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An excitonic insulator (EI) phase is a consequence of collective many-body effects where an optical band gap is formed by the condensation of electron-hole pairs or excitons. We report pressure-dependent optical pump optical probe spectroscopy of EI Ta$_2$NiSe$_5$ in an on-site in situ geometry. The fast relaxation process depicts the transition across P$_{C_1}$ $\sim$1 GPa from EI phase to a semiconductor and P$_{C_2}$ $\sim$3 GPa from a semiconductor to a semimetallic phase. The instability of the EI phase beyond P$_{C_1}$ is captured by the Rothwarf-Taylor model by incorporating the decrease of the bandgap under pressure. The pressure coefficient of the bandgap decreases, 65 meV/GPa closely agrees with the first principle calculations., Comment: 17 pages, 5 figures

Recently discovered class of 2D materials based on transition metal phosphorous trichalcogenides exhibit antiferromagnetic ground state, with potential applications in spintronics. Amongst them, FePS$ _{3} $ is a Mott insulator with a band gap of $\sim$ 1.5 eV. This study using Raman spectroscopy along with first-principles density functional theoretical analysis examines the stability of its structure and electronic properties under pressure. Raman spectroscopy reveals two phase transitions at 4.6 GPa and 12 GPa marked by the changes in pressure coefficients of the mode frequencies and the number of symmetry allowed modes. FePS$_3$ transforms from the ambient monoclinic C2/m phase with a band gap of 1.54 eV to another monoclinic C2/m (band gap of 0.1 eV) phase at 4.6 GPa, followed by another transition at 12 GPa to the metallic trigonal P-31m phase. Our work complements recently reported high pressure X-ray diffraction studies.

In the bilayer ReS$ _{2} $ channel of a field-effect transistor (FET), we demonstrate using Raman spectroscopy that electron doping (n) results in softening of frequency and broadening of linewidth of the in-plane vibrational modes, leaving out-of-plane vibrational modes unaffected. Largest change is observed for the in-plane Raman mode at $\sim$ 151 cm$^{-1} $, which also shows doping induced Fano resonance with the Fano parameter 1/q = -0.17 at doping concentration of $\sim 3.7\times10^{13}$ cm$^{-2} $. A quantitative understanding of our results is provided by first-principles density functional theory (DFT), showing that the electron-phonon coupling (EPC) of in-plane modes is stronger than that of out-of-plane modes, and its variation with doping is independent of the layer stacking. The origin of large EPC is traced to 1T to 1T$ ^{\prime} $ structural phase transition of ReS$ _{2} $ involving in-plane displacement of atoms whose instability is driven by the nested Fermi surface of the 1T structure. Results are also compared with the isostructural trilayer ReSe$ _{2} $.

Understanding of electron-phonon coupling (EPC) in two dimensional (2D) materials manifesting as phonon renormalization is essential to their possible applications in nanoelectronics. Here we report in-situ Raman measurements of electrochemically top-gated 2, 3 and 7 layered 2H-MoTe$ _{2} $ channel based field-effect transistors (FETs). While the E$ ^{1}_{2g} $ and B$ _{2g} $ phonon modes exhibit frequency softening and linewidth broadening with hole doping concentration (\textit{p}) up to $\sim$ 2.3 $\times$10$ ^{13} $/cm$ ^{2} $, A$ _{1g}$ shows relatively small frequency hardening and linewidth sharpening. The dependence of frequency renormalization of the E$ ^{1}_{2g} $ mode on the number of layers in these 2D crystals confirms that hole doping occurs primarily in the top two layers, in agreement with recent predictions. We present first-principles density functional theory (DFT) analysis of bilayer MoTe$ _{2} $ that qualitatively captures our observations, and explain that a relatively stronger coupling of holes with E$ ^{1}_{2g} $ or B$ _{2g} $ modes as compared with the A$ _{1g} $ mode originates from the in-plane orbital character and symmetry of the states at valence band maximum (VBM). The contrast between the manifestation of EPC in monolayer MoS$ _{2} $ and those observed here in a few-layered MoTe$ _{2} $ demonstrates the role of the symmetry of phonons and electronic states in determining the EPC in these isostructural systems.

