Mott Transition and Kondo Screening in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi></mml:math>-Electron Metals

Medici, Luca de’; Georges, Antoine; Kotliar, Gabriel; Biermann, Silke

doi:10.1103/physrevlett.95.066402

Cited by 126 publications

(249 citation statements)

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“…Meanwhile, Koga et al found an OSMT using exact diagonalization (ED), applied to the full J-model, 13 but not for the J z -model. 14 Consequently, the OSMT scenario was attributed to spin-flip and pairhopping processes.Very recently, four preprints appeared, 15,16,17,18 in which the OSMT was investigated in detail within the DMFT framework. Ref.…”

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Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

2005

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The anisotropic degenerate two-orbital Hubbard model is studied within dynamical mean-field theory at low temperatures. High-precision calculations on the basis of a refined quantum Monte Carlo (QMC) method reveal that two distinct orbital-selective Mott transitions occur for a bandwidth ratio of 2 even in the absence of spin-flip contributions to the Hund exchange. The second transition -not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization -is clearly exposed in a low-frequency analysis of the self-energy and in local spectra. PACS numbers: 71.30.+h, 71.10.Fd, 71.27.+a The Mott-Hubbard metal-insulator transition -a nonperturbative correlation phenomenon -has been a subject of fundamental interest in solid state theory for decades. 1 Recently, this field became even more exciting by the discovery 2,3 of a two-step metal-insulator transition in the effective 3-band system Ca 2−x Sr x RuO 4 , for which the name orbital-selective Mott-transition (OSMT) was coined. 4 The Ca 2−x Sr x RuO 4 system was investigated theoretically in detail by Anisimov et al. 4 within the local density approximation (LDA and LDA+U) and within dynamical mean-field theory 5 (DMFT) solved using the non-crossing approximation (NCA). The underlying assumption of a correlation (rather than lattice-distortion) induced OSMT found support in further band structure calculations 6,7 and strong-coupling expansions for the localized electrons in the orbital-selective Mott phase. 8 Microscopic studies of the OSMT usually consider the 2-band Hubbard model H = H 1 + H 2 , wherehopping between nearest-neighbor sites i, j with amplitude t m for orbital m ∈ {1, 2}, intra-and interorbital Coulomb repulsion parametrized by U and U ′ , respectively, and Ising-type Hund's exchange coupling; n imσ = c † imσ c imσ for spin σ ∈ {↑, ↓}. In addition,contains spin-flip and pair-hopping terms (with1 ≡ 2, ↑ ≡↓ etc.). In cubic lattices, the Hamiltonian is invariant under spin rotation, J z = J ⊥ ≡ J; furthermore U ′ = U − 2J. In the following, we refer to H 1 + H 2 in this spin-isotropic case as the J-model and to the simplified Hamiltonian H 1 as the J z -model. Liebsch 9,10,11 questioned the OSMT scenario for Ca 2−x Sr x RuO 4 on the basis of finite-temperature quantum Monte Carlo (QMC) calculations (within DMFT) for the J z -model using J z = U/4, U ′ = U/2, and semielliptic "Bethe" densities of states with a bandwidth ratio W 2 /W 1 = 2. Additional studies using iterative perturbation theory (IPT) 11 seemed 12 to confirm his conclusion of a single Mott transition of both bands at the same critical U -value. Meanwhile, Koga et al. found an OSMT using exact diagonalization (ED), applied to the full J-model, 13 but not for the J z -model. 14 Consequently, the OSMT scenario was attributed to spin-flip and pairhopping processes.Very recently, four preprints appeared, 15,16,17,18 in which the OSMT was investigated in detail within the DMFT framework. Ref. 15 applied the Gutzwiller variational approach and ED to the J-model at...

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“…Very recently, four preprints appeared, 15,16,17,18 in which the OSMT was investigated in detail within the DMFT framework. Ref.…”

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confidence: 99%

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

2005

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“…Above 0.8 GPa at 298 K, pure Ce metal undergoes an isostructural transition from an a face-centered cubic (fcc) phase (␥-Ce) to a denser, high-pressure, fcc phase (␣-Ce) accompanied by a 15% volume collapse. Since its discovery by P. W. Bridgman in 1927 (10), the ␥-␣ Ce transition has been the subject of extensive experimental (11,12) and theoretical investigations (7,(13)(14)(15)(16) and is often cited as an archetypal example of a localizeditinerant 4f electronic transition. Various scenarios including Mott transition (7), Kondo hybridization (8,13), and intermediate behaviors between the two (14, 15) have been proposed.…”

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Substitutional alloy of Ce and Al

