Session F48: Electrons, Phonons, Electron-Phonon Scattering, and Phononics I

Progress in ab initio calculations of polarons: reduced dimensionality and many-body effects

Polarons are among the most well-known quasiparticles in solid state physics, and play an important role in the electronic, optical, and transport properties of many classes of materials, from organics to oxides. Recently we introduced an ab initio formalism to investigate small and large polarons on the same footing [1,2]. This formalism does not suffer from the delocalization error introduced by self-interaction in density functional theory, and employs density-functional perturbation theory to circumvent the need for large supercell calculations. In this talk I will describe further progress on our ab initio theory of polarons on two fronts. Firstly, I will discuss the role of dimensionality on the electron-phonon coupling and the energetics and size of polarons [3]. For this discussion I will illustrate recent methodological developments on the calculations of polar electron-phonon interactions in two dimensions. Secondly, I will discuss our efforts to establish a many-body Green’s function framework for the ab initio polarons equations of Refs. [1,2]. I will show how polaron formation, phonon-induced band gap renormalization, and phonon satellites in photoelectron spectroscopy can be rationalized within a unified conceptual framework. I will also discuss how the modern ab initio theory of polarons relates to earlier model-Hamiltonian approaches to the polaron problem [4].   

Bandlike and Polaronic Charge Transport in Organic Crystals from First-Principles

Predicting charge transport in organic molecular crystals (OMCs) is challenging due to their complex crystal structures and electron-phonon (e-ph) interactions. In this talk, we will present two first-principles frameworks to accurately predict the charge carrier mobilities in OMCs. The first is the Boltzmann transport equation (BTE) with ab initio e-ph interactions, which describes the bandlike transport regime in OMCs [1]. We will show BTE calculations of hole mobilities in various molecular systems, and examine the effect of strain on charge transport. The second method is the cumulant plus Green-Kubo (CK) [2,3], which addresses the regime where the e-ph interactions are of intermediate strength and the charge carriers form polarons. We will present our recent CK calculations of electron mobilities and electron spectral functions in OMCs. Both our BTE and CK approaches provide mobilities in very good agreement with experiments over a wide temperature range. These broadly applicable methods advance the understanding of charge transport in organic semiconductors.

 

[1] Lee et al., Phys. Rev. B, 97, 115203 (2018)

[2] Zhou et al., Phys. Rev. Research, 1, 033138 (2019)

[3] Chang et al., arXiv:2106.09810   

Polarons in semilocal density functional theory: localization, many-body self-interaction, and formation energy

We develop a semilocal functional for overcoming the self-interaction of electron and hole polarons by enforcing the piece-wise linearity upon electron occupation. We obtain localized polarons with structural and electronic properties in agreement with references from a hybrid functional satisfying the same constraint. We then develop a scheme accounting for the effects of Fock exchange, further improving the formation energies. We demonstrate that the difference between the one-body and the many-body self-interaction is related to screening effects. Case studies include the electron polaron in BiVO₄, the hole polaron in MgO, and the hole trapped at the Al impurity in α-SiO₂.    

Extending the Feynman polaron model for real materials

Most new semiconductors proposed for energy storage and transformation are soft and polar leading to a large dielectric electron-phonon coupling. This coupling drives the formation of polaron quasi particles, the electron dressed with phonon excitations.

The Feynman variational path-integral solution for the polaron problem[1] integrates out the infinite degrees of freedom of the phonon field, variationally matching the true electron-phonon Lagrangian to an integrable trial Lagrangian. This is an explicitly quasi-particle theory - the equations of motion for the trial Lagrangian are the same as an effective-mass electron coupled by a spring to a fictitious mass representing the phonon drag.

We implement this technique[1] in a modern code[2], taking material parameters from density functional and QS-GW electronic structure calculations. With this we have a quantum theory of temperature- and frequency-dependent mobility with no free parameters[3,4], and an ansatz for the nature of charge carriers in the material.

