Session P44: Electrons, Phonons, Electron Phonon Scattering, and Phononics III

Theoretical Spectroscopy of 2D Materials: Exciton-phonon coupling in resonant Raman and luminescence spectroscopy

2D materials are known to exhibit very pronounced excitonic effects due to the confinement of electrons and holes in a layer and due to the weak dielectric screening of the electron-hole interaction. In spectroscopy involving vibrational degrees of freedom, the exciton-phonon coupling must therefore be included in order to obtain a qualitative understanding of the spectra and in order to obtain quantitative results. We present our methods for the calculation of exciton-phonon coupling via a finite displacement [1] and via a diagrammatic approach [2,3], both using many-body perturbation theory.

We present results for the phonon-assisted luminescence spectrum of bulk hexagonal boron nitride (hBN), where the combination of indirect band gap and strong excitonic effects leads to a complex peak structure due to coupling of excitons with various phonon branches [1]. Furthermore, we present calculations of resonant Raman intensities with the combined inclusion of both excitonic and non-adiabatic effects. In bulk hBN, which has high phonon-frequencies due to the light atoms, we demonstrate the emergence of strong quantum interference between different excitonic resonances due to non-adiabatic effects. In MoS₂ and MoTe₂, our calculations explain the observed different intensity dependences of the A₁' and E' modes on the energy of the exciting laser [3].

[1] F. Paleari, H.P.C. Miranda, A. Molina-Sánchez, L. Wirtz, Phys. Rev. Lett. 122, 187401 (2019)
[2] F. Paleari, P.-L. Cudazzo, L. Wirtz, in preparation (2020)
[3] S. Reichardt and L. Wirtz, arXiv:1904.00480 [cond-mat.mes-hall]   

Strong phonon-assisted Auger recombination in PbSe

It is commonly believed that direct Auger recombination dominates in narrow-gap semiconductors. With the example of the prototypical narrow-gap semiconductor PbSe, we demonstrate that this is not necessarily the case. By explicitly calculating both the direct and phonon-assisted indirect Auger recombination coefficients of PbSe from first principles, we show that a number of puzzling anomalies in the Auger recombination in PbSe can be well understood. These insights shed new light on the impact of electron-phonon coupling on Auger recombination in IV-VI semiconductors, which is critical for improved device design.   

Fully Anharmonic, Non-Perturbative First-Principles Theory of Electronic-Vibrational Coupling in Solids

The coupling between nuclear vibrations and the electronic structure plays a pivotal role for many material properties, including optical absorption and electronic transport. In this regard, however, todays state-of-the-art methodologies rely on two approximations [1]: the harmonic (phonon) approximation for the nuclear motion and the linear response description of the electronic structure with respect to harmonic displacements. In this work, we overcome both these approximations by performing fully anharmonic ab initio molecular dynamics (aiMD) calculations and by accounting for the non-perturbative, self-consistent response of the wavefunctions along the aiMD trajectory. By this means, we obtain fully anharmonic, vibronically renormalized spectral functions, from which macroscopic material properties like temperature-dependent band gaps and electronic transport coeffiecients are obtained. We validate our approach using silicon as an example, for which the traditional electron-phonon coupling formalism is recovered. Using cubic SrTiO₃ as example, we further demonstrate that anharmonic electronic-vibrational coupling effects not captured in traditional formalisms play a decisive role in complex materials like perovskites.
[1] F. Giustino, Rev. Mod. Phys. 89, 015003 (2017).   

Phonon-mediated Optical and Electronic Transport Properties of BAs

While boron arsenide (BAs) has attracted attention for its ultrahigh thermal conductivity, open questions remain about its use in semiconducting devices. To address this problem, we apply density functional and many body perturbation theory to understand its electronic and optical properties and guide device applications. Since BAs has an indirect band gap of approximately 2 eV and a direct gap of 4.1 eV, absorption of visible light is exclusively mediated by phonons. We therefore calculate the indirect and direct optical absorption spectra to assess its potential in photovoltaics and examine how excitonic effects alter the absorption. Our results are in excellent agreement with experimental data. We also calculate the effect of strain on the band alignment and the electron and hole mobilities, and show that bi-axial tensile strain increases the mobilities of both carriers by over 50%. Finally, we determine the band offsets of BAs heterostructures with nearly lattice-matched ZnSnN₂ and InGaN to guide heterostructure design. Our work elucidated the functional properties of BAs for technologically relevant device applications.   

