Session K22: Electrons, Phonons, Electron-Phonon Scattering and Phononics II

Predictive calculations of phonon-assisted quantum processes

Quantum processes mediated by phonons play an important role in the characterization of materials and in the operation of electronic and optoelectronic devices. I will discuss the theory and recent results in the predictive modeling of phonon-mediated quantum processes in materials with atomistic calculations based on density functional and many-body perturbation theory. I will discuss the computational methodology and results for phonon-assisted optical absorption in metals and in indirect-gap semiconductors such as silicon (Si), boron arsenide (BAs), and boron nitride (BN). I will also discuss calculations for phonon-assisted Auger recombination in wide-band-gap semiconductors, an important nonradiative mechanism that dominates carrier recombination at high free-carrier concentrations. The results shed light into the interaction of light with materials and the efficiency of light emitters. This work was performed in collaboration with Kyle Bushick, Kelsey Mengle, Guangsha Shi, Andrew McAllister, Dylan Bayerl, and Chris Van de Walle.   

Time-Resolved Second Harmonic Generation Polarimetry Study of Elemental Tellurium

Elemental tellurium (Te) is a chiral semiconductor that breaks inversion symmetry, which allows for strong optical second harmonic generation (SHG). We performed time-resolved SHG polarimetry measurements on Te single crystals to understand the effects of inter-band carrier excitations on its lattice structure. I will describe the contrasting temporal evolution of the structure and charge excitations as a function of both temperature and pump fluence.   

First-principles resonant Raman spectroscopy for 2D materials

We implement first-principles method for resonant Raman spectroscopy of solids based on a second-order Feynman diagram and the Franck-Condon principle. The Raman Intensity is calculated using an expression in the form of the Kramers-Heisenberg-Dirac (KHD) formula. Sum over all phonon configurations is performed using the Fourier transform into the time domain and evaluated with the help of Feynman path integrals. The triple integration method offers a simple and fast numerical approach that accounts for all multiple phonon processes. The ground state and excited state phonon modes are calculated to provide frequencies and equilibrium atomic positions. The computed Raman intensities for MoS2/WS2 heterostructure is in agreement with experimental data. We also explore the resonance properties of the Raman spectrum, in particular its strong dependence on the energy of incident laser and on temperature.
  

Pressure-induced destabilization and periodic lattice distortion in SnX2 (X = S, Se)

Using first-principles calculations we investigate the behavior of tin disulfide (SnS₂) and tin diselenide (SnSe₂) under compression. In agreement with single-crystal X-ray diffraction, Raman, and transport measurements, we find that a commensurate √3 × √3 × 1 superlattice forms in both SnS₂ and SnSe₂ at elevated pressures. We show that the pressure-induced transition to the commensurate periodic lattice distortion (PLD) phase is due to the combined effect of strong Fermi surface nesting and electron-phonon coupling at a certain wave vector q = (1/3, 1/3, 0). We further compare our findings to similar PLD transitions associated with charge density wave orderings in transition metal dichalcogenides.   

Microscopic dynamics in the Holstein model at high-temperature: Absence of diffusion

A single itinerant electron in the Holstein model is known to have a large conductivity at low temperatures as the electron is scattered by dilute thermally-excited phonons. At high temperatures, some theories suggest the dynamics are described by simple Boltzmann diffusion since there are many thermally excited phonons. Here, we investigate the dynamics of an itinerant particle of the Holstein model at high temperature. Our results suggest that the microscopic dynamics is not diffusion in some parameter regimes. In one dimension, the particle travels in a constant direction over time, which suggests an infinite conductivity. In higher dimensions, the particle follows a closed trajectory, a type of localization, and the trajectories are fractal.   

Generalized Fröhlich model vs accurate first-principles: zero-point renormalisation in polar semiconductors and insulators.

Computing the zero-point renormalization (ZPR) of the electronic bandgap due to electron-phonon coupling from first principles (FP) is a computationaly challenging task, especially for polar materials, for which a very fine phonon wavevector sampling is required [1]. By contrast, the well-known Fröhlich Hamiltonian gives in the perturbative regime a simple analytical formula for the polaron binding energy, based on a few parameters that can be obtained from experiments or from FP calculations.

We compute the ZPR from FP for more than 20 polar binary semiconductors and insulators, and compare these results to those from a generalized Fröhlich model, in which the needed parameters are computed from FP. Despite the lack of Debye-Waller (DW) and interband contributions, we find that the simple Fröhlich approach agrees with FP results within a factor of two for most materials. We analyze the cancellation between the DW and Fan contributions from acoustic modes, and discuss the size of interband contributions in terms of Eliashberg functions. We finally develop a method to estimate the converged ZPR from coarser phonon samplings.

[1] G. Antonius et al, PRB 92, 085137 (2015); S. Poncé et al, J. Chem. Phys. 143, 102813 (2015).   

First-principles study of self-trapped polarons

The polaron is a quasiparticles consisting of an electron or hole dressed by a cloud of phonons. Self-trapped polarons are found when the electron-phonon interaction is so strong that the electron is bound by the potential of the lattice distortion that it induces. Here we investigate the mechanisms of polaron formation in wide-gap insulators, using Li2O2 as a prototypical example. We study self-trapping both via direct density-functional theory (DFT) calculations and using a perturbation theory approach. We analyze the binding energy in terms of the underlying band structure and phonon dispersions, and we compare our findings with previous calculations and with classic models of self-trapped polarons. We discuss open questions in the ab initio study of polarons and possible solutions.   

