Transport theory for quantum crystals

A correlation function approach is developed to treat non-equilibrium phenomena of quantum crystals at low frequency and long wavelength within the renormalized harmonic approximation (RHA). The derivation of the transport equations is carried out by studying the hierarchy of equations of motion for the retarded Green's functions of a pure, nonprimitive, nonionic, anharmonic lattice. Using a factorization technique to take into account the most important terms due to the particle fluctuations and the leading contributions to the hydrodynamic singularities of the phonon self-energy, we find a differential equation for the displacement field and a generalized transport equation for the phonon gas. The microscopic RHA expressions for the local temperature, the local heat density and the energy current are derived; the quasiparticle parameters (elastic constants, generalized Grüneisen parameters, quasiparticle interaction) entering the equations of motion are shown to be consistent with the RHA. In the hydrodynamic regime the general equations are reduced to two coupled differential equations for the lattice deformations and for the local temperature. Then only the displacement-displacement, the displacement-energy density and the energy density-energy density correlation functions show macroscopic fluctuations; for these functions thermodynamical sum-rules are derived.     

On the microscopic theory of electronic contributions to lattice dynamics of anharmonic crystals

A formalism is set up to study the electronic contribution to the phonon dynamics in an arbitrary crystal, conducting or insulating, without assuming small ionic oscillations. Therefore, in contrast to a harmonic Born-Oppenheimer approximation, such an approach allows for renormalization effects due to phonon-phonon interaction over the complete temperature range of the solid phase. The “weak coupling” approximation between nuclei and electrons is shown to be sufficient in order to obtain the dynamical matrix microscopically in terms of the complete inverse dielectric function of the electrons.     

Lattice dynamics of strongly anharmonic crystals with hard core interaction

The renormalized anharmonic phonon theory and especially the self-consistent harmonic approximation can not be used for hard core interaction in it's original form. Additional short-range correlations have to be incorporated into this theory. A method is proposed which allowes to do this in a systematic way and criteria are found which have to be obeyed by the short-range correlation function. Two examples valid at high and at zero temperature, respectively, are discussed.     

Electron and Phonon in Neutron Scattering of Semiconductor Crystals

An interaction of electron with harmonic, localized and anharmonic fields has been taken to develop the theory of neutron scattering. The Fourier transformed electron Green’s function is evaluated by Zubarev equation of motion technique of quantum dynamics and Dyson equation approach. The expression of Debye-Waller factor (DWF) has been obtained from electron phonon linewidth. The study of its (DWF) effect on differential scattering cross-section through temperature, electron phonon coupling constant and excitations has been investigated in this approach.     

Lattice dynamics in heavy rare-gas crystals under pressure

The lattice dynamics of compressed rare-gas crystals is theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly includes the deformation of electron shells in the dipole approximation. The phonon frequencies of compressed rare-gas crystals are calculated with allowance made for the electron-phonon interaction at the mean-value points with the use of the dynamic matrix constructed with the ab initio short-range repulsive potential. The energy of zero-point vibrations and the heat capacity of compressed krypton and xenon face-centered cubic crystals are calculated in the harmonic approximation. The calculated temperature dependences of the specific heat capacity and the Debye temperature are in good agreement with the data available in the literature on the experiment at zero pressure and the results of the calculations within the density-functional theory for all pressures. The quantum effects, in particular, the energies E _zp of zero-point vibrations for krypton and xenon crystals, are investigated at different pressures.     

Isotopic phonon effects in β-rhombohedral boron--non-statistical isotope distribution

On the basis of the spectra of IR- and Raman-active phonons, the isotopic phonon effects in β-rhombohedral boron are analysed for polycrystalline (10)B- and (11)B-enriched samples of different origin and high-purity (nat)B single crystals. Intra- and inter-icosahedral B-B vibrations are harmonic, hence meeting the virtual crystal approximation (VCA) requirements. Deviations from the phonon shift expected according to the VCA are attributed to the anharmonic share of the lattice vibrations. In the case of icosahedral vibrations, the agreement with calculations on α-rhombohedral boron by Shirai and Katayama-Yoshida is quite satisfactory. Phonon shifts due to isotopic disorder in (nat)B are separated and determined. Some phonon frequencies are sensitive to impurities. The isotopic phonon effects yield valuable specific information on the nature of the different phonon modes. The occupation of regular boron sites by isotopes deviates significantly from the random distribution.     

