Anisotropic Electron-phonon Coupling Research Articles

Resonance-induced anomalies in temperature-dependent Raman scattering of PdSe2

Temperature dependent Raman spectroscopy combined with density functional theory calculations reveal anisotropic electron–phonon coupling in the low-symmetry transition metal dichalcogenide PdSe2.

Dimerization Triggered Magnetoelectric Coupling Effect and Magnetic Anisotropy in Organic Ternary Crystals.

Developing a new universal strategy to design all organic ferromagnets or multiferroics with satisfactory properties always remains challenging. In this work, ternary charge transfer crystals are fabricated to realize organic multiferroic magnetoelectric coupling effect. Through incorporating the third component into binary crystals, a dimerization between neighbor donor and acceptor is induced to form a lattice symmetry breaking, where a nonpolar to polar phase transition is ensuing to lead to a dipolar polarization. Magnetic field can effectively tune the dipolar polarization to present a magnetoelectric coupling effect. Moreover, the introduction of the third component can result in a rearrangement in molecular configuration to modify the electron-phonon interaction. As a result, anisotropic magnetism is observed due to anisotropic electron-phonon coupling in ternary crystals. Overall, this study forecasts that incorporating an appropriate third component is a potential method for designing all organic multiferroics.

Direct visualization of polaron formation in the thermoelectric SnSe

SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing polaron formation in the material. We employ ultrafast electron diffraction and diffuse scattering to track the response of phonons in both momentum and time to the photodoping of free carriers across the bandgap, observing the bimodal and anisotropic lattice distortions that drive carrier localization. Relatively large (18.7 Å), quasi-one-dimensional (1D) polarons are formed on the 300-fs timescale with smaller (4.2 Å) 3D polarons taking an order of magnitude longer (4 ps) to form. This difference appears to be a consequence of the profoundly anisotropic electron-phonon coupling in SnSe, with strong Fröhlich coupling only to zone-center polar optical phonons. These results demonstrate a high density of polarons in SnSe at optimal doping levels. Strong electron-phonon coupling is critical to the thermoelectric performance of this benchmark material and, potentially, high performance thermoelectrics more generally.

Evidence for nesting-driven charge density wave instabilities in the quasi-two-dimensional material LaAgSb2

Since their theoretical prediction by Peierls in the 30s, charge density waves (CDW) have been one of the most commonly encountered electronic phases in low dimensional metallic systems. The instability mechanism originally proposed combines Fermi surface nesting and electron-phonon coupling but is, strictly speaking, only valid in one dimension. In higher dimensions, its relevance is questionable as sharp maxima in the static electronic susceptibility \chi(q) are smeared out, and are, in many cases, unable to account for the periodicity of the observed charge modulations. Here, we investigate the quasi twodimensional LaAgSb2, which exhibits two CDW transitions, by a combination of diffuse xray scattering, inelastic x-ray scattering and ab initio calculations. We demonstrate that the CDW formation is driven by phonons softening. The corresponding Kohn anomalies are visualized in 3D through the momentum distribution of the x-ray diffuse scattering intensity. We show that they can be quantitatively accounted for by considering the electronic susceptibility calculated from a Dirac-like band, weighted by anisotropic electron-phonon coupling. This remarkable agreement sheds new light on the importance of Fermi surface nesting in CDW formation.

Anisotropic electron-phonon coupling in the spinel oxide superconductor LiTi2O4

Among hundreds of spinel oxides, LiTi2O4 (LTO) is the only one that exhibits superconductivity (Tc ~13 K). Although the general electron-phonon coupling is still the main mechanism for electron pairing in LTO, unconventional behaviors such as the anomalous magnetoresistance, anisotropic orbital/spin susceptibilities, etc. reveal that both the spin and the orbital interactions should also be considered for understanding the superconductivity. Here, we investigate tunneling spectra of [111]-, [110]- and [001]-oriented high quality LTO thin films. Several bosonic modes in tunneling spectra are observed in the [111]- and [110]-oriented films but not in [001]-oriented ones, and these modes still exist at T = 2Tc and beyond the upper critical field, which are confirmed as stemming from electron-phonon interaction by DFT calculations. These modes only appear in special surface orientations, indicating that the electron-phonon coupling in LTO system is highly anisotropic and may be enhanced by orbital-related state. The anisotropic electron-phonon coupling should be taken seriously in understanding the nature of LTO superconductivity.

