Berry Phase Approach Research Articles

Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice

We establish the topology of the spin-singlet superconducting states in the bare hyperhoneycomb lattice, and we derive analytically the full phase diagram using only symmetry and topology in combination with simple energy arguments. The phase diagram is dominated by two states preserving time-reversal symmetry. We find a line-nodal state dominating at low doping levels that is topologically nontrivial and exhibits surface Majorana flatbands, which we show perfectly match the bulk-boundary correspondence using the Berry phase approach. At higher doping levels, we find a fully gapped state with trivial topology. By analytically calculating the topological invariant of the nodal lines, we derive the critical point between the line-nodal and fully gapped states as a function of both pairing parameters and doping. We find that the line-nodal state is favored not only at lower doping levels but also if symmetry-allowed deformations of the lattice are present. Adding simple energy arguments, we establish that a fully gapped state with broken time-reversal symmetry likely appears covering the actual phase transition. We find this fully gapped state to be topologically trivial, while we find an additional point-nodal state at very low doing levels that also break time-reversal symmetry and has nontrivial topology with associated Fermi surface arcs. We eventually address the robustness of the phase diagram to generalized models also including adiabatic spin-orbit coupling, and we show how all but the point-nodal state are reasonably stable.

Effect of intrinsic point defects on ferroelectric polarization behavior of SrTiO3

The effect of a variety of intrinsic defects and defect clusters in bulk and thin films of SrTiO$_3$ on ferroelectric polarization and switching mechanism is investigated by means of density-functional-theory (DFT) based calculations and the Berry phase approach. Our results show that both the titanium Ti$_\mathrm{Sr}^{\bullet \bullet}$ and strontium Sr$_\mathrm{Ti}^{"}$ antisite defects induce ferroelectric polarization in SrTiO$_3$, with the Ti$_\mathrm{Sr}^{\bullet \bullet}$ defect causing a more pronounced spontaneous polarization and higher activation barriers of polarization reversal than Sr$_\mathrm{Ti}^{"}$. The presence of oxygen vacancies bound to the antisite defects can either enhance or diminish polarization depending on the configuration of the defect pair, but it always leads to larger activation barriers of polarization switching as compared to the antisite defects with no oxygen vacancies. We also show that the magnitude of spontaneous polarization in SrTiO$_3$ can be tuned by controlling the degree of Sr/Ti nonstroichiometry. Other intrinsic point defects such as Frenkel defect pairs and electron small polarons also contribute to the emergence of ferroelectric polarization in SrTiO$_{3}$.

Topological ferroelectricity in layered perovskite LaTaO4: A first principles study

Abstract The ferroelectricity in layered perovskite LaTaO 4 is investigated by first-principles calculations. The rather large polarization (about 36 μC/cm 2 ) along -c direction is obtained by the Berry phase approach. Ferroelectric phase can be induced by freezing a soft B 1 u mode from the prototype phase, and this mode involves the rotations of oxygen octahedron and the displacement of La 3+ cations. The topological ferroelectricity is adopted based on the previous work to distinguish from the typical proper ferroelectrics, such as BaTiO 3 . The 0 K stable monoclinic phase can be regarded as an antiferroelectric phase since the polarization of the neighboring layer will be canceled each other. However, the ferroelectric phase is metastable because of the unexpected small barrier between paraelectric and monoclinic phase and narrow energy gap between ferroelectric and monoclinic phase, and this result can explain the previous experimental results. From the present work, the topological ferroelectricity in layered perovskite LaTaO 4 is confirmed, and the rather high polarization makes the present compound as a promising candidate for the lead-free ferroelectric application.

Electron Scattering on a Magnetic Skyrmion in the Nonadiabatic Approximation.

We present a theory of electron scattering on a magnetic Skyrmion for the case when the exchange interaction is moderate so that the adiabatic approximation and the Berry phase approach are not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic Skyrmions, the special importance of which is its applicability to dilute magnetic semiconductors with a weak exchange interaction.

