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Register a new userAb initio lattice dynamics and electron-phonon coupling of Bi(111)
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We present a comprehensive ab initio study of structural, electronic, lattice dynamical and electron-phonon coupling properties of the Bi(111) surface within density functional perturbation theory. Relativistic corrections due to spin-orbit coupling are consistently taken into account. As calculations are carried out in a periodic slab geometry, special attention is given to the convergence with respect to the slab thickness. Although the electronic structure of Bi(111) thin films varies significantly with thickness, we found that the lattice dynamics of Bi(111) is quite robust and appears converged already for slabs as thin as 6 bilayers. Changes of interatomic couplings are confined mostly to the first two bilayers, resulting in super-bulk modes with frequencies higher than the optic bulk spectrum, and in an enhanced density of states at lower frequencies for atoms in the first bilayer. Electronic states of the surface band related to the outer part of the hole Fermi surfaces exhibit a moderate electron-phonon coupling of about 0.45, which is larger than the coupling constant of bulk Bi. States at the inner part of the hole surface as well as those forming the electron pocket close to the zone center show much increased couplings due to transitions into bulk projected states near Gamma_bar. For these cases, the state dependent Eliashberg functions exhibit pronounced peaks at low energy and strongly deviate in shape from a Debye-like spectrum, indicating that an extraction of the coupling strength from measured electronic self-energies based on this simple model is likely to fail.
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We present a combined experimental and theoretical study of the surface vibrational modes of the topological insulator (TI) Bi$_2$Se$_3$ with particular emphasis on the low-energy region below 10 meV that has been difficult to resolve experimentally. By applying inelastic helium atom scattering (HAS), the entire phonon dispersion was determined and compared with density functional perturbation theory (DFPT) calculations. The intensity of the phonon modes is dominated by a strong Rayleigh mode, in contrast to previous experimental works. Moreover, also at variance with recent reports, no Kohn-anomaly is observed. These observations are in excellent agreement with DFPT calculations. Besides these results, the experimental data reveal$-$via bound-state resonance enhancement$-$two additional dispersion curves in the gap below the Rayleigh mode. They are possibly associated with an excitation of a surface electron density superstructure that we observe in HAS diffraction patterns. The electron-phonon coupling paramenter $lambda$ = 0.23 derived from our temperature dependent Debye-Waller measurements compares well with values determined by angular resolved photoemission or Landau level spectroscopy. Our work opens up a new perspective for THz measurements on 2D materials as well as the investigation of subtle details (band bending, the presence of quantum well states) with respect to the electron-phonon coupling.
The coupling between electrons and phonons in solids plays a central role in describing many phenomena, including superconductivity and thermoelecric transport. Calculations of this coupling are exceedingly demanding as they necessitate integrations over both the electron and phonon momenta, both of which span the Brillouin zone of the crystal, independently. We present here an ab initio method for efficiently calculating electron-phonon mediated transport properties by dramatically accelerating the computation of the double integrals with a dual interpolation technique that combines maximally localized Wannier functions with symmetry-adapted plane waves. The performance gain in relation to the current state-of-the-art Wannier-Fourier interpolation is approximately 2n_s times M, where n_s is the number of crystal symmetry operations and M, a number in the range 5 - 60, governs the expansion in star functions. We demonstrate with several examples how our method performs some ab initio calculations involving electron-phonon interactions.
Electron-phonon ($e$-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons and metal-insulator transitions. First-principles approaches enable accurate calculations of $e$-ph interactions in a wide range of solids. However, they remain an open challenge in correlated electron systems (CES), where density functional theory often fails to describe the ground state. Therefore reliable $e$-ph calculations remain out of reach for many transition metal oxides, high-temperature superconductors, Mott insulators, planetary materials and multiferroics. Here we show first-principles calculations of $e$-ph interactions in CES, using the framework of Hubbard-corrected density functional theory (DFT+$U$ ) and its linear response extension (DFPT+$U$), which can describe the electronic structure and lattice dynamics of many CES. We showcase the accuracy of this approach for a prototypical Mott system, CoO, carrying out a detailed investigation of its $e$-ph interactions and electron spectral functions. While standard DFPT gives unphysically divergent and short-ranged $e$-ph interactions, DFPT+$U$ is shown to remove the divergences and properly account for the long-range Frohlich interaction, allowing us to model polaron effects in a Mott insulator. Our work establishes a broadly applicable and affordable approach for quantitative studies of e-ph interactions in CES, a novel theoretical tool to interpret experiments in this broad class of materials.
The interaction between electrons and lattice vibrations determines key physical properties of materials, including their electrical and heat transport, excited electron dynamics, phase transitions, and superconductivity. We present a new ab initio method that employs atomic orbital (AO) wavefunctions to compute the electron-phonon (e-ph) interactions in materials and interpolate the e-ph coupling matrix elements to fine Brillouin zone grids. We detail the numerical implementation of such AO-based e-ph calculations, and benchmark them against direct density functional theory calculations and Wannier function (WF) interpolation. The key advantages of AOs over WFs for e-ph calculations are outlined. Since AOs are fixed basis functions associated with the atoms, they circumvent the need to generate a material-specific localized basis set with a trial-and-error approach, as is needed in WFs. Therefore, AOs are ideal to compute e-ph interactions in chemically and structurally complex materials for which WFs are challenging to generate, and are also promising for high-throughput materials discovery. While our results focus on AOs, the formalism we present generalizes e-ph calculations to arbitrary localized basis sets, with WFs recovered as a special case.
We have studied the topological insulator Bi$_2$Te$_3$(111) by means of helium atom scattering. The average electron-phonon coupling $lambda$ of Bi$_2$Te$_3$(111) is determined by adapting a recently developed quantum-theoretical derivation of the helium scattering probabilities to the case of degenerate semiconductors. Based on the Debye-Waller attenuation of the elastic diffraction peaks of Bi$_2$Te$_3$(111), measured at surface temperatures between $110~mbox{K}$ and $355~mbox{K}$, we find $lambda$ to be in the range of $0.04-0.11$. This method allows to extract a correctly averaged $lambda$ and to address the discrepancy between previous studies. The relatively modest value of $lambda$ is not surprising even though some individual phonons may provide a larger electron-phonon interaction. Furthermore, the surface Debye temperature of Bi$_2$Te$_3$(111) is determined as ${rm Theta}_D = (81pm6)~mbox{K}$. The electronic surface corrugation was analysed based on close-coupling calculations. By using a corrugated Morse potential a peak-to-peak corrugation of 9% of the lattice constant is obtained.
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