An approximate scheme to determine the vibratory density of states in a quasi-harmonic solid

In a new and realistic conception of solids, an analytical approach is presented to find the phonon density of states in a quasi-harmonic one-dimensional solid by starting from the fact that a solid with strong interatomic forces can be regarded as an atomic array of quantum anharmonic oscillators under a Morse potential. In fact, our quasi-harmonic approximation is derived by assuming a large enough solid with an involved anharmonic parameter as a sufficiently small quantity. In this context, a mathematical relationship between the above parameter and the matrix element relative to oscillator’s strength is obtained.     

Lattice dynamics of quantum crystals

A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He³ show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results.     

Coherent optical phonons and parametrically coupled magnons induced by femtosecond laser excitation of the Gd(0001) surface

Coherent spin dynamics in the THz domain coupled to a coherent phonon is observed in the time-resolved second harmonic response of the Gd(0001) ferromagnetic metal surface. An LO phonon of 2.9 THz is excited by a transient charge displacement at the surface caused by resonant absorption of a fs laser pulse in the exchange-split surface state. This lattice vibration modulates the interlayer distance inducing a coherent variation of the exchange interaction between spins in adjacent layers. The resulting magnetization dynamics is considered as optical magnon wave packets coupled to the phonon.     

Phonons in an entropic crystal

Hard spheres crystallize due to purely entropic forces. The underlying excluded-volume interaction is completely anharmonic and the nature of the phonon spectrum is therefore of interest. To measure the single-particle motion and the phonon spectrum by dynamic light scattering we have used a collection of novel techniques including multispeckle cross correlation on a CCD chip and the growth of large single crystals using a temperature gradient. The random hexagonal close packed crystal has a dispersion relation closer to hcp than to fcc.     

Internal energy of ordered multicomponent systems in a correlation approximation

An expression for the internal energy of a multicomponent ordered many-body system has been obtained by means of the correlation expansion technique. This expression has proved to be useful for strongly anharmonic crystals in wide temperature and pressure ranges. The relation between the fundamental characteristics of a solid that are used in the correlation expansion and in the phonon approximation has been found. This is, in particular, the relation between the Debye and Einstein temperatures and the average speed of sound.     

Self-consistent treatment of superconducting hole systems and anharmonic lattices in oxides

An extention of Hirsch's Hamiltonian describing the hole system is proposed by including a coupling to the anharmonic lattice and a modulation of the hopping interaction due to lattice displacements. The model is discussed within the variational Bogoliubov's approach, assuming a BCS-like trial Hamiltonian for the hole-like subsystem and a self-consistent phonon approximation for the lattice. The model allows in general to discuss an interplay between superconductivity and ferroelectricity. The results for the critical temperature and the isotope effect coefficient in the superconducting paraelectric phase in one dimension are presented. In particular, the strong influence of the phonon softening on the superconducting transition is widely discussed.     

Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.     

基于第一性原理分子动力学的填充方钴矿热输运性质及微观过程的研究

对于重要热电材料之一的填充方钴矿材料,其低热导率的成因存在两种观点:1)填充原子的局域振动引起共振散射降低热导率;2)填充原子的引入加强了三声子倒逆过程来降低热导率.本文采用含有限温度效应的第一性原理分子动力学方法模拟了YbFe_4Sb_(12)的动力学过程,并通过温度相关有效势场方法得到了充分包含非线性作用的等效非谐力常数,研究了微扰近似下的声子输运性质.结果显示,在填充原子振动全部参与三声子倒逆散射过程的近似下,相比于纯方钴矿体系,声子寿命大幅地降低,填充原子的振动是热阻的重要来源.但即便如此,理论计算结果与实验的晶格热导率之间仍存在明显偏离.不同填充原子振动之间的较弱关联性质也揭示其明显偏离经典的声子图像,表现为一种强烈的局域特征振动模式,并以此散射其他晶格声子,因而对热阻的贡献也超出了传统三声子的理论框架.通过将填充原子Yb振动模式的寿命进行共振散射形式的修正,可以使晶格热导率与实验结果符合较好.以上结果表明,YbFe_4Sb_(12)的低晶格热导率是由声子间相互作用以及具有局域振动特征的共振散射两方面因素导致.     