Structural and response properties of all BaTiO3 phases from density functional theory using the projector-augmented-wave methods

A study of ground state properties of bulk BaTiO3 perovskite crystal was conducted using first-principles density functional theory with local-density approximation (LDA) and generalized-gradient approximation (GGA), using the projector-augmented wave methods. Two different PAW potentials developed by Jollet–Torrent–Holzwarth (JTH) and Garrity–Bennett–Rabe–Vanderbilt (GBRV) are employed in the calculations. This study emphasize on electronic, structural and response properties of all BaTiO3 phases using different exchange correlation (XC) functionals and PAW potentials. Lattice parameters, cohesion energy, bulk modulus, Born effective charge, spontaneous polarization and charge densities of all BaTiO3 phases are calculated. In addition, gamma point phonon frequencies are computed with LDA. Structural and vibrational properties predicted using the two PAW potentials are consistent with experimental and previous theoretical studies for all BaTiO3 phases. It is observed that calculations with GGA yields structural properties much closer to reported experimental values than LDA. Spontaneous polarization computed using Berry phase approach for the three structures in ferroelectric phase are consistent with other theoretical results, but differ considerably from experimental values. The deviation of lattice parameters computed using different XC functionals directly affects the computed spontaneous polarization. An analysis of phonon mode symmetries and frequencies conformed to experimental findings in the literature.

Local electric dipole moments for periodic systems via density functional theory embedding.

We describe a novel approach for the calculation of local electric dipole moments for periodic systems. Since the position operator is ill-defined in periodic systems, maximally localized Wannier functions based on the Berry-phase approach are usually employed for the evaluation of local contributions to the total electric dipole moment of the system. We propose an alternative approach: within a subsystem-density functional theory based embedding scheme, subset electric dipole moments are derived without any additional localization procedure, both for hybrid and non-hybrid exchange-correlation functionals. This opens the way to a computationally efficient evaluation of local electric dipole moments in (molecular) periodic systems as well as their rigorous splitting into atomic electric dipole moments. As examples, Infrared spectra of liquid ethylene carbonate and dimethyl carbonate are presented, which are commonly employed as solvents in Lithium ion batteries.

Born effective charges of Cu2ZnSnS4 quaternary compound: First principles calculations

Toxicity and scarceness stand as major handicaps for CuInGaSe2 and CuInGaS2 based compounds when applied as photoactive layers in solar cells. As a result, quaternary semiconductors Cu2ZnSnS4 and Cu2ZnSnSe4 are emerging as serious contenders to take their place. We report on the structural and dynamical properties of Cu2ZnSnS4 by using first principles plane-wave pseudopotential calculations. The most stable kesterite and stannite structures were considered and the Born effective charge (transverse charge) tensors were obtained by using self-consistent finite-electric field calculations within the Berry phase approach. These quantities may allow us to understand longitudinal and transverse optical splittings from vibrational spectra of this class of materials and related alloys.

BerryPI: A software for studying polarization of crystalline solids with WIEN2k density functional all-electron package

We present a module that enables computation of polarization using density functional theory based on the full potential linearized augmented plane wave package WIEN2k. The theoretical background of deriving microscopic polarization of materials using the modern theory of polarization (geometric Berry phase approach) is reviewed. The software is validated and then applied to determine spontaneous polarization and Born effective charges of several crystal structures, which are commonly studied theoretically and experimentally.

Response properties of AgCl and AgBr under an external static electric field: A density functional study

Density functional theory has been applied to investigate the effect of electric field on the electronic properties of AgCl and AgBr crystals using a static electric field perturbation. A reduction in the band gap value and widening of the band widths are observed with increase in the macroscopic field value indicating a considerable red shift in the absorption spectrum of AgCl and AgBr in the presence of an external electric field. Further, dielectric properties and lattice vibrations at the gamma point are calculated with three different functionals using the CPKS and the Berry phase approach as implemented in CRYSTAL09 code. Finally, the breakdown strength of AgCl and AgBr crystal is evaluated using Callen’s equation. In contrast to the case of alkali halides, it is found that the inclusion of the numerically calculated effective mass ratio into the Callen’s equation considerably improves the agreement between the calculated dielectric strength and the available experimental datum.

Ferroelectricity induced by cooperative orbital ordering and Peierls instability

A general mechanism by which orbital ordering, coupled to Peierls-like lattice distortions, can induce an electronic switchable polarization is discussed within a model Hamiltonian approach in the context of the modern theory of polarization. By using a Berry-phase approach, a clear picture emerges in terms of Wannier-function centers and orbital occupancies. The proposed mechanism may apply to oxide spinels whose electronic structure has effective one-dimensional character, such as CdV$_2$O$_4$, recently proposed to display multiferroic behaviour.