We will discuss: extending the Feynman theory to explicitly treat the multiple phonon branches present in complex, real, semiconductors; extending our codes to simulate the frequency dependent mobility; predicting the effect of polaron renormalisation on vibrational frequency and spectra; predicting Urbach tails from the instantaneous electric fields in a polar material; and show how charge-carrier scattering cross-sections are changed by the polaron localisation.   

Comparing the canonical-transformation and energy-functional approaches for ab initio calculations of self-localized polarons

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. Various theoretical treatments of small polarons have been proposed. We recently developed an ab initio approach based on canonical transformations that can efficiently compute the formation and energetics of small polarons with quantitative accuracy [1]. A different, energy-functional approach has also been proposed in the literature [2]. In this talk, we compare these two methods using a unified formalism, which allows us to shed light on the physical effects included or neglected in these two approaches. We show that our canonical transformation formalism can properly include lattice vibrational effects while using a fixed polaron wave function. Conversely, we show that the energy-functional approach neglects lattice vibrations and treats the electrons and phonons as decoupled; it attempts to describe the polaron wave function but misses the physics of polaron self-localization and band narrowing. We will conclude our talk by presenting extensions of the canonical transformation approach to compute the polaron wave function as well as charge transport in the polaron hopping regime.

[1] N.-E. Lee, H.-Y. Chen, J.-J. Zhou, and M. Bernardi, Phys. Rev. Materials. 5, 063805 (2021)

[2] W. H. Sio, C. Verdi, S. Ponce, and F. Giustino, Phys. Rev. B 99, 235139 (2019).   

Sum Rules of the Holstein-Hubbard Model and its Non-equilibrium Behavior

With the proliferation of experimental techniques able to probe properties of complex materials in non-equilibrium with increasing accuracy and resolution, and interesting properties such as hidden phases continuing to garner interest, there is a clear need for accurate theoretical techniques to describe complex non-equilibrium processes. Few exact, many-body theoretical solutions exist in non-equilibrium, and approximations are very important. Sum rules, which relate integrals of the spectral function to expectation values of observables, may represent a self-consistent way to check the accuracy of non-equilibrium calculations. And simple problems which can be solved exactly in non-equilibrium may provide insight on processes which may occur in more complicated non-equilibrium systems. We calculate the first three spectral moment sum rules for a general non-equilibrium Holstein-Hubbard model. These moments can be verified exactly in the atomic limit, where an exact Green's function can be obtained. The behavior of this simpler Green's function's photoemission spectrum in non-equilibrium leads us to propose a measure, the first moment of the photoemission spectrum, which may be useful in tracking non-equilibrium changes in electron-electron or electron-phonon couplings in systems with sufficiently separated energy bands.   

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The foundation of modern theory of lattice dynamics rests on the separation between short-range and long-range interatomic force constants, where the latter are associated with macroscopic electric fields acting in a neighborhood of the Brillouin zone center. In three-dimensional (3D) insulators, the famous dipole-dipole formula was established long ago by Cochran and Cowley; the subsequent work of Pick, Cohen and Martin provided a formal derivation in the framework of first-principles theory. Very recently, we have incorporated higher-order interactions involving, e.g., dynamical quadrupoles, and demonstrated their role in the accurate interpolation of phonon band structures. In this talk, I shall retrace an analogous journey in the context of two-dimensional (2D) crystals, by presenting a rigorous derivation of the long-range screening and interatomic forces in 2D. This enables a systematic generalization of the existing formulas (Sohier et al., Nano Lett. 2017, 17, 6, 3758– 3763) to an arbitrary multipolar order. In particular, I will discuss how to incorporate out-of-plane dipoles and dynamical quadrupoles in the long-range part of the dynamical matrix, and how to achieve an optimal representation of the dielectric function. Numerical tests on monolayer BN, SnS2 and BaTiO3 membranes demonstrate a drastic improvement in the description of the long-range electrostatic interactions, with comparable benefits to the quality of the interpolated phonon band structure.   

