Berry-phase treatment of the homogeneous electric field perturbation in insulators

Nunes, R. W.; Gonze, Xavier

doi:10.1103/physrevb.63.155107

Cited by 286 publications

(222 citation statements)

References 49 publications

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“…19 In this implementation, the position operator in the perturbation term is replaced by a Berry phase expression when we consider the periodic system energy function. 20,21 Since the polarization under applied field can be expressed as a Berry phase over occupied bands, this approach can be used in a density functional formalism. For all of the systems we modeled, we applied electric fields perpendicular to the graphene film ranging from −0.0002 to 0.0002 a.u.…”

Section: Approachmentioning

confidence: 99%

Ab initiostudy of polarizability and induced charge densities in multilayer graphene films

Stewart

Tiwari

2008

Phys. Rev. B

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We present an ab initio analysis of polarization of multilayer graphene systems under applied electric fields. The effects of applied electric fields are calculated using a Berry phase approach within a plane-wave density functional formalism. We have determined polarizability values for graphene films and carbon nanotubes and found that the polarizability of graphene films follows a linear relationship with the number of layers. We also examined changes in the induced charge distribution as a function of graphene layers. We focus, in particular, on the bilayer graphene system. Under applied electric fields, we found the Mexican hat band structure near the K point reported by previous groups. We found that the induced charge primarily accumulated on the B sublattice sites. This observation is supported by additional calculations with a tight-binding Green's function model. By examining the local density of states at the Fermi energy, we found a high density of states at the B sites at the Fermi energy. In contrast, coupling between A sites in neighboring graphene layers leads to negligible density of states at the Fermi level. This high density of states at the B sites results in greater induced charge under applied electric fields. This scenario of preferential induced charge on the B sublattice sites under applied electric fields could impact the stability of atoms and molecules absorbed on bilayer graphene.

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Section: Approachmentioning

confidence: 99%

Ab initiostudy of polarizability and induced charge densities in multilayer graphene films

Stewart

Tiwari

2008

Phys. Rev. B

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“…In the last decade, significant theoretical advances have been reported concerning first-principles density functional theory (DFT) calculations of the behavior of periodic systems in an external electric field [9,10] and opened the way to direct predictions of various optical phenomena. Recently, particular attention has been paid to the calculation of non-linear optical (NLO) susceptibilities and Raman cross sections [11,12].…”

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confidence: 99%

First-Principles Study of the Electro-Optic Effect in Ferroelectric Oxides

2004

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We first present a method to compute the electrooptic tensor from first principles, explicitly taking into account the electronic, ionic and piezoelectric contributions. We then study the non-linear optic behavior of three paradigmatic ferroelectric oxides. Our calculations reveal the dominant contribution of the soft mode to the electrooptic coefficients in LiNbO3 and BaTiO3 and its minor role in PbTiO3. We identify the coupling between the electric field and the polar atomic displacements along the B-O chains as the origin of the large electrooptic response in perovskite ABO3 compounds. Finding better EO materials is a desirable goal. However, the experimental characterization of optical nonlinearities requires high-quality single crystals that are not always directly accessible nor easy to make. Input from accurate theoretical calculations allowing to predict the non-linear optical behavior of crystalline solids would therefore be particularly useful.For many years, theoretical investigations of non-linear optical phenomena were restricted to semi-empirical approaches such as shell models [6] or bond-charge models [7,8]. In the last decade, significant theoretical advances have been reported concerning first-principles density functional theory (DFT) calculations of the behavior of periodic systems in an external electric field [9,10] and opened the way to direct predictions of various optical phenomena. Recently, particular attention has been paid to the calculation of non-linear optical (NLO) susceptibilities and Raman cross sections [11,12].In this Letter, we go one step further and present a method to predict the linear EO coefficients of periodic solids within DFT. Our method is very general, and can be applied to paradigmatic ferroelectric oxides : LiNbO 3 , BaTiO 3 and PbTiO 3 . We find that first-principles calculations are fully predictive, and provide significant new insights into the microscopic origin of the EO effect. In particular, we highlight the predominent role of the soft mode in the EO coupling of LiNbO 3 and BaTiO 3 , in contrast with its minor role in PbTiO 3 .At linear order, the dependence of the optical dielectric tensor ε ij on the static (or low-frequency) electric field E γ is described by the linear EO tensor r ijγ :Throughout this paper, we follow the convention of using Greek and Roman indexes (resp.) to label static and optical fields (resp.). We write all vector and tensor components in the system of cartesian coodinates defined by the principal axes of the crystal under zero field. We also refer to the atomic displacements τ κα [κ labels an atom and α a cartesian direction] within the basis defined by the zone-center transverse optic (TO) phonon eigendisplacements u m (κα):Let us first consider the clamped (zero strain) EO tensor, r η ijγ , in which all electric-field induced macroscopic strains η are forbidden. This is achieved experimentally by working at a frequency sufficiently high to avoid strain relaxations but low compared to the frequency of the TO modes. Within the ...

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“…Here, we are following the "perturbation expansion after discretization" (PEAD) approach introduced in Ref. 16. That is, we write down the energy functional in its discretized form, and then consistently derive perturbation theory from this energy functional.…”

Section: Discretized K Meshmentioning

confidence: 99%

“…(28), we use the approach of Ref. 16 to obtain the expansion of ln detS kk ′ with respect to the perturbation. It then follows that…”

Section: Discretized K Meshmentioning

confidence: 99%

First-principles perturbative computation of phonon properties of insulators in finite electric fields

Wang

Vanderbilt

2006

Phys. Rev. B

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We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the ABINIT code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

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Berry-phase treatment of the homogeneous electric field perturbation in insulators

Cited by 286 publications

References 49 publications

Ab initiostudy of polarizability and induced charge densities in multilayer graphene films

Ab initiostudy of polarizability and induced charge densities in multilayer graphene films

First-Principles Study of the Electro-Optic Effect in Ferroelectric Oxides

First-principles perturbative computation of phonon properties of insulators in finite electric fields

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