Raman study of phase transitions in rare earth vanadates

The phase transitions in DyVO₄ at about 14K and in TbVO₄ at about 33K have been investigated by Raman scattering. The E_g phonons are split below the transition temperature but the singlet phonon modes are not appreciably affected. No soft phonon mode is observed but large changes are seen in the low lying electronic levels. These results appear to be a consequence of a cooperative Jahn-Teller effect.     

Phonons in the organic conductor TEA(TCNQ)2 studied by neutron inelastic scattering

The lattice dynamics of the one-dimensional organic conductor TEA(TCNQ)₂ is studied by inelastic neutron scattering at temperatures 77, 175 and 295 K. Special attention is paid to the phonons propagating along c¹ which is approximately along the conducting axis. These phonons show a well defined Kohn anomaly at 2k_F as well as gaps which we attribute to both the tetrametic structure of the crystals and to the electron- phonon coupling. The temperature variation of the phonons along c¹ is found to be typical for a system where electron-phonon coupling dominates.     

Studies of high-temperature electron–phonon interactions with inelastic neutron scattering and first-principles computations

Several recent studies of phonons combining inelastic neutron scattering and first-principles calculations are summarized. Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V₃Si, V₃Ge, and V₃Co at temperatures from 10 K to 1273 K. It was found that phonons in V₃Si and V₃Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V₃Co have a normal softening behavior. Additional measurements of the phonon DOS of BCC V alloys were performed, and it was found that a stiffening anomaly present in pure V is suppressed upon introduction of extra d-electrons by alloying. First-principles calculations of the electronic and phonon densities of states show that in both these systems, the anomalous phonon stiffening originates with an adiabatic electron–phonon coupling mechanism. The anomaly is caused by the thermally-induced broadening of sharp peaks in the electronic density of states, which tends to decrease the electronic density at the Fermi level. These results illustrate how the combined use of first-principles calculations and inelastic neutron scattering provides powerful insights into couplings of excitations in condensed-matter.     

Anharmonic effects of phonons with Kohn anomalies

In a quasi-one-dimensional conductor, the phonons with anomaly at the Fermi diameter, 2k_F, cause the phonons at 4k_F to soften via the three-phonon coupling, mainly due to the phonon modulation of the Coulomb interaction between tight-binding electrons on different sites. The 2k_F phonons also cause strong second-order scatterings of X-rays or neutrons. These results may explain the recent observations of phonon anomalies at 4k_F in TTF-TCNQ.     

Coupling of electrons and phonons in a doped antiferromagnet

It is well-known that low-energy electronic excitations in high-T _c superconductors have energies of the order of the exchange couplingJ, i.e. of the same order as the phonon energies. Therefore, low-energy electronic excitations and phonons should strongly influence each other. To investigate this problem we consider a coupled electron-phonon system. For the electronic degrees of freedom we start from the three band Hubbard or Emery model. In analogy to the transformation of the three band Hubbard model to thet?J model, studied by Zhang and Rice, we derive an effective electron-phonon interaction. Its electronic degrees of freedom are those of thet?J model which couple to the phonons of the original system. The coupling of electrons and phonons is discussed by means of the phonon Green function for a breathing-like mode.     

Finite confining effect on electron–phonon interaction in GaAs/Ga1−xAlxAs single heterostructures

The form factors of the electron–phonon interaction for GaAs/Ga_1−xAl_xAs single heterostructures have been evaluated using a finite height barrier. The calculations are performed within the extreme quantum limit approximation, assuming for the envelope electronic wavefunction a modified Fang–Howard wavefunction. Both types of long-wave phonons, longitudinal optical and interface phonons, are considered. It is found that the effect of the finite height is to reduce the strength of the electron–phonon interaction.     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

Damping of optical phonons in metals and strongly doped semiconductors

The electron-phonon-induced damping of optical phonons arising in metals and strongly doped semiconductors under laser irradiation is investigated. The damping of both short-wave KV_F > ω₀ and long-wave KV_F < ω₀ optical phonons is calculated; K is the wavevector, ω₀ is the frequency of the optical phonon; V_F is the Fermi velocity. The electron- phonon-induced damping is important if the frequency of the optical phonon is larger than two frequencies of acoustic phonons of all branches in the range of the whole Brillouin zone. The damping of a soft transverse optical phonon in narrow-gap ferroelectric-semiconductors is also defined by the electron-phonon interaction. In other cases the main relaxation process for optical phonons in metals is the decay into two acoustic phonons due to lattice anharmonicity.     

