Exponential Localization of Wannier Functions in Insulators

Brouder, Christian; Panati, Gianluca; Calandra, Matteo; Mourougane, Christophe; Marzari, Nicola

doi:10.1103/physrevlett.98.046402

Cited by 392 publications

(318 citation statements)

References 38 publications

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“…The exponential decay of MLWFs in electronic insulators 108 suggests modeling them as Slater orbitals determined solely by their spread S k and center located at r w k determined from the localization procedure 109 . These two properties can be obtained for each type of MLWF from averages over liquid configurations.…”

Section: Beyond Force-matching: Direct Calculation Of Parametersmentioning

confidence: 99%

Including many-body effects in models for ionic liquids

Salanne¹,

Rotenberg²,

Jahn³

et al. 2012

Theor Chem Acc

127

118

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Realistic modeling of ionic systems necessitates taking explicitly account of many-body effects. In molecular dynamics simulations, it is possible to introduce explicitly these effects through the use of additional degrees of freedom. Here we present two models: The first one only includes dipole polarization effect, while the second also accounts for quadrupole polarization as well as the effects of compression and deformation of an ion by its immediate coordination environment. All the parameters involved in these models are extracted from first-principles density functional theory calculations. This step is routinely done through an extended force-matching procedure, which has proven to be very succesfull for molten oxides and molten fluorides. Recent developments based on the use of localized orbitals can be used to complement the force-matching procedure by allowing for the direct calculations of several parameters such as the individual polarizabilities.

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Section: Beyond Force-matching: Direct Calculation Of Parametersmentioning

confidence: 99%

Including many-body effects in models for ionic liquids

Salanne¹,

Rotenberg²,

Jahn³

et al. 2012

Theor Chem Acc

127

118

View full text Add to dashboard Cite

show abstract

“…After some algebraic work, it is possible to prove that Eqs. (14), (19), and (20) in Ref. 24 correspond to the first, second, and third terms, respectively, in the second line of the present Eq.…”

Section: Basic Concepts and Equationsmentioning

confidence: 99%

“…[12][13][14][15][16] Since their introduction in 1937, 17 the properties of WFs have challenged the solid-state physics community. [18][19][20] This is mainly because of their lack of uniqueness, which is a feature inherited from Bloch functions (BFs). In fact, electronic BFs are common eigenfunctions of the Hamiltonian and translation operators that are conveniently chosen as periodic functions in the reciprocal space.…”

Section: Introductionmentioning

confidence: 99%

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Nacbar¹,

Bruno-Alfonso

2012

Phys. Rev. B

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Generalized Wannier functions of a couple of bands in a one-dimensional crystal are investigated. A lower bound for the global minimum of the total spread is obtained. Assumption of such a value being the minimum leads to a first-order differential equation for the transformation matrix. Simple analytical solutions leading to real generalized Wannier functions are presented for consecutive bands in a crystal with inversion symmetry. Results are displayed for a particle in a diatomic Kronig-Penney potential. For the lowest couple of bands, calculated single-band Wannier functions resemble orbitals of a diatomic molecule, whereas generalized Wannier functions seem like orthogonalized atomic orbitals. The latter functions are neither symmetric nor antisymmetric and display increased exponential decay. For the next two pairs of bands, Wannier functions retain their centers and symmetries, and exponential decay does not increase. Results are also shown to be in agreement with solutions of the eigenvalue problem of the band-projected position operator.

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“…Without loss of generality [16], it can be assumed that 4 The action of any (anti)unitary operator on H f is lifted to H m f componentwise. 5 The presence of the reshuffling matrix ε is needed to make the time-reversal symmetry condition self-consistent.…”

Section: Obstruction Theorymentioning

confidence: 99%

Advances in Quantum Mechanics

Michelangeli¹,

Dell’Antonio²

2017

Springer INdAM Series

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The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall effect, in which the Chern number underlies the quantization of the transverse Hall conductivity. More recently, in the framework of time-reversal symmetric topological insulators and quantum spin Hall systems, a new topological classification has been proposed by Fu, Kane and Mele, where the label takes value in Z 2 . We illustrate how both the Chern number c ∈ Z and the Fu-Kane-Mele invariant δ ∈ Z 2 of 2-dimensional topological insulators can be characterized as topological obstructions. Indeed, c quantifies the obstruction to the existence of a frame of Bloch states for the crystal which is both continuous and periodic with respect to the crystal momentum. Instead, δ measures the possibility to impose a further time-reversal symmetry constraint on the Bloch frame.

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Exponential Localization of Wannier Functions in Insulators

Cited by 392 publications

References 38 publications

Including many-body effects in models for ionic liquids

Including many-body effects in models for ionic liquids

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Advances in Quantum Mechanics

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