Enhancement of electron–phonon coupling in Cs-overlayered intercalated bilayer graphene

We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on cesium (Cs) intercalated bilayer graphene with a Cs overlayer (Cs-C8CsC8). Low-energy electron diffraction shows a (2 × 2) pattern consistent with intercalation of a Cs layer similar to bulk C8Cs, in addition to the signature of a nearly commensurate superstructure created by the Cs overlayer. ARPES results reveal folding of the π bands due to the periodic (2 × 2) potential of the intercalated Cs atoms, together with a free-electron-like state at the point. Significant mass renormalization is observed in the band dispersion near the Fermi level, indicative of strong electron–phonon coupling. Based on analysis of the self-energy, we find anisotropic electron–phonon coupling with an estimated strength of ± 0.02 in the K- direction, and in the K-M direction. This coupling is much larger than that of other doped graphenes, and comparable to superconducting bulk GICs. We attribute this large electron–phonon coupling constant to the presence of the Cs overlayer, which highly dopes bands, and creates a structure similar to stage-I graphite intercalation compounds.

Anisotropic Electron–Phonon Coupling in Rb-Intercalated Bilayer Graphene

We have performed high-resolution angle-resolved photoemission spectroscopy on Rb-intercalated bilayer graphene, which is regarded as the thinnest limit of Rb-intercalated graphite (Rb-GIC). We have clearly observed a velocity renormalization of the π* bands near the Fermi level, and electron doping from Rb atoms to the graphene layers. We attribute the renormalization to strong coupling of electrons with graphene’s in-plane optical phonon mode. The electron–phonon coupling constant has been measured, and found to exhibit a strong momentum anisotropy similar to that of bulk GIC superconductors. This result provides evidence for universal electron–phonon coupling in intercalated multi-layer graphene and bulk GICs.

Anisotropic Eliashberg function and electron-phonon coupling in doped graphene

We investigate, with high-resolution angle-resolved photoemission spectroscopy, the spectral function of potassium-doped quasi-free-standing graphene on Au. Angle-dependent x-ray photoemission and density functional theory calculations demonstrate that potassium intercalates into the graphene/Au interface, leading to an upshift of the K-derived electronic band above the Fermi level. This empty band is what makes this system perfectly suited to disentangle the contributions to electron-phonon coupling coming from the $\ensuremath{\pi}$ band and K-derived bands. From a self-energy analysis we find an anisotropic electron-phonon coupling strength $\ensuremath{\lambda}$ of 0.1 (0.2) for the $K\ensuremath{\Gamma}$ ($KM$) high-symmetry directions in momentum space, respectively. Interestingly, the high-energy part of the Eliashberg function which relates to graphene's optical phonons is equal in both directions but only in $KM$ does an additional low-energy part appear.

Anisotropic electron-phonon coupling investigated by ultrafast electron crystallography: Three-temperature model

In low-dimensional electronic materials, the charge or spin ordering can be subtly controlled by specific mode or modes, giving rise to functioning states such as charge- and spin-density waves, Mott insulators, and superconductors. The coupling between the electrons and the atomic lattice can be effectively investigated by ultrafast optical, photoemission, and electron diffraction techniques providing detailed description of microscopic and collective state evolutions in separate electronic and lattice subsystems. However, the electronic and phononic relaxation time scales obtained from these techniques are often distinctly different in low-dimensional electronic materials, even in a system as simple as graphite. Here, we seek to understand their origins from examining the nonequilibrium scenarios considering anisotropic electron-phonon coupling leading to hot phonons, which can be investigated directly from the momentum-dependent scattering changes in the transmission ultrafast electron crystallography. A three-temperature model is constructed to achieve unified understandings combining ultrafast spectroscopy and diffraction results of the nonadiabatic optically driven dynamics in graphite, charge-density waves in CeTe${}_{3}$, and the Mott insulator VO${}_{2}$.