Electronic Transport in two-dimensional 2D-MXenes for Energy Storage

One of the main scientific challenges in facing the world energy crisis is the efficient storage of renewable energy. To thisend, materials science relies increasingly on two-dimensional (2D) materials for the development of high-efficiency devices.MXenes, anewfamily of 2D-transition metal carbides, nitridesand carbonitrides,with a general formula of Mn+1XnTx, have gainedgreat research attention in the energy storage devices, dueto their excellent electrical conductivity. In order to assist the design of supercapacitorselectrodes based on these materials, we investigate the structural, electronic and vibrational propertiesof pristine(Ti3C2) andfunctionalized MXenes(Ti3C2F2, Ti3C2(OH)2 and Ti2CF2)using first-principles calculations. Our goalisto understand how their electronic transport propertiesdepends on their morphology, chemical composition and surface termination,using density functional theory (DFT), density functional perturbation theory (DFPT)and the linearized Boltzmann transport equation (BTE). In this work, we will discuss the results and identifywhichone of theMXenes provide the higher electrical conductivity. This approach will pavea new way to design MXenes-based electrodesmaterials for energy storage applications   

Copropagating edge states produced by the interaction between electrons and chiral phonons in two-dimensional materials

Unlike the chirality of electrons, the intrinsic chirality of phonons has only surfaced in recent years. Here we report on the effects of the interaction between electrons and chiral phonons in two-dimensional materials by using a non-perturbative solution. We show that chiral phonons introduce inelastic Umklapp processes resulting in copropagating edge states which coexist with a continuum. Transport simulations further reveal the robustness of the edge states. Our results hint on the possibility of having a metal embedded with hybrid electron-phonon states of matter.   

Theory and Modeling of Optomechanics in Charge Density Wave Materials

Novel materials with large optomechanical coupling coefficients are useful both for the exploration of fundamental light-matter interactions, and for the application of their nonlinear response properties in nanoscale devices. Motivating and parameterizing simple phenomenological models of the dominant physics of such materials will provide an important connection between expensive first-principles calculations, and experimental observables. Using 1T-TaS2 as a case study, we develop a general model for studying the coupling between phonons and change in polarizability. This model is successfully applied to the optomechanical response of the commensurate charge density wave (CDW) phase of 1T-TaS2, where we can provide a simple physical explanation for the observation of the coherent 2.4 THz CDW amplitude mode that is observed in this system [1]. This model is generally applicable to materials where a change in symmetry is accompanied by a change in the polarizability of a system.   

Ab initio prediction of mode-selected surface electron-phonon coupling strengths probed by Helium atom scattering (HAS) from the 3x1-reconstructed Nb(001) surface oxide

Using density-functional theory (DFT), we demonstrate that our calculations are able to accurately capture the surface electron-phonon physics at the (001) surface of niobium, the elemental superconductor with the highest critical temperature. The electron-phonon interaction is the fundamental mechanism determining the properties of conventional superconductors, and theoretical predictions of surface properties of superconductors are critically important as external fields penetrating at surfaces limit the material’s overall performance. In this talk, we report surface phonon dispersions and surface electron-phonon coupling strengths of the bare Nb(001) surface and the more complex Nb(001) surface with a long-ranged ordered, 3x1-reconstructed oxide layer. We present our ab initio predictions of the 3x1-O/NbO(001) system along with recent Helium atom scattering (HAS) which provide an experimental surface probe to directly measure mode-selected electron-phonon coupling strengths. The agreement between our DFT calculations and the HAS measurements on this non-trivial surface structure demonstrate the validity of our method and provide an exciting new application to predict surface electron-phonon coupling strengths.   

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There is much interest in accessing the broken-symmetry phases of crystals using light. However, an arbitrary light pulse, whose oscillating electric field integrates to zero by definition, imparts a zero total force to the electric dipole present in the material.  Therefore, light pulses cannot in general be used to break the symmetries present in crystals.  I present theoretical results that show that this limitation can be overcome if a strong quartic coupling of the type $Q_1^2Q_{\textrm{IR}}^2$ is present between a high-frequency infrared mode $Q_{\textrm{IR}}$ and a low-frequency mode $Q_1$ with a negative coupling constant $g$.  Realistic calculations show that such a coupling is present in oxide paraelectrics and can be used to induce ferroelectric phases using midinfrared pulses.