Session B20: Electrons, Phonons, Electron-Phonon Scattering, and Phononics I

Live

Our understanding of charge transport in solids predominantly relies on the Boltzmann transport equation. However, its perturbative approximations for the nuclear dynamics and for its coupling to the electrons can be inaccurate in complex materials [1]. We present an alternative, non-perturbative ab initio Green-Kubo approach based on a new formulation of the flux viz. polarization. It can be evaluated via ab initio molecular dynamics and only requires gauge-fixed properties. At variance with Berry phase approaches [2], it is thus suitable for (semi-)conductors featuring thermal electronic excitations. We demonstrate our method by calculating the electrical conductivity for 2D honeycomb lattices, for silicon, and for the perovskite SrTiO₃. We also compare to non-perturbative Kubo-Greenwood calculations and discuss why this approach has so far only been numerically applicable for materials with strong structural disorder [3].

[1] M. Zacharias, M. Scheffler, and C. Carbogno, Phys. Rev. B 102, 045126 (2020).
[2] R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993).
[3] B. Holst, M. French, and R. Redmer, Phys. Rev. B 83, 235120 (2011); C. Di Paola, et al., Phys. Rev. Research 2, 033055 (2020).   

Live

The anharmonic lattice is a representative interacting bosonic many-body system. The self-consistent harmonic approximation has been used to study the equilibrium properties of the anharmonic lattices. However, to study the dynamical properties within this method, one needs to resort to a specific self-energy ansatz, whose validity is yet to be proven. In this presentation, we apply the time-dependent variational principle, a recently emerging tool for studying the dynamical properties of interacting many-body systems, to the anharmonic lattices. Using the Gaussian variational states and the linearized equation of motion method, we theoretically prove the dynamical self-energy ansatz of the self-consistent harmonic approximation. The calculated dynamical and spectral properties of the lattice can be understood as that of interacting 1- and 2-phonon excitations. Our work lays the groundwork for a fully variational study of dynamical properties of the anharmonic lattice and also expands the range of applicability of time-dependent variational principle to first-principle lattice Hamiltonians.   

Live

The calculation of phonon frequencies and modes is the starting point for investigating a variety of physical properties of solids, like the specific heat, thermal expansion, and properties related to electron-phonon coupling, like superconductivity. For solid Hydrogen at high pressures, the zero point motion of the protons is known to be important when determining its structures. This effect can be accounted for if the phonon frequencies are known. These calculations are routinely carried out with density functional theory (DFT). Here, we calculate the phonons of solid atomic Hydrogen with quantum Monte Carlo (QMC), a feat made possible by the calculation of forces in QMC, highly optimized wavefunctions, and careful attention to statistical error. We compare the results with those obtained within DFT.   

Live

In this talk, we will probe the accuracy limit of ab initio calculations of drift [1] and Hall [2] carrier mobilities that relies on the electron-phonon coupling, within the framework of the Boltzmann transport equation [3] for 10 semiconductors.
In particular, we consider the effect of spin-orbit coupling, optimal Wigner-Seitz cell construction, dynamical quadrupoles, iterative solution of the Boltzmann transport equation as well as the self-energy relaxation time approximation.

These calculations require extremely fine sampling of the Brillouin Zone which is made possible at an affordable computational cost through the use of efficient Fourier-Wannier interpolation of the electron-phonon matrix elements as implemented in the EPW code (https://epw-code.org).

References:
[1] S. Poncé, E. R. Margine and F. Giustino, Phys. Rev. B 97, 121201 (2018)
[2] F. Macheda and N. Bonini, Phys. Rev. B 98, 201201 (2018)
[3] S. Poncé, W. Li, S. Reichardt, and F. Giustino, Rep. Prog. Phys. 83, 036501 (2020)   

Live

Semiconductor devices are susceptible to defect-mediated nonradiative processes that degrade their performance. In optoelectronic devices, for example, these nonradiative transitions give rise to Shockley-Read-Hall recombination that limits the light-emission efficiency. The nonradiative processes occur as a result of electron-phonon coupling, and a rigorous evaluation of the resulting rates is of vital importance for analysis and improvement of devices. We have developed the Nonrad code, which implements the first-principles formalism of Alkauskas et al. [1] for the evaluation of nonradiative capture coefficients. We will discuss several improvements to the methodology, including a treatment of electron-phonon coupling within the widely used projector augmented-wave method.

