Self-consistent Phonon Approximation Research Articles

Motorized chain models of the ideal chromosome

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Lamellar Fluctuations Melt Ferroelectricity.

We consider a standard Ginzburg-Landau model of a ferroelectric whose electrical polarization is coupled to gradients of elastic strain. At the harmonic level, such flexoelectric interaction is known to hybridize acoustic and optic phonon modes and lead to phases with modulated lattice structures that precede the state with spontaneously broken inversion symmetry. Here, we use the self-consistent phonon approximation to calculate the effects of thermal and quantum polarization fluctuations on the bare hybridized modes to show that such long-range modulated order is unstable at all temperatures. We discuss the implications for the nearly ferroelectric SrTiO_{3} and KTaO_{3}, and we propose that these systems are melted versions of an underlying modulated state that is dominated by nonzero momentum thermal fluctuations except at the very lowest temperatures.

Sliding Phase Transition in Ferroelectric van der Waals Bilayers.

We address the sliding thermodynamics of van der Waals-bonded bilayers by continuum electromechanics. We attribute the robustness of the ferroelectricity recently observed in h-BN and WTe_{2} bilayers to large in-plane stiffness of the monolayers. We compute the electric susceptibility and specific heat in a mean-field self-consistent phonon approximation. We compare critical temperatures and electric switching fields with the observed values.

Anharmonic Interaction in Negative Thermal Expansion Material CaTiF6.

Although the quasi-harmonic approximation (QHA) method applies to many materials, it is necessary to study the anharmonic interaction for extremely anharmonic materials. In this work, the unusual negative thermal expansion (NTE) property of CaTiF6 is studied by combing QHA and anharmonic interaction. The improved self-consistent phonon approximation (ISCPA), which treats anharmonic effects in solids nonperturbatively, is employed. The agreement of NTE behavior between the calculation and the experiment can be further promoted from qualitative consistency by QHA to quantitative consistency by the ISCPA. From mode Grüneisen parameters, it is found that the low-frequency phonons, especially acoustic phonons, contribute greatly to the NTE behavior of CaTiF6. The rigid unit modes (RUMs) of low-frequency optical phonons can be identified. The phonon lifetime of CaTiF6 is calculated from three-phonon interactions; thereby, the NTE mechanism can be further explored by phonon lifetimes of phonons with different frequencies on heating. The anomalous lattice thermal conductivity (LTC) is predicted using the Boltzmann transport equation within the relaxation time approximation. The glasslike LTC can occur in crystal CaTiF6.

An Isotropic Empirical Intermolecular Potential for Solid H2 and D2: A Classical Molecular Calculation**Supported by the National Natural Science Foundation of China under Grant No U1430109.

We develop an isotropic empirical potential for molecular hydrogen (H2) and deuterium (D2) by fitting to solidstate data, which is appropriate for classical molecular dynamics (CMD) approach. Based on the prior isotropic intermolecular potential used in self-consistent phonon approximation, a zero-point energy term and an embedded energy term are introduced to describe the H2–H2 and D2–D2 interactions in CMD simulations. The structure, cohesive energy and elastic properties of solid H2 (D2) are used as the fitting database. The present method is tested by calculating the melting point of solid H2, and the pressure and bulk elastic modulus as a function of volume. The developed potentials well reproduce many properties of solid H2 and D2.

Phenomenological model and experimental study of DNA absorption spectra in THz range

The dielectric permittivity tensor is analyzed qualitatively for the DNA nematic liquid crystal in the THz frequency range. The analysis is performed within the self-consistent phonon approximation based on the PBD model. It is found that DNA depolarization and absorption spectra depend on such parameters as molecular length and helix period. Specifically it is shown that a localization of the absorption lines in the frequency range is determined by the DNA helix structure whereas the DNA length is responsible for a separation between the absorption lines. It is also shown that the gyrotropic properties of the considered liquid crystal depend on a relation between the molecular length and its helix period. The molecules with even number of half helix periods demonstrate the strongest gyrotrophy whereas the molecules with odd number of half helix periods have the weakest gyrotrophy. The model is used to suggest the experimental methodology for determining the DNA length and helix structure based on measurements of the depolarization and absorption spectra in aqueous solutions of biopolimers. Methods of applied THz spectroscopy for determination of the conformational state of molecules in solution is announced. Some preliminary experimental results are presented, including details of measuring the absorption spectra of dry DNA sample and aqueous solutions of biopolimers.