Theory of ultrafast quasiparticle dynamics in high-temperature superconductors: The dependence on pump fluence

We present a theory for the time-resolved optical spectroscopy of high-temperature superconductors at high excitation densities with strongly anisotropic electron-phonon coupling. A signature of the strong coupling between the out-of-plane, out-of-phase O-buckling mode (${B}_{1g}$) and electronic states near the antinode is observed as a higher-energy peak in the time-resolved optical conductivity and Raman spectra, while no evidence of strong coupling between the in-plane Cu-O-breathing mode and nodal electronic states is observed. More interestingly, it is observed that under appropriate conditions of pump fluence, this signature exhibits a reentrant behavior with time delay, following the fate of the superconducting condensate.

Theory of the time-resolved spectral function of high-temperature superconductors with bosonic modes

We develop a three-temperature model to simulate the time dependence of the electron and phonon temperatures in high-temperature superconductors displaying strong anisotropic electron-phonon coupling. This model not only takes the tight-binding band structure into account but also is valid in the superconducting state. Based on this model, we calculate the time-resolved spectral function via the double-time Green's functions. We find that the dip-hump structure evolves with the time delay. More interestingly, an unusual structure is obtained when the phonons are pumped directly. This finding may serve as a direct evidence for electron-vibration mode coupling.

Anisotropic electron-phonon coupling on a two-dimensional circular Fermi contour

Angle-resolved photoemission reveals that the electron-phonon coupling (EPC) around the circular Fermi contour of the Be(0001) $\overline{\ensuremath{\Gamma}}$ surface state is strongly anisotropic. The mass enhancement parameter $\ensuremath{\lambda}$ is found to range from values of $\ensuremath{\sim}1$, along high-symmetry directions, to $\ensuremath{\sim}0.6$ in between in stark contrast to the theoretical calculations. Given the simplicity of this system it furnishes an ideal prototype for unraveling the origin of anisotropic EPC in two-dimensional materials.

Electronic Density of States and Strong Electron–Phonon Coupling in Nb3Sn

Using the Full-Potential non-orthogonal Local-Orbital Minimum-Basis Band-structure Scheme (FPLO) coupled with the XFSF program for unconventional superconductor Nb3Sn, we perform simultaneously the Bravais lattice, the density of states (DOS), the band structure and the Fermi surface (FS) topology. The density of states shows a large number of peaks of width on the order of 20 eV near the Fermi level which is found to be dominated by Nb-4d states, contributing about 90% of the bare DOS. The electron–phonon coupling constant λ ep is estimated to be about 1.46, which indicates that Nb3Sn is a strongly coupled superconductor. The two-dimensionality (2D) of the computed Fermi surface is another proof of the pronounced strength of this coupling. On the other hand, the discrepancy between the Debye temperature Θ D as previously obtained experimentally (Θ D=234 K) and that given by our band-structure calculations (Θ D=300.2 K) may originate from a phonon anisotropy likely generated by the anisotropic electron–phonon coupling.

Direct role of structural dynamics in electron-lattice coupling of superconducting cuprates

The mechanism of electron pairing in high-temperature superconductors is still the subject of intense debate. Here, we provide direct evidence of the role of structural dynamics, with selective atomic motions (buckling of copper-oxygen planes), in the anisotropic electron-lattice coupling. The transient structures were determined using time-resolved electron diffraction, following carrier excitation with polarized femtosecond heating pulses, and examined for different dopings and temperatures. The deformation amplitude reaches 0.5% of the c axis value of 30 A when the light polarization is in the direction of the copper-oxygen bond, but its decay slows down at 45 degrees. These findings suggest a selective dynamical lattice involvement with the anisotropic electron-phonon coupling being on a time scale (1-3.5 ps depending on direction) of the same order of magnitude as that of the spin exchange of electron pairing in the high-temperature superconducting phase.