The class of layered 3D-topological insulators have shown intriguingly anomalous temperature dependence in their thermal expansion coefficients. It was proposed that stacking faults are the origin of the observed anomalous thermal expansion. Here, using femtosecond pump-probe differential reflectivity measurements we probe the carrier and coherently generated totally symmetric A1g1 optical phonons in Bi2Se3. Transient signals also show a low frequency (~GHz) oscillations due to coherent longitudinal acoustic phonons. We extract temperature dependence of optical constants, sound velocity and Young's modulus of Bi2Se3 using the strain pulse propagation model. A remarkable anomalous behavior around ~180 K is observed in the temperature dependence of optical and acoustic phonons as well as the optical constants. First-principles density functional theory (DFT) reveals that thermally activated formation of stacking faults is responsible for the anomalies observed in Bi2Se3, similar to case of Sb2Te3. We also show that inclusion of spin-orbit coupling plays an important role in reducing the total energy difference between the pristine and the faulted structures., Comment: 18 pages, 6 figures

MnV$_2$O$_4$ in the spinel structure is known to exhibit coupled orbital and spin ordering, and its Raman spectra show interesting anomalies in its low-temperature phase. With a goal to explain this behavior involving coupled spins and phonons, we determine here the spin-phonon couplings in MnV$_2$O$_4$ from a theoretical analysis of its phonon spectra and their dependence on spin-ordering and electron correlations, obtained from first-principles density functional theoretical calculations. Using these in an analysis based on a Landau-like theory, we uncover the mechanism governing the Raman anomalies observed in its low-temperature phase.

Due to competing long range ferromagnetic order, the transition metals Fe, Co and Ni are not superconductors at ambient pressure. While superconductivity was observed in a non-magnetic phase of Fe, stabilized under pressure, it is yet to be discovered in Co and Ni under any experimental conditions. Here, we report emergence of superconductivity in the recently discovered high-density nonmagnetic face centered cubic phase in Co thin films below a transition temperature (Tc) of ~5.4 K, as revealed in experiments based on point-contact spectroscopy and resistance, and four-probe measurements of resistance at ambient pressure. We confirm the non-magnetic nature of the dense fcc phase of Co within first-principles density functional theory, and show that its superconductivity below 5 K originates from anomalous softening of zone-boundary phonons and their enhanced coupling with electrons upon biaxial strain., Comment: 22 pages, 12 figures, 1 table

We determine atomic and electronic structure, formation energy, stability and magnetic properties of native point defects, such as Gallium (Ga) and Nitrogen (N) vacancies in bulk and at non-polar (10$\overline{1}$0) surface of wurtzite Gallium Nitride (\textit w-GaN) using, first-principles calculations based on Density Functional Theory (DFT). Under both Ga-rich and N-rich conditions, formation energy of N-vacancies is significantly lower than that of Ga-vacancies in bulk and at (10$\overline{1}$0) surface. Experimental evidence of the presence of N-vacancies was noted from electron energy loss spectroscopy measurements which further correlated with the high electrical conductivity observed in GaN nanowall network. We find that the Fermi level pins at 0.35 $\pm$0.02 eV below Ga derived surface state. Presence of atomic steps in the nanostructure due to formation of N-vacancies at the (10$\overline{1}$0) surface makes its electronic structure metallic. Clustering of N-vacancies and Ga-Ga metallic bond formation near these vacancies, is seen to be another source of electrical conductivity of faceted GaN nanostructure that is observed experimentally.

We report high pressure Raman, synchrotron x-ray diffraction and electrical transport studies on Weyl semimetals NbP and TaP along with first-principles density functional theoretical (DFT) analysis. The frequencies of first-order Raman modes of NbP harden with increasing pressure and exhibit a slope change at P$_c$ $\sim$ 9 GPa, and its resistivity exhibits a minimum at P$_c$. The pressure-dependent volume of NbP exhibits a change in its bulk modulus from 207 GPa to 243 GPa at P$_c$. Using DFT calculations, we show that these anomalies are associated with pressure induced Lifshitz transition which involves appearance of electron and hole pockets in its electronic structure. In contrast, results of Raman and synchrotron x-ray diffraction experiments on TaP and DFT calculations show that TaP is quite robust under pressure and does not undergo any phase transition., Comment: 10pages, 12 figures