[1] A. Alkauskas, Q. Yan, and C. G. Van de Walle, Phys. Rev. B 90, 075202 (2014).   

Live

Electron-phonon interactions play a pivotal role in simulating a wide variety of material properties. As a result, there is an ongoing effort to find more accurate and efficient algorithms to incorporate these interactions in materials simulations. To this end, we present an ab-initio density-functional-theory (DFT) approach for calculating electron-phonon interactions within the projector-augmented-wave (PAW) method. As the PAW method leads to a generalized eigenvalue problem, the resulting electron-phonon matrix elements lack some symmetries that are usually present for traditional all-electron formulations. To allow for efficient evaluation of physical properties, we use an interpolation scheme based on Wannier functions, with the required matrix elements constructed in a supercell using finite differences. While being inherently slower than most methods operating in reciprocal space, this approach has multiple advantages. Finally, we highlight results for the phonon-induced band-gap renormalization for polar and non-polar materials obtained from the implementation of this approach in the Vienna Ab-initio Simulation Package (VASP).

Phys. Rev. B 101, 184302   

Live

In this work, we present a first-principles framework to compute the thermoelectric properties of materials based on the extraction and use of deformation potentials and then the corresponding scattering rates, which is the middle ground computationally between the constant relaxation time approximation (RTA) and first-principles relaxation time extraction. Based on density functional theory (DFT) and density functional perturbation theory (DFPT), we compute the electronic bandstructures, phonon dispersion relations, and electron-phonon matrix elements. Within the polar Wannier interpolation scheme, we consider the short-range interactions between electrons and long-wavelength phonons, and the long-range optical interactions. From the short-range electron-phonon matrix elements, we derive the acoustic deformation potential (ADP) and optical deformation potential (ODP) for long-wavelength phonons. The electronic structures and deformation potentials are taken as inputs to compute the charge transport coefficients using an advanced, home-developed numerical simulator, which allows not only for the incorporation of electron-phonon scattering, but also for other (even more) important scattering mechanisms, such as ionized impurity scattering, alloy scattering, etc.   

Live

Charged defects scatter electrons and control transport in materials at low temperature. Theoretical descriptions of this interaction have mainly relied on simplified effective mass models, which cannot capture the atomic details of the defect-induced perturbation potential or treat materials with complex band structures. We recently developed ab initio calculations of electron-defect (e-d) interactions due to neutral defects [1,2]. Here we present a method to calculate these interactions for charged defects and impurities. We employ Wannier functions to compute the relevant e-d matrix elements and develop an interpolation scheme to treat the long-range part of the electron-charged defect interaction. We demonstrate results for n- and p-doped silicon, including defect-limited relaxation times and mobilities, and explain subtle aspects of low temperature transport. Our approach can overcome limitations of effective mass models as it can be applied to materials with anisotropic, multi-valley, or linear band structures. It provides a powerful tool to study ionized impurity scattering and low temperature transport in complex materials.

[1] I-T. Lu, J. Park, J.-J. Zhou, M. Bernardi, npj Comput. Mater., 6, 1 (2020)
[2] I-T. Lu, J.-J. Zhou, M. Bernardi, Phys. Rev. Mater., 3, 033804 (2019)   

Live

Lattice dynamics calculations can predict the phonon properties of insulating and semi-conducting crystals, with force constants as the primary input. Density functional theory (DFT) allows for an ab initio method to obtain these force constants accurately. These DFT calculations, however, can be computationally expensive. This is not an issue in simple materials (high symmetry and small primitive cell), where relatively few DFT calculations are necessary. In more complex materials, however, the number of calculations required will increase significantly and tax computational resources.

We address this issue by training a high-dimensional neural network potential to calculate force constants with a training set that is smaller than the required number of calculations. We used silicon as a test case, with accuracy quantified using phonon frequencies and thermal conductivity in addition to the standard force and energy metrics. We find that accurate forces, energies, and frequencies do not guarantee an accurate thermal conductivity. In addition, a single training set and hyperparameters can result in a range of thermal conductivities, with an accurate average value but significant variance. We attempt to reduce the variance in results using an adaptive selection scheme.   