Phonon Behaviors of Charged Nanocrystals: Effects of Free Charge Carriers

The precise knowledge of phonons is important to understand the electronic and photonic properties of nanocrystals (NCs) and NC-based devices. It is common to introduce free charge carriers into NCs for device applications, highlighting the significance of studying the free carrier effects on phonon behaviors. In this study, we introduced the free carriers into a series of NCs (ZnO, CdSe, PbSe) and investigated the carrier-dependent phonon behaviors by using Raman spectroscopy. For charged NCs, the change of phonon frequencies and the overtone to fundamental intensity ratios were explained by the screening and band-filling effects caused by the accumulated free carriers. By using a time-dependent model, the overtone to fundamental intensity ratios were further correlated with the electron-phonon coupling strength of the involved excited states. The effects of free carriers on phonon behaviors, usually neglected in previous studies, should be carefully considered when analyzing the properties of charged NCs. Moreover, the relationship between the free carrier densities and Raman frequencies/relative intensities are potentially useful for nondestructive characterization of free carriers in NCs.   

Experimental demonstration of generalized Fourier's Law for heat conduction at the nanoscale

Heat conduction under large temperature gradients that occur over scales of mean free paths of the energy carriers in solids is a topic of intense interest. Although the failure of Fourier's law is well understood, the appropriate replacement has been the topic of debate. A concise relation that links temperature gradient to heat flux based on a rigorous mathematical interpretation is not only necessary but crucial to advance our knowledge of nanoscale heat transport. Here, we derived a generalized Fourier's law based on Peierls-Boltzmann transport equation. This generalized Fourier's law contains two parts, nonlocality of thermal conductivity, which has been previously hypothesized, and nonlocality of external effects, i.e. volumetric heat generation, which has long been ignored in literatures. We demonstrated the validity of this generalized Fourier's law through comparisons with a series of time-domain thermoreflectance (TDTR) measurements. Furthermore, we showed that misinterpreting the generalized Fourier's law in the experimental observation of nanoscale heat conduction would lead to erroneous microscopic information of phonons. To map the macroscopic observations to intrinsic phonon properties, it is crucial to appropriately take account into the microscopic heat input.   

Computing Raman Spectra With Wavelets Using The BigDFT Code

We report the calculations of Raman spectra using the BigDFT code.

The normal modes of vibration (or phonons) and their associated energies were found by slightly displacing each atom of the system around their ground position (this was already part of the BigDFT suite). We then added the possibility of computing the Raman intensity of each normal mode via electronic polarizability tensor calculations (in practice, this only amounts to applying small electric fields to the system of interest). The Raman spectra thus obtained are compared to the literature. A further check of the quality of the normal modes thus found is done by computing vibrational polarizability tensors.

The main perspective of this work is to use the order N version of the BigDFT code (instead of the usual cubic scaling version used in this work) to perform similar computations on larger systems.   

Infrared reflectance, transmittance and emittance spectra from first-principles

Density functional theory (DFT) is considered a predictive approach to determine anharmonic phonon-phonon interactions in crystals. Such a computational tool is a necessary ingredient, for example, of the first principles computational methods recently developed to determine phonon thermal transport in real systems. In this context, finding measurable quantities that can provide an independent benchmark for theoretical approaches is of paramount importance. Surprisingly, DFT has been rarely used to interpret the anharmonic features observable in infra-red (IR) reflectance, transmittance and emittance spectra even though they provide a relatively direct probe to anharmonic properties in heteropolar materials and can be used to directly determine the anharmonic phonon self-energy of the optically active mode. I will show the influence of anharmonic effects on IR spectra of MgO, which is chosen as a test material because of the availability of different kinds of radiative properties measured experimentally and I will explain the limit of validity of a perturbative (multi-phonon) approach.   

Ab Initio Charge Transport in the Polaron Regime in Transition Metal Oxides

Strong electron-phonon (e-ph) interactions lead to the formation of polarons, quasiparticles consisting of an electron carrying a phonon cloud. Polaron formation lowers the mobility and greatly affects charge transport in transition metal oxides and other polar compounds. Here, we develop a many-body ab initio approach to compute charge transport including polaron effects. We apply our approach to the two perovskite oxides BaSnO₃ and SrTiO₃, and analyze in detail how and why polaron formation affects charge transport in these materials. The calculations are connected with our recent work on SrTiO₃, where, using the Boltzmann Transport equation with lowest-order e-ph scattering, we accurately predicted the temperature dependence of the mobility in SrTiO₃ [1], whose absolute value was however higher than experiment. We show how including polaron effects can correct the lowest-order result, improving agreement with experiment.

[1] J.-J. Zhou, O. Hellman, and M. Bernardi, arXiv:1806.05775 (2018).   

The Role of Configurational Entropy in Real-Time Mass Sensing

We present a theoretical framework for determining the mass deposited on a mechanical resonator subject to a flux of incoming particles of a single species. We consider the specific example of a vibrating nanostring and infer the history of mass deposition events from the frequency shifts in real time using a numerical optimization alogrithm that correctly compensates for the configurational entropy. Our approach is tested against simulated data and is shown to perform well. We comment on its applicability to common inverse problems in physics, such as the extraction of spectral functions from imaginary-time Green's functions, that also suffer from configurational entropy effects.