Showing papers by "Francesco Mauri published in 2018"

Position and momentum mapping of vibrations in graphene nanostructures in the electron microscope

Abstract: Propagating atomic vibrational waves, phonons, rule important thermal, mechanical, optoelectronic and transport characteristics of materials. Thus the knowledge of phonon dispersion, namely the dependence of vibrational energy on momentum is a key ingredient to understand and optimize the material's behavior. However, despite its scientific importance in the last decade, the phonon dispersion of a freestanding monolayer of two dimensional (2D) materials such as graphene and its local variations has still remained elusive because of experimental limitations of vibrational spectroscopy. Even though electron energy loss spectroscopy (EELS) in transmission has recently been shown to probe the local vibrational charge responses, these studies are yet limited to polar materials like boron nitride or oxides, in which huge signals induced by strong dipole moments are present. On the other hand, measurements on graphene performed by inelastic x-ray (neutron) scattering spectroscopy or EELS in reflection do not have any spatial resolution and require large microcrystals. Here we provide a new pathway to determine the phonon dispersions down to the scale of an individual freestanding graphene monolayer by mapping the distinct vibration modes for a large momentum transfer. The measured scattering intensities are accurately reproduced and interpreted with density functional perturbation theory (DFPT). Additionally, a nanometre-scale mapping of selected momentum (q) resolved vibration modes using graphene nanoribbon structures has enabled us to spatially disentangle bulk, edge and surface vibrations.

Raman spectroscopy of graphene under ultrafast laser excitation.

Abstract: The equilibrium optical phonons of graphene are well characterized in terms of anharmonicity and electron–phonon interactions; however, their non-equilibrium properties in the presence of hot charge carriers are still not fully explored. Here we study the Raman spectrum of graphene under ultrafast laser excitation with 3 ps pulses, which trade off between impulsive stimulation and spectral resolution. We localize energy into hot carriers, generating non-equilibrium temperatures in the ~1700–3100 K range, far exceeding that of the phonon bath, while simultaneously detecting the Raman response. The linewidths of both G and 2D peaks show an increase as function of the electronic temperature. We explain this as a result of the Dirac cones’ broadening and electron–phonon scattering in the highly excited transient regime, important for the emerging field of graphene-based photonics and optoelectronics. Non-equilibrium ultrafast processes in graphene entail relaxation pathways involving electron–electron and electron–phonon scattering events. Here, the authors probe graphene optical phonons at high electronic temperatures by means of Raman spectroscopy under pulsed excitation

Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles

Abstract: At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient $\ensuremath{\gamma}=2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$, finding it to be in good agreement with experimental value of $\ensuremath{\gamma}=2.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$. Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $\mathrm{\ensuremath{\Gamma}}\mathrm{X}$ direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the self-consistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the third- and fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high-temperature $Fm\overline{3}m$ structure to the low-temperature $R3m$ one. The transition temperature is, however, underestimated with respect to the experimental one. No satellites are present in the SnTe phonon spectra despite a not negligible anharmonic broadening of the zone-center TO mode.

Pressure and stress tensor of complex anharmonic crystals within the stochastic self-consistent harmonic approximation

Abstract: The self-consistent harmonic approximation (SCHA) allows the computation of free energy of anharmonic crystals considering both quantum and thermal fluctuations. Recently, a stochastic implementation of the SCHA has been developed, tailored for applications that use total energy and forces computed from first principles. In this paper, we extend the applicability of the stochastic SCHA to complex crystals, i.e., systems in which symmetries do not fix the inner coordinates and require the optimization of both the lattice vectors and the atomic positions. To this goal, we provide an expression for the evaluation of the pressure and stress tensor within the stochastic SCHA formalism. Moreover, we develop a more robust free-energy minimization algorithm, which allows us to perform the SCHA variational minimization very efficiently in systems having a broad spectrum of phonon frequencies and many degrees of freedom. We test and illustrate the approach with an application to the phase XI of water ice using density-functional theory. We find that the SCHA reproduces extremely well the experimental thermal expansion of ice in the whole temperature range between 0 and $270\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, in contrast with the results obtained within the quasiharmonic approximation, that underestimates the effect by about 25%.

Flat electronic bands in long sequences of rhombohedral-stacked graphene

Abstract: The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic properties. It has been predicted that a rhombohedral (ABC) stacking displays a conducting surface state with flat electronic dispersion. In such a flat band, the role of electron-electron correlation is enhanced, possibly resulting in high ${T}_{\mathrm{c}}$ superconductivity, charge-density wave, or magnetic orders. Clean experimental band-structure measurements of ABC-stacked specimens are missing because the samples are usually too small in size. Here, we directly image the band structure of large multilayer graphene flakes containing approximately 14 consecutive ABC layers. Angle-resolved photoemission spectroscopy experiments reveal the flat electronic bands near the $K$ point extends by $0.13\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$ at the Fermi level at liquid nitrogen temperature. First-principles calculations identify the electronic ground state as an antiferromagnetic state with a band gap of about 40 meV.