Live

Recently, it has been shown computationally that the inclusion of higher-order anharmonic phonon renormalization and higher-order four-phonon scattering is crucial to accurately represent the thermal conductivities of weakly-bonded solids like sodium chloride (NaCl) [1]. Here we show, using our recently-developed unified first-principles framework, that four-phonon scattering also critically affects the phonon lineshapes of NaCl, typically observed in inelastic neutron and Raman scattering experiments. To capture these higher-order effects accurately, our calculations include the lowest-order three-phonon and higher-order four-phonon scattering processes, and a many-body self-consistent anharmonic phonon renormalization step to address the ill-defined nature of phonon quasiparticles. By performing these calculations over a broad range of temperatures, we show that four-phonon processes significantly broaden the phonon lineshapes compared to their three-phonon counterparts - particularly at high temperatures, and their inclusion into the calculations is pivotal to explain the experimental data.

[1] Navaneetha K. Ravichandran and David Broido, Phys. Rev. B 98 (8), 085205 (2018).   

Live

The standard first-principles approach for calculating lattice dynamics in crystals is based on the harmonic approximation, which expands the crystal potential to second-order. However, higher-order (anharmonic) contributions are often important, especially in materials relevant for modern electronic, optical, thermal, and energy storage applications. In such materials, the harmonic approximation yields very poor predictions; therefore, advanced computational techniques that can incorporate anharmonic effects are essential for efficient material screening for advanced device applications. We apply two such computational methods, compressive sensing lattice dynamics (CSLD) and quantum self-consistent ab intio lattice dynamics (QSCAILD), to all four phases (cubic, tetragonal, orthorhombic, and rhombohedral) of perovskite BaTiO₃, a highly anharmonic crystal with promising device applications, and calculate the phonon dispersions and static dielectric constants as functions of temperature. Finally, we compare our predictions to calculations done in the harmonic approximation, and to experiment.   

Live

Novel phenomena arise from the non-equilibrium excitation of materials, and the complex interplay between their various degrees of freedom. Understanding this at a microscopic level requires detailed knowledge about a material’s atomic structure on fast timescales. In this talk, I will discuss the application of ultrafast diffraction techniques to probe structural dynamics in correlated oxides and two-dimensional (2D) materials. First, I will describe a new time-resolved ‘electrical-pump’ technique based on femtosecond electron diffraction, that enables direct measurements of atomic motions in microelectronic devices. In an archetypal correlated oxide, we discover signatures of a transient metastable phase under pulsed electrical bias [1]. Next, I will discuss phonon transport in van der Waals (vdW) heterostructures, which are promising candidates for phononics applications [2]. I will describe our efforts to rationally synthesize ‘3D’ solids with tailored thermal properties using layer-by-layer assembly of 2D crystals. Ultrafast X-ray diffraction is demonstrated as a useful technique to probe heat transport across buried interfaces in vdW stacks [3]. Finally, using ultrafast electron diffraction, I will show how we can interrogate the coupling between charge and lattice dynamics in photoexcited 2D heterostructures, enabling direct observations of heat flow across single vdW junctions on picosecond timescales.

[1] A. Sood et al. in review (2020)
[2] A. Sood*, F. Xiong* et al., Nature Comm. 9, 4510 (2018)
[3] C. Nyby*, A. Sood* et al., Adv. Func. Mater. 30, 2002282 (2020)   

On Demand

Over the past decades molecular crystals have been studied extensively - especially in terms of electronic structure - to improve their performance in organic semiconductor-based devices. Many of the properties relevant in this context are crucially affected by phonons. For example, electron-phonon coupling is often found to be one of the main limiting factors for charge transport, or entropic contributions from phonons play a decisive role when it comes to reliably predicting phase stability of polymorphs close in energy. Despite their importance, measurements and ab initio simulations are often methodologically impeded in such complex systems. Thus, approximate simulation approaches are typically employed: density-functional based tight binding (DFTB) or classical force fields (FFs). Here, we quantitatively studied the errors one must expect when resorting to such methods for various phonon-related properties in crystalline naphthalene¹. Besides off-the-shelf solutions using publicly available parameters for DFTB or widely used FFs such as COMPASS and GAFF, we also critically test the performance of our own parametrization of the MOF-FF² for naphthalene.

¹ J. Chem. Theory Comput. 2020, 16, 4, 2716–2735
² Phys. Status Solidi B 2013, 250, 1128– 1141