High pressure Raman spectroscopy of bulk 2H-MoTe$_2$ upto $\sim$ 29 GPa is shown to reveal two phase transitions (at $\sim$ 6 and 16.5 GPa), which are analyzed using first-principles density functional theoretical calculations. The transition at 6 GPa is marked by changes in the pressure coefficients of A$_{1g}$ and E$^{1}_{2g}$ Raman mode frequencies as well as in their relative intensity. Our calculations show that this is an isostructural semiconductor to a semimetal transition. The transition at $\sim$ 16.5 GPa is identified with the changes in linewidths of the Raman modes as well as in the pressure coefficients of their frequencies. Our theoretical analysis clearly shows that the structure remains the same upto 30 GPa. However, the topology of the Fermi-surface evolves as a function of pressure, and abrupt appearance of electron and hole pockets at P $\sim$ 20 GPa marks a Lifshitz transition., Comment: 20 Pages, 8 Figures

We report high pressure Raman experiments of Black phosphorus up to 24 GPa. The line widths of first order Raman modes A$^1_g$, B$_{2g}$ and A$^2_g$ of the orthorhombic phase show a minimum at 1.1 GPa. Our first-principles density functional analysis reveals that this is associated with the anomalies in electron-phonon coupling at the semiconductor to topological insulator transition through inversion of valence and conduction bands marking a change from trivial to nontrivial electronic topology. The frequencies of B$_{2g}$ and A$^2_g$ modes become anomalous in the rhombohedral phase at 7.4 GPa, and new modes appearing in the rhombohedral phase show anomalous softening with pressure. This is shown to originate from unusual structural evolution of black phosphorous with pressure, based on first-principles theoretical analysis., Comment: 13pages, 12figures

Using in-situ Raman scattering from phosphorene channel in an electrochemically top-gated field effect transistor, we show that its phonons with A$_g$ symmetry depend much more strongly on concentration of electrons than that of holes, while the phonons with B$_g$ symmetry are insensitive to doping. With first-principles theoretical analysis, we show that the observed electon-hole asymmetry arises from the radically different constitution of its conduction and valence bands involving $\pi$ and $\sigma$ bonding states respectively, whose symmetry permits coupling with only the phonons that preserve the lattice symmetry. Thus, Raman spectroscopy is a non-invasive tool for measuring electron concentration in phosphorene-based nanoelectronic devices.

In recent years, a low pressure transition around P $\sim$ 3 GPa exhibited by the A$_2$B$_3$-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi$_2$Se$_3$) using Raman spectroscopy at pressure upto 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P $\sim$ 2.4 GPa followed by structural transitions at $\sim$ 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P $\sim$ 3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated $\mathbb{Z}_2$ invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition., Comment: 18 pages , 6 figures

Earths lower mantle extending from 670 to 2,990 km deep is predominantly composed of a perovskite-type (Mg,Fe)SiO3 phase1,2. The perovskite phase undergoes a structural phase transition to a post-perovskite phase responsible for D" layer seismic discontinuity2,3 at about 2690 km depth in the lowermost region of the lower mantle. However, structural basis of other seismic discontinuities occurring in the upper region of the lower mantle (700 km to 1,200 km deep) remains unexplained4-7, as no apparent change in the crystal symmetry of the orthorhombic perovskite phase has been reported5. We present here unambiguous evidence for a non-apparent isostructural phase transition8 in the stable orthorhombic perovskite phase of CaTiO3 which may have relevance to phase transitions in the perovskite phase of (Mg,Fe)SiO3 also, as both the compounds have similar structure, tolerance factor and thermochemical properties9-11. Our results are based on the analysis of neutron powder diffraction patterns using Rietveld and mode crystallography techniques and are supported by density functional and Landau theory calculations. The present results on CaTiO3 would encourage search for isostructural phase transition in the perovskite phase of (Mg,Fe)SiO3 that may provide clue to the unexplained geophysical phenomena in the upper part of the earths lower mantle., Comment: 24 pages, 3 Figures in main text and 6 figures in extended data

The nontrivial electronic topology of a topological insulator is thus far known to display signatures in a robust metallic state at the surface. Here, we establish vibrational anomalies in Raman spectra of the bulk that signify changes in electronic topology: an E2 g phonon softens unusually and its linewidth exhibits an asymmetric peak at the pressure induced electronic topological transition (ETT) in Sb2Se3 crystal. Our first-principles calculations confirm the electronic transition from band to topological insulating state with reversal of parity of electronic bands passing through a metallic state at the ETT, but do not capture the phonon anomalies which involve breakdown of adiabatic approximation due to strongly coupled dynamics of phonons and electrons. Treating this within a four-band model of topological insulators, we elucidate how nonadiabatic renormalization of phonons constitutes readily measurable bulk signatures of an ETT, which will facilitate efforts to develop topological insulators by modifying a band insulator.