Enhancement of anisotropic electron–phonon coupling in the cuprates

Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the electron–phonon coupling in a two-dimensional t– t′– U Hubbard model. We consider a momentum-dependent bare electron–phonon coupling, i.e., the electronic coupling to the B 1g oxygen bond-buckling phonon. We find that the on-site Coulomb interaction U acts to effectively enhance the electron–phonon coupling at all electron- and phonon-momenta. Our numerical simulations are in good agreement with the results of functional renormalization group calculations. On the other hand, the forward scattering process near the anti-node is enhanced more than near the nodal region, leading to an enhancement of anisotropic electron–phonon coupling. Our results support the interpretation of the bosonic renormalization effects seen in angle resolved photoemission spectroscopy as electronic coupling to the B 1g oxygen bond-buckling phonon.

Infrared signatures of hole and spin stripes inLa2−xSrxCuO4

We investigate the hole and lattice dynamics in a prototypical high temperature superconducting system La{2-x}Sr{x}CuO{4} using infrared spectroscopy. By exploring the anisotropy in the electronic response of CuO2 planes we show that our results support the notion of stripes. Nevertheless, charge ordering effects are not apparent in the phonon spectra. All crystals show only the expected infrared active modes for orthorhombic phases without evidence for additional peaks that may be indicative of static charge ordering. Strong electron-phonon interaction manifests itself through the Fano lineshape of several phonon modes. This analysis reveals anisotropic electron-phonon coupling across the phase diagram, including superconducting crystals. Due to the ubiquity of the CuO2 plane, these results may have implications for other high Tc superconductors.

Phonon-mediated anisotropic superconductivity in the Y and Lu nickel borocarbides

We present scanning tunneling spectroscopy and microscopy measurements at low temperatures in the borocarbide materials RNi2B2C (R=Y, Lu). The characteristic strong coupling structure due to the pairing interaction is unambiguously resolved in the superconducting density of states. It is located at the superconducting gap plus the energy corresponding to a phonon mode identified in previous neutron scattering experiments. These measurements also show that this mode is coupled to the electrons through a highly anisotropic electron-phonon interaction originated by a nesting feature of the Fermi surface. Our experiments, from which we can extract a large electron-phonon coupling parameter lambda (between 0.5 and 0.8), demonstrate that this anisotropic electron-phonon coupling has an essential contribution to the pairing interaction. The tunneling spectra show an anisotropic s-wave superconducting gap function.

Existence of boths andd-wave solutions of Eliashberg equations

We solve Eliashberg equations in the case of strong anisotropic electron-phonon coupling and low energy cutoff. In a simplified model representing the Fermi Surface of (CuO2)n planes, we exhibit ad-wave solution as well as a generalizeds-wave one.

Anisotropy of the thermal conductivity of YBa2Cu3O7-y.

The thermal conductivity, both in-plane (${\ensuremath{\kappa}}_{\mathrm{ab}}$) and out-of-plane (${\ensuremath{\kappa}}_{c}$), has been measured in ``90-K'' crystals of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{y}}$ from 10 to 330 K. ${\ensuremath{\kappa}}_{\mathrm{ab}}$ displays an 18 to 40% increase below the transition temperature ${T}_{c}$ (as in ceramic data). ${\ensuremath{\kappa}}_{c}$, however, is four to five times smaller and shows no anomaly at ${T}_{c}$. Comparing these results to ${\ensuremath{\kappa}}_{\mathrm{ab}}$ of insulating crystals, we find evidence for very strong but highly anisotropic electron-phonon coupling in the normal state. Our results are consistent with a phonon origin for the peak in ${\ensuremath{\kappa}}_{\mathrm{ab}}$. .AE

Superconductivity and Hc2-anisotropy in vanadium

Abstract We report on a systematic investigation of the superconductivity in vanadium and its impurity dependence. Starting from a high-purity single crystal (Γ = 1200) we find that no changes of the Fermi surface seem to occur for resistivity ratios ≥ 450. On the contrary, the second anisotropy coefficient a6 is still sensitive to variations of the impurity parameter in this range indicating contributions of an anisotropic electron-phonon coupling. The overall Hc2-anisotropy is larger than in Nb and still significant at an impurity parameter α = 2.81. The attractive flux line interaction is found to be comparable with the results reported for Nb.