Electron-phonon Matrix Elements Research Articles

Theory of coherent phonons coupled to excitons

The interaction of excitons with lattice vibrations underlies the scattering from bright to dark excitons as well as the coherent modulation of the exciton energy. Unlike the former mechanism, which involves phonons with finite momentum, the latter can be exclusively attributed to coherent phonons with zero momentum. We here lay down the microscopic theory of coherent phonons interacting with resonantly pumped bright excitons and provide the explicit expression of the corresponding coupling. The coupling notably resembles the exciton-phonon one, but with a crucial distinction: it contains the bare electron-phonon matrix elements rather than the screened ones. Our theory predicts that the exciton energy features a polaronic-like red-shift and monochromatic oscillations or beatings, depending on the number of coupled optical modes. Both the red-shift and the amplitude of the oscillations are proportional to the excitation density and to the square of the exciton-coherent-phonon coupling. We validate our analytical findings through comparisons with numerical simulations of time-resolved optical absorbance in resonantly pumped MoS2 monolayers.

Superconductivity induced by ionized σ-bond at 10 GPa

Discovering high-temperature superconductors under low pressures and elucidating the underlying critical factors governing superconductivity are central issues in condensed matter physics. Here, we developed a strategy for the metallization of σ-bonds through incorporating NH3-units into the filled f-shell Lu-lattice and obtained a Luδ+(NH3)4σ− hydride to investigate the potential high-temperature superconductivity. Based on the density-functional theory calculations, our proposed I-43m-Luδ+(NH3)4σ− phase exhibits a Tc of 33.44 K at 10 GPa. Further analyses unveil that the Tc is attributed to strong electron-phonon coupling (EPC), which originated from the electron-phonon matrix element primarily driven by H–N–H bending and twisting vibrations, and Fermi surface nesting induced softening of optical phonons to scatter itinerant electrons on phonon-coupling bands to form Cooper pairs. Importantly, the emergence of phonon-coupling bands is mainly dependent on the ionization of sp3-hybridized σ-bonds within NH3, resulting in the manifestation of metallicity. Due to the enhanced ionization of σ-bands and strengthened interatomic coupling effect with pressurization, the Tc is further enhanced to 130 K. Our study offers novel insights towards the realization of phonon-mediated high-temperature superconductivity at comparatively low-pressures and highlights the potential for achieving high-Tc in filled f-shell metal hydrides through strategic engineering of metallized σ-bonds.

Infrared Resonance Raman of Bilayer Graphene: Signatures of Massive Fermions and Band Structure on the 2D Peak.

Few-layer graphene possesses low-energy carriers that behave as massive Fermions, exhibiting intriguing properties in both transport and light scattering experiments. Lowering the excitation energy of resonance Raman spectroscopy down to 1.17 eV, we target these massive quasiparticles in the split bands close to the K point. The low excitation energy weakens some of the Raman processes that are resonant in the visible, and induces a clearer frequency-separation of the substructures of the resonance 2D peak in bi- and trilayer samples. We follow the excitation-energy dependence of the intensity of each substructure, and comparing experimental measurements on bilayer graphene with ab initio theoretical calculations, we trace back such modifications on the joint effects of probing the electronic dispersion close to the band splitting and enhancement of electron-phonon matrix elements.

Efficient first-principles electronic transport approach to complex band structure materials: the case of n-type Mg3Sb2

We present an efficient method for accurately computing electronic scattering rates and transport properties in materials with complex band structures. Using ab initio simulations, we calculate a limited number of electron–phonon matrix elements, and extract scattering rates for acoustic and optical processes based on deformation potential theory. Polar optical phonon scattering rates are determined using the Fröhlich model, and ionized impurity scattering rates are derived from the Brooks-Herring theory. Subsequently, electronic transport coefficients are computed within the Boltzmann transport theory. We exemplify our approach with n-type Mg3Sb2, a promising thermoelectric material with a challenging large unit cell and low symmetry. Notably, our method attains competitive accuracy, requiring less than 10% of the computational cost compared to state-of-the-art ab initio methods, dropping to 1% for simpler materials. Additionally, our approach provides explicit information on individual scattering processes, offering an alternative that combines efficiency, robustness, and flexibility beyond the commonly employed constant relaxation time approximation with the accuracy of fully first-principles calculations.

