Glassy dynamics of electrons near the metal-insulator transition
Dragana Popović
备注：
46 pages, 18 figures; added references; To be published in "Conductor Insulator Quantum Phase Transitions", edited by V. Dobrosavljevic, N. Trivedi, and J.M. Valles Jr., Oxford University Press, 2012, ISBN 9780199592593
This review first describes the evidence that strongly suggests the existence of the metal-insulator transition (MIT) in a two-dimensional electron system in Si regardless of the amount of disorder. Extensive studies of the charge dynamics demonstrate that this transition is closely related to the glassy freezing of electrons as temperature T->0. Similarities to the behavior of three-dimensional materials raise the intriguing possibility that such correlated dynamics might be a universal feature of the MIT regardless of the dimensionality.
The emergence of glassy behavior of electrons is investigated for systems close to the disorder and/or interaction-driven metal-insulator transitions. Our results indicate that Anderson localization effects strongly stabilize such glassy behavior, while Mott localization tends to suppress it. We predict the emergence of an intermediate metallic glassy phase separating the insulator from the normal metal. This effect is expected to be most pronounced for sufficiently disordered systems, in agreement with recent experimental observations.
Glassy behavior is a generic feature of electrons close to disorder-driven metal-insulator transitions. Deep in the insulating phase, electrons are tightly bound to impurities, and thus classical models for electron glasses have long been used. As the metallic phase is approached, quantum fluctuations become more important, as they control the electronic mobility. In this paper we review recent work that used extended dynamical mean-field approaches to discuss the influence of such quantum fluctuations on the glassy behavior of electrons, and examine how the stability of the glassy phase is af…
Studies of low-frequency resistance noise demonstrate that glassy freezing occurs in a two-dimensional electron system in silicon in the vicinity of the metal-insulator transition (MIT). The width of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility (low-disorder) samples. The glass transition is manifested by a sudden and dramatic slowing down of the electron dynamics, and by a very abrupt change to the sort of statistics characteristic of complicated multistate systems. In particular, the…
A theoretical model is presented, describing the glassy freezing of electrons in the vicinity of disorder driven metal-insulator transitions. Our results indicate that the onset of glassy dynamics should emerge before the localization transition is reached, thus predicting the existence of an intermediate metallic glass phase between the normal metal and the insulator.
Studies of low-frequency resistance noise show that the glassy freezing of the two-dimensional (2D) electron system in the vicinity of the metal-insulator transition occurs in all Si inversion layers. The size of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility samples. The behavior of the second spectrum, an important fourth-order noise statistic, indicates the presence of long-range correlations between fluctuators in the glassy phase, consistent with the hierarchical picture of glassy d…
We present a detailed study of the electronic transport properties on a single crystalline specimen of the moderately disordered heavy fermion system URh$_2$Ge$_2$. For this material, we find glassy electronic transport in a single crystalline compound. We derive the temperature dependence of the electrical conductivity and establish metallicity by means of optical conductivity and Hall effect measurements. The overall behavior of the electronic transport properties closely resembles that of metallic glasses, with at low temperatures an additional minor spin disorder contribution. We argue tha…
Non magnetic insulators/semiconductors with induced magnetism introduced via transition metal substitution are one of the promising materials in the field of spintronic, magnetoelectronics and magneto optical devices. In this context, here, we focus on magnetism induced in a non magnetic insulator CaHfO3, by the substitution of 4d element Ru, at Hf site. Structural investigations indicate that substitution of Ru4+ (up to 50%) does not affect the original crystal structure of the parent compound. Magnetic studies divulge a crossover from a diamagnetic to paramagnetic state with 20% Ru substitut…
The elucidation of nonequilibrium states in strongly correlated systems holds the key to emergence of novel quantum phases. The nonequilibrium-induced insulator-to-metal transition is particularly interesting since it reflects the fundamental nature of competition between itinerancy and localization of the charge degrees of freedom. We investigate pulse-excited insulator-to-metal transition of the half-filled one-dimensional extended Hubbard model. Calculating the time-dependent optical conductivity with the time-dependent density-matrix renormalization group, we find that strong mono- and hal…
Aging effects in the relaxations of conductivity of a two-dimensional electron system in Si have been studied as a function of carrier density. They reveal an abrupt change in the nature of the glassy phase at the metal-insulator transition (MIT): (a) while full aging is observed in the insulating regime, there are significant departures from full aging on the metallic side of the MIT, before the glassy phase disappears completely at a higher density $n_g$; (b) the amplitude of the relaxations peaks just below the MIT, and it is strongly suppressed in the insulating phase. Other aspects of agi…
Motivated by the rich interplay among electronic correlation, spin-orbit coupling (SOC), crystal-field splitting, and geometric frustrations in the honeycomb-like lattice, we systematically investigated the electronic and magnetic properties of Li$_2$RhO$_3$. The material is semiconducting with a narrow band gap of $Δ\sim$78 meV, and its temperature dependence of resistivity conforms to 3D variable range hopping mechanism. No long-range magnetic ordering was found down to 0.5 K, due to the geometric frustrations. Instead, single atomic spin-glass behavior below the spin-freezing temperature ($…
