filling, observed in many perovskite oxides, we study the Mott metal-insulator transition (MIT) in the doped Hubbard-Holstein model using the Hatree-Fock mean field theory. The Hubbard-Holstein model is the simplest model containing both the Coulomb and the electron-lattice interactions, which are important ingredients in the physics of the perovskite oxides. In contrast to the half-filled Hubbard model, which always results in a single phase (either metallic or insulating), our results show that away from half-filling, a mixed phase of metallic and insulating regions occur. As the dopant concentration is increased, the metallic part progressively grows in volume, until it exceeds the percolation threshold, leading to percolative conduction. This happens above a critical dopant concentration $\delta_c$, which, depending on the strength of the electron-lattice interaction, can be a significant fraction of unity. This means that the material could be insulating even for a substantial amount of doping, in contrast to the expectation that doped holes would destroy the insulating behavior of the half-filled Hubbard model. Our theory provides a framework for the understanding of the density-driven metal-insulator transition observed in many complex oxides.