Strong electron-phonon interaction which limits electronic mobility of semiconductors can also have significant effects on phonon frequencies. The latter is the key to the use of Raman spectroscopy for nondestructive characterization of doping in graphene-based devices. Using in-situ Raman scattering from single layer MoS$_2$ electrochemically top-gated field effect transistor (FET), we show softening and broadening of A$_{1g}$ phonon with electron doping whereas the other Raman active E$_{2g}^{1}$ mode remains essentially inert. Confirming these results with first-principles density functional theory based calculations, we use group theoretical arguments to explain why A$_{1g}$ mode specifically exhibits a strong sensitivity to electron doping. Our work opens up the use of Raman spectroscopy in probing the level of doping in single layer MoS$_2$-based FETs, which have a high on-off ratio and are of enormous technological significance., Comment: 5 pages, 3 figures

We determine the nature of coupled phonons and magnetic excitations in AlFeO3 using inelastic light scattering from 5 K to 315 K covering a spectral range from 100-2200 cm-1 and complementary first-principles density functional theory-based calculations. A strong spin-phonon coupling and magnetic ordering induced phonon renormalization are evident in (a) anomalous temperature dependence of many modes with frequencies below 850 cm-1, particularly near the magnetic transition temperature Tc ~ 250 K, (b) distinct changes in band positions of high frequency Raman bands between 1100-1800 cm-1, in particular a broad mode near 1250 cm-1 appears only below Tc attributed to the two-magnon Raman scattering. We also observe weak anomalies in the mode frequencies at ~ 100 K, due to a magnetically driven ferroelectric phase transition. Understanding of these experimental observations has been possible on the basis of first-principles calculations of phonons spectrum and their coupling with spins.

We report magnetic, dielectric and magnetodielectric responses of pure monoclinic bulk phase of partially-disordered La2NiMnO6, exhibiting a spectrum of unusual properties and establish that this system intrinsically is a true multiglass with a large magnetodielectric coupling (8-20%) over a wide range of temperatures (150 - 300 K). Specifically, our results establish a unique way to obtain colossal magnetodielectricity, independent of any striction effects, by engineering the asymmetric hopping contribution to the dielectric constant via the tuning of the relative spin orientations between neighboring magnetic ions in a transition metal oxide system. We discuss the role of anti-site (Ni-Mn) disorder in emergence of these unusual properties., Comment: 5 pages, 4 figures, Slightly revised version of previous article in condmat: arXiv:1202.4319v1

We report temperature-dependent Raman spectra of CeFeAsO0.9F0.1 from 4 K to 300 K in spectral range of 60 to 1800 cm-1 and interpret them using estimates of phonon frequencies obtained from first-principles density functional calculations. We find evidence for a strong coupling between the phonons and crystal field excitations; in particular Ce3+ crystal field excitation at 432 cm-1 couples strongly with Eg oxygen vibration at 389 cm-1 . Below the superconducting transition temperature, the phonon mode near 280 cm-1 shows softening, signaling its coupling with the superconducting gap. The ratio of the superconducting gap to Tc thus estimated to be ~ 10 suggests CeFeAsO0.9F0.1 as a strong coupling superconductor. In addition, two high frequency modes observed at 1342 cm-1 and 1600 cm-1

Inelastic light scattering studies on single crystal of electron-doped Ca(Fe0.95Co0.05)2As2 superconductor, covering the tetragonal to orthorhombic structural transition as well as magnetic transition at TSM ~ 140 K and superconducting transition temperature Tc ~ 23 K, reveal evidence for superconductivity-induced phonon renormalization; in particular the phonon mode near 260 cm-1 shows hardening below Tc, signaling its coupling with the superconducting gap. All the three Raman active phonon modes show anomalous temperature dependence between room temperature and Tc i.e phonon frequency decreases with lowering temperature. Further, frequency of one of the modes shows a sudden change in temperature dependence at TSM. Using first-principles density functional theory-based calculations, we show that the low temperature phase (Tc < T < TSM) exhibits short-ranged stripe anti-ferromagnetic ordering, and estimate the spin-phonon couplings that are responsible for these phonon anomalies.