Electron and Phonon Hydrodynamics in Antimony

We present a study of the electrical and thermal resistivities in millimetric samples of the semimetal Sb down to sub-Kelvin temperatures. By applying a large magnetic field, we can clearly separate the electronic and phononic thermal resistivities. The Wiedemann-Franz (WF) law is recovered at low temperature (T ≈ 4K) in all samples. Yet, a size-dependent departure from the WF law is observed at higher temperatures. We show that this deviation is due to a mismatch between the prefactors of the thermal and electrical T²-resistivities. By analogy with the case of normal-state liquid ³He, where fermion-fermion collisions generate a thermal conductivity inversely proportional to temperature [1], we can associate the larger T²-thermal resistivity to the momentum-conserving electronic collisions [2]. In this scenario, the size-dependence of the ratio of the thermal to the electrical T²-prefactors in Sb points to a hydrodynamic flow of electrons [3]. Furthermore, in the 1K-7K range, we also report on a large increase of the thermal diffusivity of phonons, in the same samples, i.e. a signature that the flow of phonons is partially hydrodynamic.

[1] W. R. Abel et al., Phys. Rev. Lett. 18 (1967)
[2] A. Jaoui et al., npj Quant. Mat. 3 (2018)
[3] R.N. Gurzhi, Sov. Phys. Uspekhi 11 (1968)   

Unraveling a New Heat Transport Regime at The Nanoscale.

The understanding of heat transport in nanoscale semiconductors is of fundamental importance because of its huge technological impact in electronics and renewable energy harvesting and conversion. A particularly interesting question is related to the understanding of how thermal properties of dielectrics, like silicon, change when their size of the order of a few hundred nanometers, which is the characteristic size of state of the art electronic circuits. In this size range heat transport is in a regime in between ballistic and diffusive, which is inaccurately described by either approximation.
In this work, we analyze the current state of the art of heat transport in semiconductor nanostructures. We identify substantial gaps in the theoretical treatment of the quasi-ballistic transport regime, and we propose a new atomistic model to compute the thermal conductivity of nanoscale systems, including both quantum and finite boundaries effects. Our novel approach is implemented in a computational environment, which gives to the powerful framework of anharmonic lattice dynamics, the ability to perform high accuracy predictions for finite size systems, and provide a rigorous alternative to non-equilibrium molecular dynamics.   

Electron wind force in an atomistic non-equilibrium molecular dynamics simulation

We demonstrate electronic friction on metals by addressing the reverse process – the force imparted on the atoms by the flow of an electronic current in the metal. By well established Ehrenfest dynamics we implement a quantum-classical simulation of the motion of a chain of classical atoms forming a contactless monatomic ring, where electrons flow by nearest neighbor hopping between atomic-like orbitals in an electric field generated by a linearly growing external magnetic field threading the ring. In the real time dynamics, electron-phonon scattering events take the form of Landau-Zener processes, each of them imparting momentum to the classical atoms, that can vibrate and also dissipate to a bath. The realistic features of electron conduction and resistivity are recovered in this model, plus a microscopic description of the current-induced momentum transfer to the atoms which vibrate and to the whole chain which drifts. When one additional adatom is added to the chain, the quantum mechanics of the wind force and the resulting electromigration drift are controlled by the weak hybridization of the adatom orbital to the chain atomic orbitals where the current flows, suggestive of a rather general mechanism.   

Thickness-dependent electron-phonon coupling and transport in metals from first principles

Recent strides in thin-film deposition technology have made the next generation of ultrathin plasmonic devices and ultrascaled metallic interconnects plausible. It has led to a renewed interest in the study of properties of metals and semiconductors in the low dimensional limit. Here, starting with a single layer, we systematically investigate the effect of thickness on the electronic properties and electron-phonon (e-ph) coupling of ultrathin metallic films. Such ab initio studies have typically been challenging because of the inability of the state-of-the-art DFT codes to correctly predict the phonon dispersion curves of finite thickness materials, especially in the q→0 limit. We propose a new computationally-inexpensive correction scheme for the phonon force matrix based on rotational invariance of the elasticity tensor. This scheme facilitates accurate computation of phonon bandstructures and e-ph coupling for arbitrary film geometries. Using this capability, we determine the variation of electronic transport properties as a function of layer number, fully accounting for effects such as phonon confinement. These ab initio calculations give us an insight into the effect of surface and interfacial strain on the e-ph scattering in thin metallic films.   

Phonon interactions in rock salt and fluorite structures

Space group irreducible derivatives of the Born Oppenheimer potential are computed from density functional theory for materials with the rock salt and fluorite structures, including PbTe and ThO2. We utilize our recently developed group theoretical approach which allows the extraction of the irreducible derivatives from finite displacement calculations on the smallest possible supercells using the smallest possible number of calculations. Quadratic (i.e. phonons), cubic, and quartic irreducible derivatives have been computed. The fidelity of the irreducible derivatives is tested via comparison to strain derivatives of the phonons. Both dynamics and thermodynamics are evaluated using our irreducible Taylor series, yielding observables such as phonon linewidths, thermal conductivity, thermal expansion, mean square displacements, etc. Results on PbTe and ThO2 are compared to experiment.   