Theoretical analysis of gyrotropy and absorption of terahertz electromagnetic waves in layer of DNA molecules

Certain type of low-frequency DNA molecular oscillations was analysed within the self-consistent phonon approximation. There were calculated dispersion relationship, exiting the oscillations by electromagnetic wave and corresponding contribution to the absorption spectrum of ensemble of parallel DNA molecules. The dependence of the DNA spectral characteristics on the length and period of the DNA duplex structure is revealed. The method of experimental check of obtained results is suggested. If the described model is confirmed by experiment, the obtained results available to reconstruct the length and duplex period of the DNA in a sample by its absorption spectrum.

Precursor dynamics to the structural instability in SrTiO3

The structural instability of SrTiO3 at T S = 105 K is reinvestigated experimentally and theoretically by birefringence measurements and within the self-consistent phonon approximation. Analogous to BaTiO3 the phase transition shows precursor dynamics starting approximately 60 K above the phase transition temperature. These rotational dynamic clusters compete with precursor effects stemming from the polar soft mode and appear on different length scales as compared to BaTiO3.

Tuning the structural instability of SrTiO3by Eu doping: The phase diagram of Sr1−xEuxTiO3

The phase diagram of Sr_1-xEu_xTiO_3 is determined experimentally by electron paramagnetic resonance and resistivity measurements and analyzed theoretically within the self-consistent phonon approximation as a function of x ([0.03-1.0]). The transition temperature of the structural instability of the system increases nonlinearly to higher temperatures with increasing x. This is interpreted theoretically by a substantial alteration in the dynamics caused by a change in the double-well potential from broad and shallow to narrow and deep.

Temperature-induced martensitic phase transitions in gum-metal approximants: First-principles investigations for Ti3Nb

We present a first-principles investigation of the structures and the dynamical stability of the austenite and martensite phases of binary Ti${}_{3}$Nb alloys, used as a model system for the superelastic and superplastic gum-metal alloy. For the body-centered cubic high-temperature $\ensuremath{\beta}$ phase, structural models are constructed by optimizing the chemical decoration of a large supercell and by a cluster expansion method. The energetically most favorable structure is found to be elastically stable but dynamically unstable in the harmonic approximation. At finite temperature anharmonic phonon-phonon interactions treated in a self-consistent phonon approximation stabilize the structure already at room temperature. For the low-temperature ${\ensuremath{\alpha}}^{\ensuremath{'}}$, $\ensuremath{\omega}$, and ${\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}$ phases stable structure models have been constructed. For the hexagonal ${\ensuremath{\alpha}}^{\ensuremath{'}}$ phase a model is generated by optimizing the chemical decoration of a supercell based on the hexagonal ${B}_{h}$ lattice. The hexagonal $\ensuremath{\omega}$ structure may be derived from the body-centered cubic $\ensuremath{\beta}$ phase using the (111) plane collapse model. The structure of the orthorhombic ${\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}$ phase may be viewed as produced by a strain-induced transformation of the body-centered cubic $\ensuremath{\beta}$ phase, albeit with a different chemical decoration. The relaxed structures of the ${\ensuremath{\alpha}}^{\ensuremath{'}}$, $\ensuremath{\omega}$, and ${\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}$ phases were found to be both elastically and dynamically stable in the low-temperature limit. The martensitic temperatures for the $\ensuremath{\beta}\ensuremath{\rightarrow}{\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}$, $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\omega}$, and $\ensuremath{\beta}\ensuremath{\rightarrow}{\ensuremath{\alpha}}^{\ensuremath{'}}$ transitions were estimated by comparing the Helmholtz free energies as a function of temperature.