The anelastic spectra (elastic energy loss and dynamic modulus versus temperature) of La1-xCaxMnO3 have been measured for 0.33< x < 0.5. A peak in the imaginary part of the elastic susceptibility is found slightly below the Curie temperature, whose temperature and frequency dependences are typical of the dielectric and magnetic susceptibilities of relaxor ferroelectrics, spin glasses and other inhomogeneous frustrated systems. The fluctuations can be associated with the magnetic clusters which are observed by several techniques or with charge-ordered insulating domains in the low temperature i…
We propose a phase diagram for FexBi2Te3 (0 < x < 0.1) single crystals, which belong to a class of magnetically bulk-doped topological insulators. The evolution of magnetic correlations from ferromagnetic- to antiferromagnetic- gives rise to topological phase transitions, where the paramagnetic topological insulator of Bi2Te3 turns into a band insulator with ferromagnetic-cluster glassy behaviours around x ~ 0.025, and it further evolves to a topological insulator with valence-bond glassy behaviours, which spans over the region between x ~ 0.03 up to x ~ 0.1. This phase diagram is verified by …
Frustrated Mott insulators such as transition metal dichalcogenides present an ideal platform for the experimental realization of externally tuned insulator-metal transition. In this paper, we present the first nonperturbative numerical investigation of the disorder-induced insulator-metal transition in a two-dimensional frustrated Mott insulator. Our approach is generic and captures the essential physics of Mott insulator-metal transition in geometrically frustrated lattices. For concreteness, we have compared our results with the experimental observations on copper (Cu) intercalated 1T-TaS2.…
We discuss the recently discovered two-dimensional metal-insulator transition in zero magnetic field in the light of the scaling theory of localization. We demonstrate that the observed symmetry relating conductivity and resistivity follows directly from the quantum critical behavior associated with such a transition. In addition, we show that very general scaling considerations imply that any disordered two dimensional metal is a perfect metal, but most likely not a Fermi liquid.
The metal-insulator transition (MIT) observed in two-dimensional (2D) systems is apparently contradictory to the well known scaling theory of localization. By investigating the conductance of disordered one-dimensional systems with a finite phase coherence length, we show that by changing the phase coherence length or the localization length, it is possible to observe the transition from insulator-like behavior to metal-like behavior, and the transition is a crossover between the quantum and classical regimes. The resemblance between our calculated results and the experimental findings of 2D M…
The time-dependent fluctuations of conductivity σhave been studied in a two-dimensional electron system in low-mobility, small-size Si inversion layers. The noise power spectrum is ~1/f^α with αexhibiting a sharp jump at a certain electron density n_s=n_g. An enormous increase in the relative variance of σis observed as n_s is reduced below n_g, reflecting a dramatic slowing down of the electron dynamics. This is attributed to the freezing of the electron glass. The data strongly suggest that glassy dynamics persists in the metallic phase.
The quantum spin continuum and classical spin freezing, associated with a glassy state, represent two opposite extremes of a correlated electronic material. Here, we report the coexistence of a quantum spin continuum with a weak spin glass order in Co-doped CaRuO$_{3}$ perovskite near the chemical doping dependent metal-insulator transition boundary. Inelastic neutron measurements on Ca(Co$_{0.15}$Ru$_{0.85}$)O$_{3}$ at low temperature, $T$ = 1.5 K, reveal a continuum spectrum in the $Q-E$ space due to uncorrelated spin fluctuations. This persists across the glass transition at $T_G \simeq$23 …
We report on the dramatic slowing down of the charge carrier dynamics in a quasi-two-dimensional organic conductor, which can be reversibly tuned through the Mott metal-insulator transition (MIT). At the finite-temperature critical endpoint we observe a divergent increase of the resistance fluctuations accompanied by a drastic shift of spectral weight to low frequencies, demonstrating the critical slowing down of the order parameter (doublon density) fluctuations. The slow dynamics is accompanied by non-Gaussian fluctuations, indicative of correlated charge carrier dynamics. A possible explana…
We investigate relaxation in the recently discovered "fracton" models and discover that these models naturally host glassy quantum dynamics in the absence of quenched disorder. We begin with a discussion of "type I" fracton models, in the taxonomy of Vijay, Haah, and Fu. We demonstrate that in these systems, the mobility of charges is suppressed exponentially in the inverse temperature. We further demonstrate that when a zero temperature type I fracton model is placed in contact with a finite temperature heat bath, the approach to equilibrium is a logarithmic function of time over an exponenti…
We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emery-Luther mapping. The gapless glassy edge state spontaneously breaks time-reversal symmetry in a `spin glass' fashion, and may be viewed as a localized state of solitons which carry half integer charge. Such a qualitatively distinct edge state provides a simple explanation for heretofore puzzling experimental observations. This phase exhibits a str…
The ground state phase diagrams of the Falicov--Kimball model with local disorder is derived within the dynamical mean--field theory and using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases are identified. The metal--insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.