Wigner model for quantum transport in graphene

The single graphene layer is a novel material consisting of a flat monolayer of carbon atoms packed in a two-dimensional honeycomb lattice, in which the electron dynamics is governed by the Dirac equation. A pseudo-spin phase-space approach based on the Wigner–Weyl formalism is used to describe the ballistic transport of electrons in graphene including quantum effects. Our two-band quantum mechanical representation of the particles reveals itself to be particularly close to the classical description of the particle motion. We analyze the Klein tunneling and correction to the total current in graphene induced by this phenomenon. The equations of motion are analytically investigated and some numerical tests are presented. The temporal evolution of the electron–hole pairs in the presence of an external electric field and rigid potential step is investigated. The connection of our formalism with the Berry phase approach is also discussed.

Origin of the multiferroicity in BiMn 2O 5 from first-principles calculations

Electronic structure, Born effective charges, and spontaneous polarization of multiferroic single crystal BiMn 2O 5 have been investigated in the framework of density functional theory. The relative stability of the ground state and the origin of multiferroicity for magnetism and ferroelectricity are addressed. The results reveal that the stability of antiferromagnetic (AFM) state is better than the ferromagnetic (FM) and ferrimagnetic configurations. The Born effective charge tensors ( Z ⁎) have been calculated for this compound using a Berry-phase approach, compared to their nominal ionic values, the Z * of Mn atoms show anomalous difference. By investigating the electric structure of BiMn 2O 5, there exists obviously hybridization between Bi 6s and O 2p states, our calculations indicate that the 6s 2 lone pair on the formally trivalent Bi ion plays an important role in inducing the ferroelectric distortion.

Effects of anisotropic charge on transverse optical phonons in NiO: Inelastic x-ray scattering spectroscopy study

Phonon dispersion of detwinned NiO is measured using inelastic x-ray scattering. It is found that, near the zone center, the energy of the transverse-optical-phonon mode polarized parallel to the antiferromagnetic order is $\ensuremath{\sim}1\text{ }\text{meV}$ lower than that of the mode polarized perpendicular to the order, at room temperature. This is explained via anisotropic polarization of the Ni and O atoms, as confirmed using a Berry's phase approach with first-principles calculations. Our explanation avoids an apparent contradiction in previous discussions focusing on Heisenberg interaction.

First‐Principles Studies on Novel Polar Oxide ZnSnO3; Pressure‐Induced Phase Transition and Electric Properties

A novel polar oxide of ZnSnO3 with LiNbO3-type structure has been investigated using first-principles density functional theory. The calculated pressure dependence of the phase stability in the ternary Zn2+Sn4+O2− system confirms the experimental results and detailed mechanism of the pressure-induced phase transition (see Fig.). High spontaneous polarization of 56.9 °C cm−2 is calculated by the Berry-phase approach, and it is attributed to the large displacement of Zn2+ and its strong ionicity. Further improvement of the spontaneous polarization is suggested by enhancing the covalency of Sn4+ sites.

First-principle study of the electronic structures and ferroelectric properties in BaZnF4

The electronic structures and ferroelectric properties of barium fluoride BaZnF4were investigated by employing ab initio calculations based on the density-functional theory within generalized gradient approximation. We discussed the possible origin of ferroelectricity of BaZnF4 by the analysis of Born effective charges, orbital-resolved density of states, and distribution of charge density. The results show that the barium and fluorine atoms are very important polarization unity. The calculated spontaneous polarization of 14.2 μC/cm2 by using Berry-phase approach is reasonable agreement with previous experimental data. Barium fluorides are promising candidates for use in nonvolatile memories devices.