Kinks and d-waves from phonons: The intermediate coupling story

I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling Wλ<ω₀, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in λ. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.     

Second order resonant Raman scattering at the E1 and E1 + Δ1 edges of germanium

The resonance of the 2TO phonon second order Raman band of germanium was investigated in the vicinity of the E₁, E₁ + Δ₁ gaps. The peak reported earlier for 2TO phonons at Γ is interpreted as due to a resonant process of the iterative type, involving two first order electron-phonon vertices. The rest of the 2TO band is interpreted as a process involving a second order electron-two phonon interaction vertex. From these measurements three phonon coupling constants for the electron-two phonon interaction are obtained.     

Mode dependent scattering of phonons by domain walls in ferroelectric KDP

Thermal conductivity and ballistic phonon imaging measurements in KH₂PO₄ (KDP) at low temperature (T<3K) indicate that scattering from domain walls has a large effect on phonon transport. kDP has a ferroelectric phase transition from tetragonal to orthorhombic structure atT _c =122 K. BelowT _c domains of opposite electric polarization and crystal orientation form unless the sample is colled in an electric field. Thermal conductivity measured along the [100] (tetragonal) axis drops 30% when domain walls are present, which is independent of sample size and temperature. We attribute this decrease to phonon polarization-dependent scattering at the domain boundaries. This is verified by measurements of ballistic transport, using phonon imaging techniques, which reveal the phonon polarization and mode dependence of the scattering. The scattering is successfully modelled using continuum acoustics with simple acoustic mismatch at the domainwall. The interface scattering is found to be mode dependent: Caustic structures in the phonon images due to slow transverse phonons are most affected by the domain wall scattering, which channels these phonons along parallel planes by multiple reflections without mode conversion. Mode conversion scattering, though possible for a number of phonons, has little effect on the overall phonon transmission.     

Effect of optical phonons scattering on electronic current in metallic carbon nanotubes

The effect of optical phonons scattering on electronic current has been studied in metallic carbon nanotubes. The current has been calculated self-consistently by total voltage equation and the heat transport equation. The total voltage equation consists of three terms, optical phonons collision term, acoustic phonon scattering term, and contact resistance one. Including LO, A₁, and E₁(2) phonons in collision term, we can reproduce the experimental I-V curves displaying negative differential conductance. Furthermore, one conclusion is made that the more optical phonons are scattered by electron, the lower current is in metallic carbon nanotubes. By comparing the current under different conditions, we can make another conclusion that there should be nonequilibrium optical phonons under high bias in spite of whether the metallic nanotube is suspended or not. This result agrees well with the others [M. Lazzeri, F. Mauri, Phys. Rev. B 73 (2006) 165419]. Based on these results, we do not only explain the experiment, but also propose to design a heat-controlling electronic transistor with metallic carbon nanotubes as its channel, in which the electronic current can be controlled by optical phonons.     

Phonon-mediated electron pairing in graphene

The possibility of superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is studied. Quadratic coupling of electrons with out-of-plane phonons is considered in details, taking into account both deformation potential and bond-stretch contributions. The order parameter of electron-electron pairing can have different structures due to four-component spinor character of electrons wave function. We consider s-wave pairing, diagonal on conduction and valence bands, but having arbitrary structure with respect to valley degree of freedom. The sign and magnitude of contribution of each phonon mode to effective electron-electron interaction turns out to depend on both the symmetry of phonon mode and the structure of the order parameter. Unconventional orbital-spin symmetry of the order parameter is found.     