Isotope-Induced Ferroelectric Phase Transition in Strontium Titanate Only by a Decrease in Zero-Point Vibration Frequency

The possibility of the ferroelectric phase transition in SrTi 18 O 3 only by decreasing the frequency of zero-point vibration due to the substitution of 18 O for 16 O is investigated by the self-consistent phonon approximation (SCPA) of an anharmonic lattice vibration system. The SC equation for the soft-mode frequency is shown to be described by only two parameters; the paraelectric Curie–Weiss temperature T 0 in SrTi 16 O 3 and the quantum factor T 1 inversely proportional to the square root of the effective mass M . The experimental finding that T c =0 in the mixed crystal SrTi( 18 O x 16 O 1- x ) 3 at x =0.33 is used to determine T 1 at this concentration and that at another x using only the ratio of M . The transition temperature T c in SrTi 18 O 3 is numerically calculated for comparison with the experimental value. Several factors determining T c are discussed on the basis of numerical results.

Theoretical Investigation of the Isotope-Induced Ferroelectric Phase Transition in Quantum Paraelectric Strontium Titanate

The isotope-induced ferroelectric phase transition is theoretically investigated in terms of a compact formula based on the self-consistent phonon approximation (SCA) on the anharmonic lattice vibration system. The T c − T 1 phase diagram, where T c and T 1 are the transition temperature T c and the quantum fluctuation parameter T 1, respectively, is numerically calculated to demonstrate the nonlinear dependence of T c on T 1 sensitive to the increase of the oxygen mass. Experimental results of the small transition entropy and the perfect softening are discussed from the viewpoint of the ideal displacive type phase transition.

Microscopic mechanism of stability in yttria-doped zirconia

The relaxed configurations of yttria-stabilised zirconia (YSZ) between 3 and 10 mol % of Y2O3 were modeled using the pseudopotential technique. In the displacive limit of a double-well potential model, the vibrational mode corresponding to the soft phonon in pure c-ZrO2 was calculated for each Y2O3 composition. These anharmonic vibrations, associated with the stabilization of YSZ, were investigated within the self-consistent phonon approximation making obtainable the fine structure in spectral density. In studying the phonon dynamics, we use the displacement probability density, which can quantify very accurately the transition temperature necessary for stabilizing the YSZ cubic phase.

Quantum paraelectricity in the self-consistent phonon approximation

The dielectric susceptibility of potassium tantalate has been computed in the framework of an approach, earlier proposed by Vaks [V.G. Vaks. Vvedenie v mikroskopicheskuiu teoriju segnetoelektrikov. Moskva, Nauka 1973 (in Russian)]. This theory deals with a perturbation series for the temperature Green functions rather than with the mean field approach. The small parameter is the anharmonicity potential. The phonon spectrum, required for the computation, was taken from a recent study by Farhi et. al. [Europ. Phys. J. B (in print)]. Qualitative agreement has been obtained between theory and experiment.

Local structural anomalies in perovskite-type lattices

Perovskite oxides show various structural instabilities which are related to ferroelectricity, antiferroelectricity, Jahn-Teller effects, ferromagnetism, charge- and spin-density instabilities. The electronic, spin and lattice instabilities are described within an anharmonic lattice model extended by electron (spin) phonon interactions and higher-order multiphonon density–density interactions. The model yields within the self-consistent phonon approximation (SPA) mode softening at arbitrary q-values, charge and spin ordering. Exact solutions of the nonlinear equations of motion have been obtained numerically and show highly anomalous q-dependences of the ionic displacements. In real space correlated dynamic displacement patterns are obtained which are mostly related to the oxygen ions which define new length and time scales. The results are related to recent local structure studies.

Influence of order parameter phase fluctuations on the physical properties of quasi-two dimensional superconductors