Ab initio calculations of Born charges in ferroelectrics with a perovskite structure

A method has been proposed for calculating Born effective charges in compounds with a cubic perovskite structure. The method is based on the first-principles calculation of individual contributions from the short-range interaction and the intercell dipole-dipole interaction to the Born tensor Zii(s) for crystalline dielectrics. It has been shown that the contribution from the short-range interaction Ziisr(s) to the Born tensor components can be derived from ab initio calculations performed for polyatomic clusters. The results of the calculations of the short-range interactions Ziisr(s) for the cubic phases of the BaTiO3, SrTiO3, CaTiO3, PbTiO3, BaZrO3, PbZrO3, KNbO3, and KTaO3 compounds with the use of the electronic structure calculations within the Hartree-Fock approximation and the density functional theory are presented. For the BaTiO3, SrTiO3, CaTiO3, PbTiO3, KNbO3, and KTaO3 compounds, the components of the complete Born tensor have been also calculated. The obtained values of Zii(s) are in good agreement with the results of the calculations in terms of the linear response theory and the Berry phase approach.

Optical and piezoelectric anomalies of ordered (Sc, Ga) N and (Sc, In) N ternaries

Theoretical results are presented regarding the incorporation of Scandium into wurtzite GaN and InN binaries. The electric, optical and piezoelectric properties of the resulting ScGaN and ScInN systems are reported by using first-principles Local-density approximation (LDA) within density functional theory (DFT), Berry phase approach within modern theory of polarization and phonon calculations within the density functional perturbation theory. Our results predict the existence of breaking-symmetry structural phase transition in ordered Sc0.5Ga0.5N and Sc0.5In0.5N alloys when subjected to a compressive or tensile strain. Moreover, our results demonstrate the existence of symmetry preserving pressure-induced isostructural phase transitions in ordered ScGaN and ScInN systems for different Sc concentrations. It has been shown that the existence of isostructural phase transitions leads to dramatic changes in optical, acoustic, and piezoelectric properties of ordered ScGaN and ScInN systems under high pressure. In particular, this study demonstrates that the existence of first-order isostructural phase transitions in Sc1Ga1N2 at a critical hydrostatic pressure of 12.3 GPa leads to a huge enhancement of piezoelectricity (i.e., the e 33 piezoelectric coefficient adopts a huge value as large as 13 C/m2). In addition, It has been shown that ordered Sc0.5Ga0.5N and Sc0.5In0.5N alloys exhibit tremendous piezoelectric response, associated with a breaking-symmetry phase transition from nonpolar P63/mcc(D6h) space group to a polar P63 mc(C6v) structure, at fixed Ga, In and Sc compositions, as a function of the in-plane compressive and tensile strains. We also reveal the reason behind, and consequences of, these unusual properties associated with the strain-induced and pressure-induced structural phase transitions in the novel ScGaN and ScInN ordered structures.

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

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.

First-principles prediction of coexistence of magnetism and ferroelectricity in rhombohedral Bi2FeTiO6

First principles calculations based on the density functional theory within the local spin density approximation plus U(LSDA+U)scheme, show rhombohedral Bi$_2$FeTiO$_6$ is a potential multiferroic in which the magnetism and ferroelectricity coexist . A ferromagnetic configuration with magnetic moment of 4 $\mu_B$ per formula unit have been reported with respect to the minimum total energy. Spontaneous polarization of 27.3 $\mu$ C/cm$^2$, caused mainly by the ferroelectric distortions of Ti, was evaluated using the berry phase approach in the modern theory of polarization. The Bi-6s stereochemical activity of long-pair and the `d$^0$-ness' criterion in off-centring of Ti were coexisting in the predicted new system. In view of the oxidation state of Bi$^{3+}$,Fe$^{2+}$,Ti$^{4+}$, and O$^{2-}$ from the orbital-resolved density of states of the Bi-6p, Fe-3d,Ti-3d, and O-2p states,the valence state of Bi$_2$FeTiO$_6$ in the rhombohedral phase was found to be Bi$_2$$^{3+}$Fe$^{2+}$Ti$^{4+}$O$_6$.

Structural phase transitions and piezoelectric anomalies in ordered Sc0·5Ga0·5N alloys

Local-density approximation calculations (LDA) within density functional theory (DFT) and Berry phase approach within modern theory of polarization are performed to predict the structural and piezoelectric properties of ordered Sc0·5Ga0·5N alloys under compressive and tensile in-plane strain. This alloy is found to exhibit a tremendous piezoelectric response, associated with a phase transition from nonpolar p63/mcc(D 6h) space group to a polar p63 mc(C 6v) structure, at fixed Ga and Sc compositions when continuously changing the experimental accessible parameters (i.e. the compressive and tensile strain). The mechanism of the effects behind such anomalous behaviour is revealed and explained.