Zeng

Ding

Mao

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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The formation of substitutional alloys has been restricted to elements with similar atomic radii and electronegativity. Using high-pressure at 298 K, we synthesized a face-centered cubic disordered alloy of highly dissimilar elements (large Ce and small Al atoms) by compressing the Ce 3Al intermetallic compound >15 GPa or the Ce3Al metallic glass >25 GPa. Synchrotron X-ray diffraction, Ce L3-edge absorption spectroscopy, and ab initio calculations revealed that the pressure-induced Kondo volume collapse and 4f electron delocalization of Ce reduced the differences between Ce and Al and brought them within the Hume-Rothery (HR) limit for substitutional alloying. The alloy remained after complete release of pressure, which was also accompanied by the transformation of Ce back to its ambient 4f electron localized state and reversal of the Kondo volume collapse, resulting in a non-HR alloy at ambient conditions. 4f electron delocalization ͉ Ce-Al solid solution alloy ͉ high pressure ͉ Hume-Rothery rules ͉ metallic glass C ombining one metal with another leads to a range of alloys with properties superior to each individual end member. Since the Bronze and Iron Ages, the quest for new metallic alloys through various chemical and metastable quenching paths has played a crucial role in the advancement of civilizations. The most common type of alloy is a substitutional crystalline solid solution in which atoms of one element randomly substitute for atoms of another element in a crystal structure. The possibilities for substitution, however, are restricted by the classic empirical Hume-Rothery (HR) rules (1), which require the components have atomic size within 15% and electronegativity within 0.4 of each other. For instance, the archetypal 4f metal Ce alloys with similar rare-earth metals to form ''mischmetal,'' which has unusual pyrophoric properties and strength for a broad range of chemical and physical applications, and the sp-bonded light metal Al alloys with similar atoms to form a family of aluminum alloys that have enormous technological importance and application in everyday life. No known binary substitutional crystalline alloy exists between Ce and Al because their differences of 28% in atomic radii and 0.45 in electronegativity far exceed the HR limit. They can only form stoichiometric compounds in which Ce and Al are chemically ordered and occupy separate crystallographic sites, or metallic glass synthesized by rapidly quenched from melt in which Ce and Al are disordered both chemically and structurally. Here, we report the formation of a Ce-Al substitutional crystalline alloy from intermetallic compound and metallic glass at high pressure and room temperature, this alloy can be recovered as a non-HR alloy to ambient conditions. Pressure is a powerful tool for altering individual atoms and their electronic structures, changing the bonding chemistry, and creating novel materials (see, for example, ref. 2). This has been demonstrated by the discovery of intermetallic compounds in the incompatible K-Ni and K-Ag...

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“…(1) What is the role of the spin-orbit interaction (SOC) for the volume-collapse? (2) What is the fate of the pressure-temperature transition-line at very low temperatures [16][17][18]? (3) Can a first-principle based theory be made computationally efficient so as to access both the γ and the α Cerium at zero temperature?…”

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γ−αIsostructural Transition in Cerium

et al. 2013

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Below the critical temperature Tc ≃ 600K, an iso-structural transition, named γ-α transition, can be induced in Cerium by applying pressure. This transition is first-order, and is accompanied by a sizable volume collapse. A conclusive theoretical explanation of this intriguing phenomenon has still not been achieved, and the physical pictures proposed so far are still under debate. In this work, we illustrate zero-temperature first-principle calculations which clearly demonstrate that the γ-α transition is induced by the interplay between the electron-electron Coulomb interaction and the spin-orbit coupling. We address the still unresolved problem on the existence of a second low-T critical point, i.e., whether the energetic effects alone are sufficient or not to induce the γ-α transition at zero temperature.The γ-α iso-structural transition in Cerium [1] was discovered in 1949 [2]. Since then, a lot of theoretical and experimental work has been devoted to its understanding. The great interest in this phenomenon arises from the fact that the transition is isostructural, i.e., the lattice structure of the system is equal in the two phases. Furthermore, the possibility that the underlying mechanism lies in the electronic structure only -i.e., without it being necessary to involve other effects -makes Cerium a potential theoretical testing ground for basic concepts of correlated electron systems. Two main theoretical pictures are still under debate to explain the volume collapse: the Kondo volume collapse (KVC) [3,4] and the orbital-selective Mott transition within the Hubbard model (HM) [5]. According to the KVC the transition is induced by the rapid change of the coherence temperature across the transition boundaries, which affect dramatically the structure of the conduction spd electrons through Kondo effect. According to the HM, instead, it is the hopping between f orbitals that changes drastically across the transition between the α phase (with delocalized f electrons) and the γ phase (with localized f electrons), as for the Mott transition in the Hubbard model.Consistently with both the HM and the KVC pictures, the f -electrons are strongly correlated both in the α and in the γ phase. This fact is clearly indicated, e.g., by the photoemission spectra, which is known experimentally [6][7][8] and theoretically [9][10][11]. Despite this similarity, there is a key difference between these two models: while the KVC attributes a very important role to the interplay between the localized 4f orbitals and the itinerant spd conduction bands, the itinerant electrons are "spectators" in the HM picture.The development of LDA+DMFT (Local Density Approximation plus Dynamical Mean Field Theory) [12] results [13][14][15] has successfully reproduced many aspects of this transition, and different aspects of these studies can be understood in both physical pictures. There are still fundamental questions which have not been answered. (1) What is the role of the spin-orbit interaction (SOC) for the volume-collapse? (2) What is the ...

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Mott Transition and Kondo Screening inf-Electron Metals

Cited by 126 publications

References 25 publications

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

Substitutional alloy of Ce and Al

γ−αIsostructural Transition in Cerium

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