Resonant Raman scattering in nanostructures with InGaAs/AlAs quantum dots

Raman scattering by optical phonons in In_xGa_{1 ? x} As/AlAs nanostructures with quantum dots has been studied experimentally for compositions corresponding to x = 0.3?1 under out-resonance conditions. Features due to scattering by GaAs-and InAs-like optical phonons in quantum dots have been detected, and the phonon frequencies have been determined as a function of the dot composition. With increasing excitation energy, a red shift is observed in the frequency of the GaAs-like phonon in quantum dots, which testifies to Raman scattering selective by the size of quantum dots. Under resonant conditions, multiphonon light scattering by optical and interface phonons is observed up to the third order, including overtones of the first-order phonons of InGaAs and AlAs materials and their combinations.     

Electronic thermal conductivity in suspended and supported bilayer graphene

Electronic thermal conductivity κ_e is investigated, using Boltzmann transport equation approach, in a suspended and supported bilayer graphene (BLG) as a function of temperature and electron concentration. The electron scattering due to screened charged impurity, short-range disorder and acoustic phonon via deformation potential are considered for both suspended and supported BLG. Additionally, scattering due to surface polar phonons, is considered in supported BLG. In suspended BLG, calculated κ_e is compared with the experimental data leaving the phonon thermal conductivity. It is emphasized that κ_e is important in samples with very high electron concentration and reduced phonon thermal conductivity. κ_e is found to be about two times smaller in supported BLG compared to that in suspended BLG. With the reduced extrinsic disorders, in principle, the intrinsic scattering by acoustic phonons can set a fundamental limit on possible intrinsic κ_e.     

Ternary mixed crystal effects on interface optical phonon and electron-phonon coupling in zinc-blende GaN/AlxGa1−xN spherical quantum dots

The theoretical investigations of the interface optical phonons, electron–phonon couplings and its ternary mixed effects in zinc-blende spherical quantum dots are obtained by using the dielectric continuum model and modified random-element isodisplacement model. The features of dispersion curves, electron–phonon coupling strengths, and its ternary mixed effects for interface optical phonons in a single zinc-blende GaN/Al_xGa_1−xN spherical quantum dot are calculated and discussed in detail. The numerical results show that there are three branches of interface optical phonons. One branch exists in low frequency region; another two branches exist in high frequency region. The interface optical phonons with small quantum number l have more important contributions to the electron–phonon interactions. It is also found that ternary mixed effects have important influences on the interface optical phonon properties in a single zinc-blende GaN/Al_xGa_1−xN quantum dot. With the increase of Al component, the interface optical phonon frequencies appear linear changes, and the electron–phonon coupling strengths appear non-linear changes in high frequency region. But in low frequency region, the frequencies appear non-linear changes, and the electron–phonon coupling strengths appear linear changes.     

Effect of nonequilibrium phonons on the tunnel current in superlattices

We present the first measurements of the effect of nonequilibrium phonons on the tunnel current in a weakly coupled GaAs/AlAs superlattice. The phonon-induced current has a maximum at a bias voltage which varies linearly with phonon source temperature at both zero and applied magnetic fields (B = 6 T). We attribute these results to assisted tunnelling by stimulated phonon emission and show that this system can be used as a phonon spectrometer.     

Bosonization of coupled electron-phonon systems

We calculate the single-particle Green’s function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is not based on the assumption that the electronic system is a Fermi liquid. For isotropic threedimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure or in the phonon frequencies.     

Phonon-plasmon interaction in tunneling GaAs/AlAs superlattices

The phonon-plasmon interaction in tunneling GaAs _n /AlAs _m superlattices (m=5and 6≥n≥0.6 monolayers) was studied by Raman scattering spectroscopy. The interaction of optical phonons localized in GaAs and AlAs layers with quasi-three-dimensional plasmons strengthens as the thickness of GaAs quantum wells decreases and the electronic states in the superlattices become delocalized due to tunneling. It is assumed that the plasmons also interact with the TO-like phonon modes localized in quantum islands or in thin ruffled layers.     

Lattice dynamics in the mixed valence compounds Sm(Y)S,CeSn3 and CePd3

Renormalized phonon energies of typical mixed valence compounds such as Sm(Y)S, CeSn₃ and CePd₃ are calculated. The renormalization is caused by the additional interaction of localized 4f electrons with phonons which can lead to drastic phonon anomalies. These anomalies are found to be completely different for the various systems under consideration.