Session G61: Electrons, Phonons, Electron-Phonon Scattering and Phononics IV

Theory of non-linear electron-phonon coupling and its first-principles implementation

Despite a huge effort has been devoted to develop first principles methods to calculate efficiently the impact of lattice quantum effects and anharmonicity on the structural, vibrational, and superconducting properties of materials, the electron-phonon interaction is always calculated in the linear approximation, i.e., truncating the expansion of the electronic potential at first order. This approach is questionable, at least, whenever anharmonic effects on the vibrational properties are large, such as in superconducting hydrides and systems undergoing charge-density wave or ferroelectric transitions. Here we present a novel non-perturbative theory for the electron-phonon coupling that can be implemented from first principles. We apply the new theory to superconducting palladium hydrides and show that, remarkably, high-order non-linear effects are comparable in magnitude to the standard linear term. Non-linearity reveals crucial to explain the superconductivity as well as the inverse isotope effect in this system. Our new theory may have a large impact on the ab initio calculation of all properties related to the electron-phonon interaction, e.g. superconductivity and electrical conductivity, in highly anharmonic systems.   

Electron-phonon Renormalization of the Band Gaps of Solids from Wannier-localized Optimally Tuned Screened Range-Separated Hybrid Functionals

Density functional theory (DFT) calculations of thermal and zero-point properties of solids due to electron-phonon interactions are known to be sensitive to the choice of exchange-correlation functional. Furthermore, the use of the GW approximation can improve results but at a significant increase in computational cost. Recently, we have demonstrated the Wannier-localized optimally tuned screened range-separated hybrid (WOT-SRSH) functional [1] can be used to compute the band gaps of a variety of solids to a high degree of accuracy. Here, we present the use of the WOT-SRSH functional to calculate the phonon spectrum and band-gap renormalization of representative semiconductors and insulators and find it can reproduce the accuracy of higher order methods like GW at a reduced computational cost.

[1] D. Wing, G. Ohad, J. B. Haber, M. R. Filip, S. E. Gant, J. B. Neaton, and L. Kronik, PNAS 118, (2021).   

Nonuniform grids for Brillouin zone integration and interpolation

We present two developments for the numerical integration over the Brillouin zone. First, we introduce a nonuniform grid, which we refer to as the Farey grid, that generalizes traditional regular grids. Second, we introduce symmetry-adapted Voronoi tessellation, a general technique to assign weights to the points in an arbitrary grid. Combining these two developments, we propose a strategy to perform Brillouin zone integration and interpolation that provides a significant computational advantage compared to the usual approach based on regular grids. We demonstrate our methodology in the context of first-principles calculations with the study of Kohn anomalies in the phonon dispersions of graphene and MgB₂, and in the evaluation of the electron-phonon driven renormalization of the band gaps of diamond and bismuthene. In both cases, we find large speedups, whether density functional perturbation theory or finite difference methods are used. Besides, our results of bismuthene reveal that it preserves a sizable topological band gap at room temperature. In summary, our method opens up an avenue for designing the most appropriate nonuniform grid for any given task, with the prospect of saving valuable computational time and allowing for new frontiers in computational condensed matter physics to be charted.    

Anisotropic Migdal-Eliashberg analysis of superconductivity in layered Li-Mg-B compounds

LiB, a predicted compound analogous to the MgB₂ superconductor, has been recently synthesized via cold compression and quenched to ambient pressure. We reinvestigate the superconducting properties of LiB and find that the electron-phonon coupling anisotropy is as essential as in MgB₂. Using the anisotropic Eliashberg formalism, we predict a critical temperature (T_c) to be in the 32-42 K range, three times higher than prior estimates based on isotropic calculations. We probe other Li-Mg-B binary and ternary layered materials and find metastable phases with T_c close to or even 10-20% above the record 39 K value in MgB₂.

    

Calculating Temperature-Dependent Electronic Structure of Semiconductors using a Dynamic Tight-Binding Model

For theoretical calculations of large-scale system sizes or longer time-scale phenomena the computational costs of typical density functional theory can present a steep barrier, which motivates the development of alternative approaches. Here, we propose an extension of the tight-binding (TB) formalism which allows for the efficient calculation of temperature-dependent properties of semiconductors with little computational effort. Our TB approach employs hybrid-orbital basis functions and distance-dependent matrix elements that are calculated by numerical integration of the respective orbitals. Our method is straightforward since the TB parameters are only optimized at 0 K, which still provides a transferable scheme for accurate calculations of the electronic structure of semiconductors at finite temperatures. Combining the dynamic TB method with molecular dynamics, we show that it can account for dynamic changes to the symmetry of the crystal that are due to, e.g., lattice distortions.   