The influence of the order parameter's phase fluctuations on the Meissner effect is studied for strong anisotropic layered superconductors in the presence of a weak magnetic field, H, less than the lower critical field H c1 ( H< H c1). The Josephson coupling between the layers can be realized in quasi-two dimensional (quasi-2d) superconductors when the interlayer tunnelling integral J ⊥ satisfies the condition J ⊥< κ T c (2)< ϵ F, where ϵ F and T c (2) are the Fermi energy and the mean-field transition temperature for a single superconducting layer, respectively. The system of equations of motion is obtained for the order parameter phases ϕ j( r → ) at the r-th point of the j-th layer. This system of coupled equations is investigated by applying the self consistent phonon approximation (SCPA) method. There exists the plasmon mode in the Josephson coupled layered superconductors in the frame of the SCPA approximation. The square of the transverse effective velocity, v ph,⊥, of collective excitations become proportional to the interlayer phase–phase correlator 〈cos ( ϕ j − ϕ j−1 )〉. When this correlator approaches zero, correlations of the superconducting phases on the different layers disappear, i.e. the phase transition from quasi-2d superconducting state to a pure 2d state occurs at the critical temperature T c1. The transverse rigidity of the system and the plasmon's effective velocity v ph,⊥ vanish at this temperature. T c1 is less than T c (2) and ( T c (2)− T c1)∼ T c (2)( κ T c (2)/ ϵ F). In the temperature interval of ( T c1− T)∼ T c1( κT c1/ ϵ F) ln ( κT c1/ J ⊥) below T c1, the fluctuations of the order parameter's phases become essential in the quasi-2d superconductor. In this interval the ratio of the longitudinal λ ‖ and transverse λ ⊥ components of the London penetration depths, λ ‖/ λ ⊥, should exhibit strong temperature dependence, unlike the prediction of the usual Ginzburg–Landau phenomenological theory. λ ‖ and λ ⊥ diverge at different critical temperatures, namely at T c2≡ T c (2) and T c1, respectively. At T c1< T< T c2 the phases ϕ j on the different layers become non-correlative and the Kosterlitz–Thouless vortices appear in each superconducting layers.

Self-consistent phonon studies of a model diatomic ferroelectric

A model of a diatomic crystal loosely patterned on tin telluride is developed. The crystal has the sodium chloride structure at high temperatures, but displays a soft-mode instability as the temperature is lowered. The lattice dynamics of the model is treated in the self-consistent phonon approximation. The free energy is found to show the behaviour characteristic of a second-order phase transition, but the temperature of the transition is not the same as the temperature at which the frequency of the soft mode becomes zero. Additional contributions to the anharmonic frequency shift, the bubble diagrams, are shown to shift the frequency of the soft mode so that it does go to zero at the transition temperature.

Sequence and temperature effect on hydrogen bond disruption in DNA determined by a statistical analysis.

We use the modified self-consistent phonon approximation theory to calculate temperature dependent interbase hydrogen bond disruption profiles for a number of six base pair repeating sequence infinite B-DNA polymers with various guanine-cytosine/adenine-thymine ratios. For comparison we also include results we have obtained in our earlier work on several B-DNA homopolymers, copolymers and a four-base-pair repeating sequence polymer. Our theory gives a statistical estimate of thermal fluctuational disruption probability of individual hydrogen bonds in individual base pairs in DNA as a function of temperature. The calculated probabilities show no sequence dependence at premelting temperatures, in agreement with proton exchange measurements. These probabilities however become very sensitive to base sequence at temperatures close to the observed melting temperatures. Multiphasic critical transitions are found in which a portion of base pairs are disrupted at temperature below the final disruption temperature. These transitions include localized as well as non-localized base pair opening. The localized transitions involve disruption of a few base-pairs at every other location without large scale base unstacking, and they may not appear in the observed UV curves with current resolution. On the other hand the overall disruption behavior is consistent with observations. The midpoint transition temperatures are close to the observed melting temperatures and these temperatures show the observed linear dependence on guanine-cytosine content. Our calculations indicate that our theory can be used effectively to calculate H-bond disruption behavior of different DNA sequences.

Structural phase transitions and superconductivity in La-M-Cu-O compounds

Abstract The structural phase transitions D17 4h→D18 2h→D164h in La2-x M x CuO4 compounds and their influence on electronic spectrum for oxygen doped holes in CuO2 plane are considered on the basis of a micro-scopical anharmonic model. The free energy and equation for the two-component order parameter are calculated in the self-consistent phonon approximation. Taking into account the electron-phonon interaction with the soft tilting mode and other phonon branches the dependence of the superconducting temperature Tc on hole concentration n is obtained. A dip in Tc(n) dependence is found at the transition to the low temperature tetragonal phase (LTT) owing to splitting of two oxygen bands at half-filling.

Lattice Dynamical Theory of Successive Structural Phase Transitions of a Mixed Crystal of Perovskite-Type Compounds

A microscopic theory of successive structural phase transitions of a mixed binary system of Perovskite-type compounds is presented on the basis of lattice dynamics, which is determined by optimizing the free energy obtained using a self-consistent phonon approximation and a coherent potential approximation for nonlinearity and randomness of the system respectively.