High-pressure phase diagram of hydrogen and deuterium sulfides from first principles: Structural and vibrational properties including quantum and anharmonic effects

Abstract: We study the structural and vibrational properties of the high-temperature superconducting sulfur trihydride and trideuteride in the high-pressure $Im\overline{3}m$ and $R3m$ phases by first-principles density-functional-theory calculations. On lowering pressure, the rhombohedral transition $Im\overline{3}m\ensuremath{\rightarrow}R3m$ is expected, with hydrogen-bond desymmetrization and occurrence of trigonal lattice distortion. With both Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, in hydrostatic conditions we find that, contrary to what is suggested in some recent experiments, if the rhombohedral distortion exists it affects mainly the hydrogen bonds, whereas the resulting cell distortion is minimal. We estimate that the occurrence of a stress anisotropy of approximately $10%$ could explain this discrepancy. Assuming hydrostatic conditions, we calculate the critical pressure at which the rhombohedral transition occurs. Quantum and anharmonic effects, which are relevant in this system, are included at nonperturbative level with the stochastic self-consistent harmonic approximation. Within this approach, we determine the transition pressure by calculating the free-energy Hessian, a method that allows to estimate the critical pressure with much higher precision (and much lower computational cost) compared with the free-energy ``finite-difference'' approach previously used. Using PBE and BLYP, we find that quantum anharmonic effects are responsible for a strong reduction of the critical pressure with respect to the one obtained with the classical harmonic approach. Interestingly, for the two functionals, even if the transition pressures at classical harmonic level differ by 83 GPa, the transition pressures including quantum anharmonic effects differ only by 23 GPa. Moreover, we observe a prominent isotope effect, as we estimate higher transition pressure for ${\mathrm{D}}_{3}\mathrm{S}$ than for ${\mathrm{H}}_{3}\mathrm{S}$. Finally, within the stochastic self-consistent harmonic approximation, with PBE we calculate the anharmonic phonon spectral functions in the $Im\overline{3}m$ phase. The strong anharmonicity of the system is confirmed by the occurrence of very large anharmonic broadenings leading to complex non-Lorentzian line shapes. Generally, for the high-energy hydrogen bond-stretching modes, the anharmonic phonon broadening is of the same magnitude of the electron-phonon one. However, for the vibrational spectra at zone center, accessible, e.g., by infrared spectroscopy, the broadenings are very small (linewidth at most around 2 meV) and anharmonic phonon quasiparticles are well defined.

Hydrodynamic Heat Transport Regime in Bismuth: A Theoretical Viewpoint.

Abstract: Bismuth is one of the rare materials in which second sound has been experimentally observed. Our exact calculations of thermal transport with the Boltzmann equation predict the occurrence of this Poiseuille phonon flow between $\ensuremath{\approx}1.5$ and $\ensuremath{\approx}3.5\text{ }\text{ }\mathrm{K}$, in a sample size of 3.86 and 9.06 mm, consistent with the experimental observations. Hydrodynamic heat flow characteristics are given for any temperature: heat wave propagation length, drift velocity, and Knudsen number. We discuss a gedanken experiment allowing us to assess the presence of a hydrodynamic regime in any bulk material.

Energy relaxation mechanism of hot-electron ensembles in GaAs: Theoretical and experimental study of its temperature dependence

Abstract: We have recently demonstrated that the fast momentum relaxation due to electron-phonon scattering of hot electrons excited into the conduction band of GaAs leads to the formation of hot-electron ensembles spread over the Brillouin zone. In the present work, we study the energy relaxation of hot-electron ensembles in GaAs, by means of ab initio calculations and time-, energy-, and momentum-resolved spectroscopy. We theoretically show that when the temperature decreases, the energy relaxation time ascribed to electron-phonon interaction becomes faster than at ambient temperature and prove that this is indeed the case in the experimental results.

Field-effect-driven half-metallic multilayer graphene

Abstract: Rhombohedral stacked multilayer graphene displays the occurrence of a magnetic surface state at low temperatures. Recent angular resolved photoemission experiments demonstrate the robustness of the magnetic state in long sequences of ABC graphene. Here, by using first-principles calculations, we show that field-effect doping of these graphene multilayers induces a nonrigid electronic structure deformation and stabilizes a perfect half-metallic behavior with nearly 100% of spin current polarization and sizable conductivity already at dopings attainable in conventional field-effect transistors with solid state dielectrics. At high doping, magnetism disappears and a flat electronic band prone to correlated, charge density wave, or superconducting instabilities occurs at the Fermi level. Our work demonstrates the realizability of a new kind of spintronic devices where the transition between the low resistance and the high resistance state is driven only by electric fields.

Field-effect-driven half-metallic multilayer graphene

Abstract: Rhombohedral stacked multilayer graphene displays the occurrence of a magnetic surface state at low temperatures. Recent angular resolved photoemission experiments demonstrate the robustness of the magnetic state in long sequences of ABC graphene. Here, by using first-principles calculations, we show that field-effect doping of these graphene multilayers induces a nonrigid electronic structure deformation and stabilizes a perfect half-metallic behavior with nearly 100% of spin current polarization and sizable conductivity already at dopings attainable in conventional field-effect transistors with solid state dielectrics. At high doping, magnetism disappears and a flat electronic band prone to correlated, charge density wave, or superconducting instabilities occurs at the Fermi level. Our work demonstrates the realizability of a new kind of spintronic devices where the transition between the low resistance and the high resistance state is driven only by electric fields.