Angle-resolved photoemission spectroscopy was used to investigate the evolution of the electronic structure across the metal-insulator transition in bi-layer manganite $La_{1.24}Sr_{1.76}Mn_2O_7$. We found that this system is a metal for $T<T_C$, a local metal but global insulator for $T<T_C<T^*$, and a global insulator for $T>T^*$. These results indicate the critical role of electronic phase separation and percolation effects for the metal-insulator transition in $La_{1.24}Sr_{1.76}Mn_2O_7$.
We study the Hubbard-Holstein model, which includes both the electron-electron and electron-phonon interactions characterized by $U$ and $g$, respectively, employing the dynamical mean-field theory combined with Wilson's numerical renormalization group technique. A zero temperature phase diagram of metal-insulator and insulator-insulator transitions at half-filling is mapped out which exhibits the interplay between $U$ and $g$. As $U$ ($g$) is increased, a metal to Mott-Hubbard insulator (bipolaron insulator) transition occurs, and the two insulating states are distinct and can not be adiabati…
Metal-insulator transition features as a transformation, from a highly charge conductive state to another state where charge conductivity is greatly suppressed when decreasing the temperature. Here we demonstrate two consecutive transitions in NdNiO3 films with CoFe2O4 capping, in which the metal-insulator transition occurs at 85 K, followed by an unprecedented insulator-metal transition below 40 K. The emerging insulator-metal transition associated with a weak antiferromagnetic behavior is observed in 20 unit cell-thick NdNiO3 with more than 5 unit cell CoFe2O4 capping. Differently, the NdNiO…
We show that the resistivity perpendicular $ρ_c$ and parallel $ρ_a$ to the basal planes of different graphite samples show similar magnetic-field-driven metal-insulator-transitions at a field $B_c \sim 0.1 T$ applied parallel to the c-axis. Our results demonstrate the universality of the recently found scaling in $ρ_a$ of graphite and indicate that the metallic-like temperature dependence of $ρ_c$ is directly correlated to that of $ρ_a$. The similar magnetoresistance found for both resistivities, the violation of Kohler's rule and the field-induced transition indicate that the semiclassical tr…
Ruthenates provide comprehensive platform to study a plethora of novel properties, such as quantum magnetism, superconductivity and magnetic fluctuation mediated metal-insulator transition. In this article, we provide an overview of quantum mechanical phenomenology in calcium ruthenium oxide with varying compositions. While the stochiometric composition of CaRuO$_{3}$ exhibits non-Fermi liquid behavior with quasi-criticality, chemically doped compounds depict prominent signatures of quantum magnetic fluctuations at low temperature that in some cases are argued to mediate in metal-insulator tra…
The periodic Anderson lattice model for the crystalline electric field (CEF)split 4f quartet states is used to describe the Yb-based Kondo insulators/semiconductors. In the slave-boson mean-field approximation, we derive the hybridized quasiparticle bands, and find that decreasing the hybridization difference of the two CEF quartets may induce an insulator-to-metal phase transition. The resulting metallic phase has a hole and an electron Fermi pockets. Such a phase transition may be realized experimentally by applying pressure, reducing the difference in hybridization of the two CEF quartets.
A theoretical study has been undertaken of the Peltier effect in normal metal - insulator - heavy fermion metal junctions. The results indicate that, at temperatures below the Kondo temperature, such junctions can be used as electronic microrefrigerators to cool the normal metal electrode and are several times more efficient in cooling than the normal metal - heavy fermion metal junctions.
