Screened Coulomb interaction of localized electrons in solids from first principles

Shih, Bi-Ching; Zhang, Yubo; Zhang, Wenqing; Zhang, Peihong

doi:10.1103/physrevb.85.045132

Cited by 70 publications

(57 citation statements)

References 40 publications

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“…If the bands are completely entangled or if one defines Wannier functions |W Rσ km from a larger energy window, then the preceding assumption of Eq. (5) cannot be made 26,33 and some authors have proposed the more general assumption 31,35 : Then, the values of the famous Hubbard U and Hund J are simply extracted by taking the average among the considered localized orbitals: (8) Note that this definition of U is also sometimes referred to as the F 0 Slater integral. We emphasize that this definition is different from the average of the diagonal elements of the Coulomb interaction matrix…”

Section: The Constrained Rpa Methodsmentioning

confidence: 99%

“…6 in Eq. 4 31,56 . This is a more general way of doing because it is applicable to any system, even when bands are entangled.…”

Section: Definition Of the Models For Uranium Dioxide And Ceriummentioning

confidence: 99%

“…The cRPA scheme very clearly defines which screening processes have to be taken into account. The method has been implemented in several electronic structure codes using the LMTO 25, 26 , FLAPW [27][28][29] , FPLMTO 30 ,Plane Wave 31,32 and Projector Augmented-Wave (PAW) 32 methods and applied to different systems in the last few years [27][28][29][30][31][32][33][34][35] . An important point emphasized in several works is that the calculation of the cRPA screened interaction based on a previous DFT calculation depends crucially on the definition of a many-body model 29, 35 .…”

Section: Introductionmentioning

confidence: 99%

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Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium

2014

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We report an implementation of the constrained Random Phase Approximation (cRPA) method within the Projector Augmented-Wave framework. It allows for the calculation of the screened interaction in the same Wannier orbitals as our recent DFT+U and DFT+DMFT implementations. We present calculations of the dynamical Coulomb screened interaction in uranium dioxide and α and γ cerium on Wannier functions. We show that a self-consistent calculation of the static screened interaction in DFT+U together with a consistent Wannier basis is mandatory for γ cerium and uranium dioxide. We emphasize that a static approximation for the screened interaction in α cerium is too drastic.

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Section: The Constrained Rpa Methodsmentioning

confidence: 99%

“…6 in Eq. 4 31,56 . This is a more general way of doing because it is applicable to any system, even when bands are entangled.…”

Section: Definition Of the Models For Uranium Dioxide And Ceriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium

2014

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“…II E), as well as the H-Ge hybridization, it is still beneficial to understand the physical value of the interactions in order to both analyze the validity of our range of considered U and of the predictions of PCK and to motivate and guide future material-specific studies. We do this by employing the constrained random-phase approximation (cRPA), [25][26][27][28] performed within the full-potential linearized augmentedplane-wave (FLAPW) method using maximally localized Wannier functions (MLWFs). 29,30 We use the FLAPW method as implemented in the FLEUR code 31 with the PerdewBurke-Ernzerhof (PBE) exchange-correlation potential 32 for the ground-state calculations.…”

Section: Constrained Random-phase Approximationmentioning

confidence: 99%

Effect of local electron-electron correlation in hydrogen-like impurities in Ge

et al. 2013

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We have studied the electronic and local magnetic structure of the hydrogen interstitial impurity at the tetrahedral site in diamond-structure Ge, using an empirical tight binding + dynamical mean-field-theory approach because within the local-density approximation (LDA) Ge has no gap. We first establish that within LDA the 1s spectral density bifurcates due to entanglement with the four neighboring sp 3 antibonding orbitals, providing an unanticipated richness of behavior in determining under what conditions a local moment hyperdeep donor or Anderson impurity will result, or on the other hand, a gap state might appear. Using a supercell approach, we show that the spectrum, the occupation, and the local moment of the impurity state displays a strong dependence on the strength of the local on-site Coulomb interaction U , the H-Ge hopping amplitude, the depth of the bare 1s energy level H , and we address to some extent the impurity concentration dependence. In the isolated impurity, strong interaction regime a local moment emerges over most of the parameter ranges, indicating magnetic activity, and spectral density structure very near (or in) the gap suggests possible electrical activity in this regime.

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“…Thus, the localized states are largely eliminated, and the screening is dominated by itinerant s and p states, which are well described by LDA and GGA. The cRPA is, therefore, -even with these standarad xc potentials -considered a reliable approach to calculate the Hubbard U parameter and its frequency dependence [25,26]. Then, the frequency-dependent effective Coulomb interaction is given schematically by the matrix equation U (ω) = [1 − vP r (ω)] −1 v, where v is the bare Coulomb interaction.…”

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confidence: 99%

Strength of the Effective Coulomb Interaction at Metal and Insulator Surfaces

2012

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The effective on-site Coulomb interaction (Hubbard U ) between localized electrons at crystal surfaces is expected to be enhanced due to the reduced coordination number and reduced subsequent screening. By means of first principles calculations employing the constrained random-phase approximation (cRPA) we show that this is indeed the case for simple metals and insulators but not necessarily for transition metals and insulators that exhibit pronounced surface states. In the latter case, the screening contribution from surface states as well as the influence of the band narrowing increases the electron polarization to such an extent as to overcompensate the decrease resulting from the reduced effective screening volume. The Hubbard U parameter is thus substantially reduced in some cases, e.g., by around 30% for the (100) surface of bcc Cr. The effective on-site Coulomb interaction (Hubbard U ) between localized electrons at surfaces of solids is expected to be enhanced since the effective screening volume of the surface is reduced with respect to the bulk. As a consequence, the electron polarization decreases at the surface, which reduces the effect of screening and gives rise to a larger U value. These arguments are underscored by interpolating between the Hubbard U values of an isolated atom and an atom in a bulk solid, the former being 3 to 5 times larger than the latter [1]. Neither experimental nor theoretical works have been reported so far that would address the strength of the surface U parameter explicitly. However, a large number of phenomena observed in solids indicates an enhancement of the U at surfaces. For instance, the metal-insulator transition at the surface of correlated materials [2], the appearance of magnetism at the surface of paramagnetic transition metals [3], and the enhanced exchange splitting at the surface of 3d ferromagnets [4] have been attributed to an increase of the correlation strength, which is defined by the ratio U/W , where W is the bandwidth. In the theoretical description of surfaces, the U is usually assumed to be unchanged [5][6][7] so that the enhancement of correlation at the surface (S) with respect to the bulk (B) is provided by the effective band narrowing, i.e., W S < W B . In principle, depending on the relative values of the surface U and the bandwidth W , the correlation strength can further increase or decrease even below the bulk value. However, the latter case is considered to be unlikely because it is believed that U always increases at surfaces. In this Letter, we show by means of first-principles calculations that contrary to this conventional wisdom, this is not always the case. It decreases at many transition-metal (TM) surfaces and insulator surfaces with pronounced surface states, as a result of additional screening channels that open up due to surface-related changes in the electronic structure.Recently, the calculation of the Hubbard U parameter in solids from first principles has been addressed by several authors [8][9][10][11][12][13][14][15]. A nu...

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Screened Coulomb interaction of localized electrons in solids from first principles

Cited by 70 publications

References 40 publications

Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium

Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium

Effect of local electron-electron correlation in hydrogen-like impurities in Ge

Strength of the Effective Coulomb Interaction at Metal and Insulator Surfaces

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