First principles lattice dynamical calculation of semiboride Be2B and its ternary alloys XBeB (X=Na, Mg, Al)

We present results of first principles total energy calculations of the structure, electronic and lattice dynamics for beryllium semiboride and its three ternary alloys using generalized gradient and local density approximations under the framework of density functional theory. The generalized gradient approximation is used for all compounds except MgBeB using the Perdew-Burke-Ernzehorf exchange correlation functional while local density approximations use the Perdew-Zunger ultrasoft exchange correlation functional. The calculated ground state structural parameters are in good agreement with those of experimental and previous theoretical studies. The electronic band structure calculations show that Be₂B may transform to a semiconductor after Al substitution. A linear response approach to density functional theory is used to calculate phonon dispersion curves and vibrational density of states. The phonon dispersion curves of Be₂B and AlBeB are positive indicating a dynamical stablility of the structure for these compounds. The phonon dispersion curves of NaBeB and MgBeB show the imaginary phonons throughout the Brillouin zone, which confirms dynamical instability as indicated in band structures for these alloys. We also present the partial phonon density of states for different species of Be₂B and AlBeB to bring out the details of the participation of different atoms in the total phonon density of state, particularly the role played by Al atom. The first time calculated phonon properties are clearly able to bring out the significant effect of isoelectronic substitution in Be₂B.     

Theoretical study of NMR relaxation due to rattling phonons

We calculate the NMR relaxation rate due to quadrupolar coupling of the nucleus to a local, strongly anharmonic phonon mode. As a model potential for a “rattling” motion we consider a square-well potential. We calculate the free phonon Green's function analytically and derive the low and high temperature limits of the NMR relaxation rate. It is shown that the temperature dependence of the NMR relaxation rate possesses a peak in contrast to harmonic phonons but in qualitative agreement with a recent NMR study on KOs₂O₆. We discuss the influence of phonon renormalization due to electron-phonon interaction.     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Ab initio calculation of local vibrational modes by the Green’s function method. Application to GaAs:C and GaN:As

We present an ab initio technique for the calculation of vibrational modes at deep defects in semiconductors outside and inside the host-phonon bands. The dynamical matrix is calculated using density-functional theory in the local density approximation. In the results presented here all interatomic harmonic forces up to the eleventh nearest neighbour of a particular atom of the perturbed or unperturbed crystal are included. The Green's function method is used to obtain the difference of the density of phonon states between the perturbed and the perfect crystal. This technique is applied to calculate the split-off mode at the C impurity at As site in GaAs and its isotope shifts, which are in good agreement with Raman scattering experiments. It is demonstrated that the impurities generate resonances and localized modes inside the host-phonon bands. The resonances arise at specific energies of the density of phonon states of the perfect crystal which are practically independent of the chemical nature of the defect, whereas the localized modes show distinct impurity or ligand isotope shifts. Our calculations of GaAs and cubic GaN lead to the assignment of a number of low energy Raman-scattering peaks between 7.2 meV and 31.0 meV, observed at a layer of cubic GaN on a GaAs substrate, to resonances inside the phonon bands of GaAs and GaN. Received 5 March 1999     

Molecular dynamics calculations of anharmonic properties of the vibrational spectrum of BCC zirconium under pressure

The structural stability and lattice dynamics of the high-pressure bcc phase of Zr at a constant temperature T = 500 K are studied for various volumes using molecular dynamics simulation with the Animalu pair pseudopotential. Dispersion curves of the vibrational spectrum calculated by the molecular dynamics method for various volumes are compared to the phonon spectrum obtained in the harmonic approximation. It is demonstrated that, as the volume decreases, all frequencies of the vibrational spectrum increase gradually and bcc zirconium remains strongly anharmonic along all high-symmetry directions of the Brillouin zone over the entire range of volumes studied. The strongly anharmonic N _T1 phonon is significantly softened near the point of structural instability of bcc-Zr at T = 500 K and V = 0.87V ₀. As the volume decreases to V = 0.73V ₀ under pressure, the anharmonic corrections for this phonon decrease by almost an order of magnitude and the phonons near the H point of the Brillouin zone become anharmonic. The damping of the T ₁ phonon mode along the [110] direction is calculated as a function of pressure.     

Mode-coupling theory for the lattice dynamics of anharmonic crystals: self-consistent damping and the 1d Lennard-Jones chain

We present a self-consistent theory for the dynamical one-phonon structure factor in anharmonic crystals. The theory is the phonon analogue of the mode-coupling theory of liquid dynamics of Götze and his coworkers. Starting point is the lattice dynamics treatment based on the Mori- Zwanzig technique as formulated by Götze and Michel. We apply the theory to the one-dimensional (1d) Lennard-Jones chain and show that the nonlinear mode-coupling equations can be readily solved in the time domain. The vertices entering the equations as input are calculated exactly by a Monte Carlo technique. We compare our findings with molecular dynamics (MD) simulations and the results of other theoretical approaches.