Efficient Migdal-Eliashberg calculations with Intermediate Representation basis using the EPW code

Recent attempts have been made to reduce the number of frequency points for the Matsubara Green’s functions in finite-temperature many-body calculations in order to reduce the computational cost. A method based on the intermediate Representation (IR) basis [1] has proven successful for computing the transition temperature within the Migdal-Eliashberg approach for several superconductors, such as Nb and H₃S [2,3]. However, the calculations performed in these studies have been limited to a k-averaged electron-phonon interaction kernel. We have taken a step forward and implemented the IR basis method in the EPW code to solve the anisotropic full-bandwidth Migdal-Eliashberg equations [4]. This enables accurate and efficient calculations of the superconducting gap and critical temperature on ultra-dense electron k and phonon q grids. In this talk, we will discuss the implementation and show results of some representative systems obtained using the EPW code with the IR basis.

[1] H. Shinaoka et al., Phys. Rev. B 96, 035147 (2017).

[2] T. Wang et al., Phys. Rev. B 102, 134503 (2020).

[3] T. Wang et al., Phys. Rev. B 104, 064510 (2021).

[4] S. Poncé et al., Comput. Phys. Commun. 209 116 (2016).   

Differential Formalism of Power Series Correction for Single particle Electron Green's Function: Applications to 1D Holstein Chain.

Based on our previous work on self-consistent power series correction formalism¹ present for single particle green's function we present two ODE based formalisms of Power series correction that go beyond the cumulant approximation and are scalable and fast. The first differential formalism of the power series gives the exact results on the Holstein chain for a large range or electron-boson coupling constant and is faster than the self-consistent formalism. The second differential formalism is even faster but faces severe instability for the same problem when the boson energy scale is comparable or smaller than the band width. We discuss this instability and show that it stems from the assumption made on the nature of correction to simplify the correction form. We finally discuss its implication to self-consistent cumulant expansion.

[1] B. Pandey and P.B. Littlewood, Phys. Rev. Lett. 129, 136401   

Efficient compression of first-principles electron-phonon interactions

First-principles calculations of electron-phonon (e-ph) interactions have advanced materials science and physics. Combined with Wannier interpolation of e-ph matrix elements, one can compute a wide range of e-ph physical effects in real materials, including phonon-limited transport, band structure renormalization, and superconductivity. However, Wannier interpolation remains a trial-and-error, material-specific computational step that currently hinders workflow automation and bottlenecks efficiency. 

  In this talk, we present a more efficient approach to parametrize e-ph interactions using a widely used compression technique, singular value decomposition (SVD). With proper improvements of the basic SVD scheme, we show a constrained SVD (c-SVD) method that achieves high accuracy for e-ph coupling and related properties (transport, renormalized band structure, superconducting Tc, etc) at significantly reduced computational cost compared to Wannier interpolation. This material-independent approach can systematically achieve a Pareto-optimal parametrization of e-ph interactions, leading to order-of-magnitude speed-ups. The talk will conclude by discussing future extensions to other interactions and incorporation of this computational tool in the Perturbo code [1].   

[1] ] J.-J. Zhou, J. Park, I.-T. Lu, I. Maliyov, X. Tong, and M. Bernardi, PERTURBO: A software package for ab initio electron–phonon interactions, charge transport and ultrafast dynamics. Comput. Phys. Commun. 264,107970 (2021)   

Ab initio investigations of optical properties of MgS and CaS beyond the harmonic approximation.

Using first-principles calculations based on density functional theory (DFT), we study the infrared (IR) optical properties of MgS and CaS. Firstly, we assess the efficacy of the harmonic approximation in the modeling of their vibrational spectra. Secondly, by comparing our results to available experimental data [1], we show that a more accurate description of the IR optical properties requires the inclusion of anharmonic effects. A more precise determination of the dielectric constant of these binary sulfides could help in the effective computation of microscopic mechanisms correlated to their macroscopic radiative behavior. Our results could, on one hand, shed light on using more effectively MgS and CaS towards energy storage materials [2], and on the other hand, help in the interpretation of data collected by future missions to Mercury to study the planet's surface, which is hypothesized to have an abundance of volatiles such as sulfur [3]. 