Combining experiments with first principles calculations, we show that site-specific doping of Mn into SrTiO3 has a decisive influence on the dielectric properties of these doped systems. We find that phonon contributions to the dielectric constant invariably decrease sharply on doping at any site. However, a sizable, random dipolar contribution only for Mn at the Sr site arises from a strong off-centric displacement of Mn in spite of Mn being in a non-d0 state; this leads to a large dielectric constant at higher temperatures and gives rise to a relaxor ferroelectric behavior at lower temperatures. We also investigate magnetic properties in detail and critically reevaluate the possibility of a true multi-glass state in such systems., Comment: 24 Pages, 2 Tables, 9 Figures

We report interesting anomalies in the temperature dependent Raman spectra of FeSe$_{0.82}$ measured from 3K to 300K in the spectral range from 60 to 1800 cm$^{-1}$ and determine their origin using complementary first-principles density functional calculations. A phonon mode near 100 cm$^{-1}$ exhibits a sharp increase by $\sim$ 5% in frequency below a temperature T$_s$ ($\sim$ 100 K) attributed to strong spin-phonon coupling and onset of short-range antiferromagnetic order. In addition, two high frequency modes are observed at 1350 cm$^{-1}$ and 1600 cm$^{-1}$, attributed to electronic Raman scattering from ($x^2-y^2$)to $xz$ / $yz$ $d$-orbitals of Fe., Comment: 19 pages, 4 figures, 1 table

Ab initio calculations and statistical mechanics are combined to elucidate the thermodynamics of H vacancies in MgH2. A general method based on a grand-canonical ensemble of defect configurations is introduced to model the exchange of hydrogen between crystalline MgH2 and gas-phase H2. We find that, at temperatures and hydrogen partial pressures of practical interest, MgH2 is capable of accommodating only very small concentrations of hydrogen vacancies, which consist mainly of isolated defects rather than vacancy clusters, contrary to what is expected from a simple energetic analysis., Comment: 13 pages, 5 figures. Paper accepted in Physical Review B

Two-dimensional graphene exhibits many fascinating properties such as ballistic electronic conduction and quantum Hall effect at room temperature.1-4 Graphene doped electrochemically or through charge-transfer with electron-donor and -acceptor molecules,5-7 shows marked changes in electronic structure, with characteristic signatures in the Raman spectra.5-10 Substitutional doping, universally used in tuning properties of semiconductors, could be a powerful tool to control the electronic properties of graphene. Here, we present the structure and properties of boron and nitrogen doped graphenes, obtained by more than one method involving arc discharge in appropriate gaseous atmosphere, by using modified graphite electrode or by the transformation of nano-diamond. Using a combination of experiment and firstprinciples theory, we demonstrate systematic changes in the carrier-concentration and electronic structure of graphenes with B/N-doping, accompanied by stiffening of the Gband and intensification of the defect related D-band in the Raman spectra. Such n/p - type graphenes obtained without external fields or chemical agents should find device applications., Comment: 12 pages, 5 figures, 1 table

We demonstrate electrochemical top gating of graphene by using a solid polymer electrolyte. This allows to reach much higher electron and hole doping than standard back gating. In-situ Raman measurements monitor the doping. The G peak stiffens and sharpens for both electron and hole doping, while the 2D peak shows a different response to holes and electrons. Its position increases for hole doping, while it softens for high electron doping. The variation of G peak position is a signature of the non-adiabatic Kohn anomaly at $\Gamma$. On the other hand, for visible excitation, the variation of the 2D peak position is ruled by charge transfer. The intensity ratio of G and 2D peaks shows a strong dependence on doping, making it a sensitive parameter to monitor charges., Comment: 7 pages, 8 figures