Quantum transitions between the Mott insulator and metals by controlling filling in two-dimensional square lattice are characterized by a large dynamical exponent $z=4$ where the origin of unusual metallic properties near the Mott insulator are ascribed to the proximity of the transition. The scaling near the transition indicates the formation of flat dispersion area due to singular momentum dependence of the single-particle renormalization. The flat dispersion controls critical properties of the Mott transition. An instability of the flat dispersion to the d-wave superconducting order is disc…
We consider a heterostructure of a metal and a paramagnetic Mott insulator using an adaptation of dynamical mean field theory to describe inhomogeneous systems. The metal can penetrate into the insulator via the Kondo effect. We investigate the scaling properties of the metal-insulator interface close to the critical point of the Mott insulator. At criticality, the quasiparticle weight decays as 1/x^2 with distance x from the metal within our mean field theory. Our numerical results (using the numerical renormalization group as an impurity solver) show that the prefactor of this power law is e…
We investigate the metal insulator transitions at finite temperature for the Hubbard model with diagonal alloy disorder. We solve the dynamical mean field theory equations with the non crossing approximation and we use the coherent potential approximation to handle disorder. The excitation spectrum is given for various correlation strength $U$ and disorder. Two successive metal insulator transitions are observed at integer filling values as $U$ is increased. An important selective transfer of spectral weight arises upon doping. The strong influence of the temperature on the low energy dynamics…
A brief review of metal-insulator transitions in three-dimensional doped semiconductors, with emphasis on the "critical exponent puzzle"; and new experimental findings that signal the possibility of an unexpected metal-insulator transition in dilute two-dimensional systems, such as silicon MOSFETs and GaAs/AlGaAs heterostructures.
We show that the metal to insulator transition, whether generated by decreasing the electron density or by increasing the spin alignment, is determined by a universal functional form of the two-electron correlation function g(r). This result provides direct evidence of the central role of the Coulomb repulsion and exchange in driving the metal-insulator transition.
The role of orbital ordering on metal-insulator transition of transition-metal oxides is investigated by the cluster self-consistent field approach in the strong correlation regime. A clear dependence of the insulating gap on the orbital order parameter is found in the single-particle excitation spectra. The thermal fluctuation drives the orbital order-disorder transition, diminishes the gap and leads to the metal-insulator transition. The interplay between spins and orbits results in unusual temperature dependence of the orbital polarization in the orbital insulator, which can be seen in the …
We consider a model for a metal-insulator transition of correlated electrons in an external magnetic field. We find a broad region in interaction and magnetic field where metallic and insulating (fully magnetized) solutions coexist and the system undergoes a first-order metal-insulator transition. A global instability of the magnetically saturated solution precedes the local ones and is caused by collective fluctuations due to poles in electron-hole vertex functions.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition, even in the half-filled band case…
We derived a simple metal-insulator criterion in analytical form for the doped Mott-Hubbard materials. Its readings closely related to the orbital and spin nature of the ground states of the unit cell. The available criterion readings (metal or insulator) in the paramagnetic phase points to the possibility of the insulator state of doped materials with the forbidden first removal electron states. According to its physical meaning the result is similar to Wilsons criterion in the itinerant electron systems. An application of the criterion to the high-Tc cuprates discussed.
It is well established that for non-interacting electrons, increasing disorder drives a metal into a gapless localized Anderson insulator. While in three dimensions a threshold in disorder must be crossed for the transition, in two dimensions and lower, the smallest amount of disorder destabilizes the metal. The nature of the metal-insulator transition in an interacting system remains unresolved. Here we explore the effect of disorder on a strongly correlated Mott insulator without changing the carrier concentration. Angle resolved photoemission spectroscopy (ARPES) measurements on copper inte…
The spin-one-half Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition (rather than the character of the electronic states changing from insulating to metallic as in a Mott-Hubbard transition). The exact solution displays both continuous and discontinuous (first-order) transitions.
We investigate how the antiferromagnetic Mott insulator evolves into the d-wave BCS superconductor through hole doping. Allowing spin fluctuations in the strong coupling approach, we find a spin-gapped incoherent metal with preformed pairing as an intermediate phase between the antiferromagnetic Mott insulator and d-wave superconductor. This non-Fermi liquid metal is identified with an infrared stable fixed point in the spin-decomposition gauge theory, analogous to the spin liquid insulator in the slave-boson gauge theory. We consider the single particle spectrum and dynamical spin susceptibil…
Experimental results on the metal-insulator transitions and the anomalous properties of strongly interacting two-dimensional electron systems are reviewed and critically analyzed. Special attention is given to recent results for the strongly enhanced spin susceptibility and effective mass in low-disordered silicon MOSFETs.
We obtain exact numerical solutions of the degenerate Hubbard model in the limit of large dimensions (or large lattice connectivity). Successive Mott-Hubbard metal insulator transitions at integer fillings occur at intermediate values of the interaction and low enough temperature in the paramagnetic phase. The results are relevant for transition metal oxides with partially filled narrow degenerate bands.