Predictive calculations of electron and heat transport in ultra-wide-band-gap semiconductors

Ultrawide-band-gap semiconductors are used for energy-efficient power electronics, but there is a pressing need to imrpove on current materials. Beta gallium oxide (β-Ga₂O₃) outperforms materials such as Si, SiC, and GaN due to its wide band gap and corresponding large breakdown field. However, three drawbacks of β-Ga₂O₃ are its lack of p-type doping, its low thermal conductivity, and its inferior electron mobility. Using first-principles calculations we calculate the electron-phonon coupling of β-Ga₂O₃ to understand the origin of the limits to the electron mobility and thermal conductivity. We also explore rutile germanium dioxide (r-GeO₂) as a semiconductor for power-electronic applications. The calculated band gap and optical absorption spectrum is in good agreement with optical measurements. We also determine the phonon-limited carrier mobilities and lattice thermal conductivity as a function of temperature and crystal orientation. We find that the electronic and thermal transport properties of r-GeO₂ outperform current materials, while it can also be ambipolarly doped. Our results highlight the potential of r-GeO₂ for power electronics.   

Optical absorption in gallium oxide

Transparent conducting oxides (TCOs) are a technologically important class of materials used in optoelectronic devices, as TCOs balance two conflicting properties: transparency and conductivity. The requirement of transparency is typically tied to the band gap of the material being sufficiently large to prevent absorption of visible photons. This is a necessary but not sufficient condition: indeed, the high concentration of free carriers, required for conductivity, can also lead to optical absorption. This absorption can occur through direct absorption to higher-lying conduction band states, or by an indirect process, for example mediated by phonons or charged impurities.
We performed a detailed first-principles study of these absorption processes in Ga₂O₃ [1,2], a material with promising applications in high-power devices and UV photodetectors. Our results elucidate the fundamental limitations of optical absorption in Ga₂O₃ and shed light on experimental observations.

[1] H. Peelaers and C.G. Van de Walle, Appl. Phys. Lett. 111, 182104 (2017).
[2] H. Peelaers and C.G. Van de Walle, Phys. Rev. B 100, 081202 (2019).   

Low and high field transport in 2-dimensional electron gas in β-(AlxGa1-x)2O3/Ga2O3 heterostructures

β-Ga₂O₃ is an emerging wide-bandgap semiconductor for potential application in power and RF electronics. The 2-dimensional electron gas (2-DEG) in β-(Al_xGa_1-x)₂O₃/Ga₂O₃ heterostructures show the promise for high speed transistors. We will present both the low- and high- field 2-DEG transport properties in the AlGa₂O₃/Ga₂O₃ heterostructure. A self-consistent Poisson-Schrodinger simulation of heterostructure is used to obtain the subband energies and wavefunctions. Intra-subband, inter-subband, 2D-3D, 3D-2D and 3D-3D scattering rates are calculated for all the different scattering mechanisms. The electronic structure, assuming confinement in a particular direction, and the phonon dispersion is calculated based on first principle methods under DFT and DFPT framework. Phonon confinement is not considered for the sake of simplicity. The different scattering mechanisms that are included in the calculation are phonon (polar and non-polar), remote impurity, alloy and interface-roughness. We include the full dynamic screening in polar optical phonon scattering. We will use Full Band Monte Carlo to calculate the velocity-field profile in different crystal directions. We will also report the low field mobility by solving the Boltzmann transport equation using Rode’s iterative method.   

Phonon RIXS calculations using Green's function Momentum Average technique

Spectroscopic experiments are the most extensively used probes for characterizing the physical properties of condensed matter. However, their understanding often requires a theoretical calculation of the spectra in question, usually starting from some simplified model of the underlying system. One of the problems that are key to the understanding of many properties of materials is the physics of phonons and their interaction with the conduction electrons. These are the issues lying at the base of conventional superconductivity and it is hoped that their better understanding in high temperature superconductors might help elucidate some of the mysteries still surrounding those materials. The RIXS spectroscopy is a novel, emerging technique, that only recently started to approach the resolving power necessary to observe the phononic features. Thus, theoretical predictions concerning phonon RIXS are now becoming timely in this rapidly progressing field of research. Our aim is to use the Momentum Average Green's function technique and apply it to the problem of phonon RIXS calculations, thus going beyond the current dichotomy of exact diagonalization vs. perturbative expansion methods that are the two dominating methodologies in RIXS theory.