[1] Y. Kaneko, K. Morimoto and T. Koda, J. Phys. Soc. Jpn., 51, 2247-2254 (1982)

[2] S. Pervez and M. Z. Iqbal, Int. J. Energy Res., 46, 8093 (2022)

[3] I. Varatharajan, A. Maturilli, J. Helbert, et al., Earth Planet. Sci. Lett., 520, 127-140 (2019)   

Anomalous pressure dependence of lattice dynamics in PbTe: a simulation study

Understanding the high-pressure lattice dynamics is crucial to modulate the thermal transport in thermoelectric materials beyond ambient environment. Herein, using molecular dynamics simulations in combination with an accurate machine-learning potential, we find an anomalous non-monotonic pressure dependence of the frequency of the transverse acoustic (TA) phonon in PbTe. The longitudinal acoustic (LA), longitudinal optical (LO) and transverse optical (TO) phonons harden as expected when pressure increases. The well-known double-peak feature of the TO mode in PbTe gradually vanishes when pressure is enhanced. The theoretical results are compared with available experimental data to verify our calculations. Moreover, we have also calculated the lattice thermal conductivity under pressure and revealed the phonon transport mechanism.

 

    

Efficient full relaxation of crystal structures with quasiharmonic approximation: Application to pyroelectricity of GaN and ZnO

We develop an efficient calculation scheme of quasiharmonic approximation (QHA) which enables the simultaneous optimization of all the structural degrees of freedom, i.e., the shape of the unit cell and the internal coordinates. We employ the IFC renormalization [1], which efficiently calculates the harmonic phonon dispersion of updated crystal structures without additional expensive DFT calculations.

Our method removes the constraints on the internal coordinates or the anisotropy of the thermal expansion, which are conventionally imposed to reduce computational cost.

We implement the methodology to the ALAMODE package [2], an open-source package for first-principles phonon calculation.

 

We apply the method to the pyroelectricity of wurtzite materials GaN and ZnO, which shows good agreement with experiments. By comparing the results with conventional methods, we show that simultaneous optimization of the unit cell and the atomic positions is crucial to the quantitative prediction of anisotropy in thermal expansion. Furthermore, we show that relatively small changes in the anisotropic thermal expansion lead to a significant difference in the pyroelectricity.

 

[1] R.Masuki, et al arXiv:2205.08789 (2022)

[2] T. Tadano, et al. J. Phys.: Condens. Matter 26, 225402 (2014)

    

Anderson localization of phonons in multi-branch mass-disordered systems

The Anderson localization (AL) of phonons in disordered media has been receiving increasing interest

due to potential impact on thermoelectric materials. However, despite extensive study, the influence of

the directional nature of phonons on the AL transition remains elusive. Recently, we have formulated the

typical medium cluster approach which allows to study the AL of phonons in multibranch systems.

Considering the model with three directions of lattice vibrations in the presence of mass disorder, we

have investigated the interplay of inter-branch mixing and diagonal disorder in the context of phonon

localization. We have validated the new formalism against several limiting cases and exact

diagonalization results. We have also contrasted the mechanism of AL for the single branch versus

multiple branch case, and elucidated the role of directional nature of phonon on AL.   

Pair distribution function analysis of CoZr2-structure alloys

The intermetallic compounds AZr₂ are a diverse array of materials with interesting properties. CoZr₂, for example, has a negative c-axis thermal expansion, even though the c-axis thermal expansion of the isostructural NiZr₂ is positive. Furthermore, CoZr₂ has an anomalous decrease in its unit cell volume on warming above ~400 K. The AZr₂ materials are also platforms for high-entropy alloys such as Co_0.2Ni_0.1Cu_0.1Rh_0.3Ir_0.3Zr₂, which can provide an opportunity to study superconductivity in the high-disorder regime. Characterization of the local structure would be helpful in understanding the properties of the AZr₂ compounds. To that end, we have performed pair distribution function (PDF) analysis on neutron diffraction data taken on NOMAD at the Spallation Neutron Source. We measured four samples, including CoZr₂ and variants with Co partially substituted by Cu, Cu/Rh, and Ni/Cu/Rh/Ir. Across all samples, our data show a consistent discrepancy in the local structure relative to the average structure of AZr₂. We discuss possible causes for this discrepancy, as well as the role that the additional elements have in modifying the thermal expansion behavior.