We use first-principles density-functional calculations to determine the frequency shift of the A$'_1$-${\bf K}$ phonon (Raman D band) in monolayer graphene, as a function of the charge doping. A detailed DFT study on the electron-phonon coupling and the phonon line width of E$_{2g}$-${\bm \Gamma}$ and A$'_1$-${\bf K}$ phonons are also performed for graphene multi-layers. Furthermore, we explain the experimentally observed '1/(Number of Layers)' behaviour of the Raman G band position after including the dynamic response treated within time dependent perturbation theory., Comment: 4 pages, 3 figures, 1 table

The ground-state structural and electronic properties of ferroelectric BiFeO$_3$ are calculated using density functional theory within the local spin-density approximation and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group $R3c$, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 $\mu$C/cm$^2$ is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation., Comment: (9 pages, 5 figures, 5 tables)

In this paper, we present a microscopic model for heterogeneous ferroelectric and an order parameter for relaxor phase. We write a Landau theory based on this model and its application to ferroelectric PbFe$_{1/2}$Ta$_{1/2}$O$_3$ (PFT) and antiferroelectric NaNbO$_3$:Gd. We later discuss the coupling between soft mode and domain walls, soft mode and quasi-local vibration and resulting susceptibility function., Comment: 6 pages, Fundamental physics of ferroelectrics 2003

We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which we call HARES (for High-performance-fortran Adaptive grid Real-space Electronic Structure) aims at making the method widely applicable and efficient, using high performance Fortran on parallel architectures. The scaling of various parts of a HARES calculation is analyzed and compared to that of plane-wave based methods. The new developments that lead to enhanced performance, and their parallel implementation, are presented in detail. We illustrate the application of HARES to the study of elemental crystalline solids, molecules and complex crystalline materials, such as blue bronze and zeolites., Comment: 17 two-column pages, including 9 figures, 5 tables. To appear in Computer Physics Communications. Several minor revisions based on feedback

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions., Comment: 9 pages, 2 figures (one in colors), revised version (small changes essentially in Sec. III)

Molecular-dynamics simulations of KNbO$_3$ reveal preformed dynamic chain-like structures, present even in the paraelectric phase, that are related to the softening of phonon branches over large regions of the Brillouin zone. The phase sequence of ferroelectric transitions is correctly reproduced, showing that the first-principles effective Hamiltonian used in the simulations captures the essential behavior of the microscopic fluctuations driving the transitions. Real space chains provide a framework for understanding both the displacive and order-disorder characteristics of these phase transitions., Comment: 4 pages, REVTeX, three eps figures

An effective Hamiltonian for the ferroelectric transition in PbTiO3 is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Explicit parametrization of the polar lattice Wannier functions is used for subspace projection, addressing the issues of LO-TO splitting and coupling to the complementary subspace. In contrast with ferroelectric BaTiO3 and KNbO3, we find significant involvement of the Pb atom in the lattice instability. Monte Carlo simulations for this Hamiltonian show a first-order cubic-tetragonal transition at 660 K. Resulting temperature dependence of spontaneous polarization, c/a ratio and unit-cell volume near the transition are in good agreement with experiment. Comparison of Monte Carlo results with mean field theory analysis shows that both strain and fluctuations are necessary to produce the first order character of this transition., Comment: LateX file, 32 pages, 10 figures

An effective Hamiltonian for the ferroelectric transition in $PbTiO_3$ is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Preliminary results of Monte Carlo simulations for this system show a first-order cubic-tetragonal transition at 660 K. The involvement of the Pb atom in the lattice instability and the coupling of local distortions to strain are found to be particularly important in producing the behavior characteristic of the $PbTiO_3$ transition. A tentative explanation for the presence of local distortions experimentally observed above $T_c$ is suggested. Further applications of this method to a variety of systems and structures are proposed for first-principles study of finite-temperature structural properties in individual materials., Comment: 14 pages, harvmac, 4 uuencoded figures

A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corresponding invariant energy expansion, can be obtained for individual materials using first- principles density-functional-theory total energy and linear response techniques, or any technique that can reliably calculate force constants and distortion energies. A practical approach to the determination of these parameters is presented and the application to ferroelectric $PbTiO_3$ discussed., Comment: extensive revisions in presentation, 32 pages, Revtex, 7 Postscript figures