The metal-insulator transition of the quarter-filled Hubbard model on triangular lattice is studied at the mean field level. We find a quasi-one dimensional metallic state with a collinear magnetic order competes closely with an insulating state with a non-coplanar magnetic order for both signs of the hopping integral $t$. In the strong correlation regime($U/|t|\gg1$), it is found that the metal-insulator transition of the system occurs in a two-step manner. The quasi-one dimensional metallic state with collinear magnetic order is found to be stable in an intermediate temperature region betwee…
The review of the modern results in the theoretical and experimental study of the localized interacting electrons is given. After theoretical prediction of the Coulomb gap and the new temperature law in the variable range hopping conduction many efforts have been made to discover it experimentally. The most important of them are attempts to demonstrate experimentally that the long range Coulomb interaction is not screened in this system and that it is the origin of the gap. The next stage begins when the recent experiments have discovered glassy properties of the interacting system with locali…
We consider a heterostructure of a metal and a barrier with onsite correlation at half filling using unrestricted Hartree Fock. We find that above a certain value of correlation strength in the barrier planes, the system is a Mott insulator, while below this value the system still behaves like a gapless insulator. The energy spectrum is found to be very novel with the presence of multiple gaps. Thus the system remains non metallic for any finite value of correlation.
By means of first principles schemes based on magnetically constrained density functional theory and on the band unfolding technique we study the effect of doping on the conducting behaviour of the Lifshitz magnetic insulator NaOsO3. Electron doping is treated realistically within a supercell approach by replacing sodium with magnesium at different concentrations. Our data indicate that by increasing carrier concentration the system is subjected to two types of transition: (i) insulator to bad metal at low doping and low temperature and (ii) bad metal to metal at high doping and/or high-temper…
In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.
The organic salt $α$-(BEDT-TTF)$_2$I$_3$ is considered a model system for metal-insulator transition due to electronic charge ordering at $T_{\rm CO}=135$~K. The optical properties obtained from polarized reflection measurements above and below $T_{\rm CO}$ can be well described by calculations based on first-principle density-functional theory (DFT). We discuss the effect of electronic correlations on the metal-insulator transition.
On the basis of experimental thermoelectric power results and ab initio calculations, we propose that a metal-insulator transition takes place at high pressure (approximately 6 GPa) in MgV_2O_4.
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator…
We propose a two-orbital Hubbard model on an emergent honeycomb lattice to describe the low-energy physics of twisted bilayer graphene. Our model provides a theoretical basis for studying metal-insulator transition, Landau level degeneracy lifting and unconventional superconductivity that are recently observed.
Metal-insulator transitions driven by disorder (Delta) and/or by electron correlations (U) are investigated within the Anderson-Hubbard model with local binary-alloy disorder using a simple but consistent mean-field approach. The Delta-U phase diagram is derived and discussed for T=0 and finite temperatures.
We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for $U$ larger than a critical value $U_c$, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-f…
We solve the Periodic Anderson model in the Mott-Hubbard regime, using Dynamical Mean Field Theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the Periodic Anderson model, even in the Mott-Hubbard re…
We describe a new possible route to the metal-insulator transition in doped semiconductors such as Si:P or Si:B. We explore the possibility that the loss of metallic transport occurs through Mott localization of electrons into a quantum spin liquid state with diffusive charge neutral "spinon" excitations. Such a quantum spin liquid state can appear as an intermediate phase between the metal and the Anderson-Mott insulator. An immediate testable consequence is the presence of metallic thermal conductivity at low temperature in the electrical insulator near the metal-insulator transition. Furthe…
It is shown that the spectacular metal-insulator transition in Eu-rich EuO can be simulated within an extended Kondo lattice model. The different orders of magnitude of the jump in resistivity in dependence on the concentration of oxygen vacancies as well as the low-temperature resistance minimum in high-resistivity samples are reproduced quantitatively. The huge colossal magnetoresistance (CMR) is calculated and discussed.
We have explored the critical metal-insulator phenomena for pyrochlore-type $R_2$Ir$_2$O$_7$, in which electron correlation strength and magnetic configuration are systematically controlled by varying the average rare-earth ionic radius ($R$=Nd$_{1-x}$Pr$_{x}$ and Sm$_{y}$Nd$_{1-y}$), external pressure, and magnetic field. Metal-insulator transitions in bulk are caused by increasing $x$ or tuning external pressure, indicating that the effective electron correlation is responsible for the transition. The metallic state intervenes between the paramagnetic insulating and antiferromagnetically ord…