QERaman: An open-source program for calculating resonance Raman spectra based on Quantum ESPRESSO

We present an open-source program QERaman that computes first-order resonance Raman spectroscopy of materials using the output data from Quantum ESPRESSO. Complex values of Raman tensors are calculated based on the quantum description of the Raman scattering from calculations of electron-photon and electron-phonon matrix elements, which are obtained by using the modified Quantum ESPRESSO. Our program also calculates the resonant Raman spectra as a function of incident laser energy for linearly- or circularly-polarized light. Hands-on tutorials for graphene and MoS2 are given to show how to run QERaman. All codes, examples, and scripts are available on the GitHub repository. Program summaryProgram Title:QERamanCPC Library link to program files:https://doi.org/10.17632/ddcrrrmxw9.1Developer's repository link:https://github.com/nguyen-group/QERamanLicensing provisions: GNU General Public Licence 3.0Programming language: FortranExternal routines:Quantum ESPRESSO v7.2Nature of problem: Resonance Raman spectra with first-principles calculations.Solution method: The Raman intensity formula is given by the quantum theory, in which the electron-photon and the electron-phonon matrix elements are obtained from the modified Quantum ESPRESSO package.

A DFT study of electron–phonon interactions for the and defects in hexagonal boron nitride: investigating the role of the transition dipole direction

Quantum emitters in two-dimensional hexagonal boron nitride (h-BN) have generated significant interest due to observations of ultra-bright emission made at room temperature. The expectation that solid-state emitters exhibit broad zero-phonon lines at elevated temperatures has been put in question by recent observations of Fourier transform (FT) limited photons emitted from h-BN flakes at room temperature. All decoupled emitters produce photons that are directed in-plane, suggesting that the dipoles are perpendicular to the h-BN plane. Motivated by the promise of an efficient and scalable source of indistinguishable photons that can operate at room temperature, we have developed an approach using density functional theory (DFT) to determine the electron-phonon coupling for defects that have in- and out-of-plane transition dipole moments. Our DFT calculations reveal that the transition dipole for the defect is parallel to the h-BN plane, and for the defect is perpendicular to the plane. We calculate both the phonon density of states and the electron–phonon matrix elements associated with the h-BN defective structures. We find no indication that an out-of-plane transition dipole by itself will result in the low electron–phonon coupling that is expected to produce FT-limited photons at room temperature. Our work provides direction to future DFT software developments and adds to the growing list of calculations relevant to researchers in the field of solid-state quantum information processing.

Accurate Prediction of Hall Mobilities in Two-Dimensional Materials through Gauge-Covariant Quadrupolar Contributions.

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS_{2} monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room-temperature electron and hole Hall mobilities, respectively.

Quantitative spin-dependent electron-electron interaction to calculate the superconducting parameters μ and λ

The spin-dependent Kukkonen-Overhauser (KO) effective electron-electron interaction in electron gas with a deformable background is used to calculate the BCS superconducting parameters $\ensuremath{\mu}$, ${\ensuremath{\mu}}^{*}$, and $\ensuremath{\lambda}$. The density and spin local field factors are utilized to incorporate the quantitative effects of exchange and correlation. The repulsive parameter $\ensuremath{\mu}$ is compared to results using the historical Thomas-Fermi or nearly equivalent random phase approximation (RPA) interactions. The resulting $\ensuremath{\mu}$ using the KO interaction is $45%$ larger at ${r}_{s}=1.65$; rising to $153%$ larger at ${r}_{s}=5.62$. Retardation reduces the effective repulsion, but ${\ensuremath{\mu}}^{*}$ is still $20\ensuremath{-}25%$ larger. The predicted superconducting transition temperature would be reduced by $5\ensuremath{-}20%$ using the McMillan formula. The attractive superconducting parameter $\ensuremath{\lambda}$, which depends on the electron-test charge interaction and the phonon spectrum, is also calculated using simple Debye-based models for phonon dispersion. This leads to a larger value of $\ensuremath{\lambda}$ than the same calculation using Thomas-Fermi or RPA interactions. Modern calculations of the phonon dispersion relations are often done using density functional theory. With the proper exchange and correlation kernel, the self-consistency of the method should yield the correct phonon dispersion relation and electron-phonon matrix elements. If the Thomas-Fermi or RPA interactions are used at any stage, the results for $\ensuremath{\lambda}$ are probably quantitatively inaccurate.

Interplay of charge ordering and superconductivity in two-dimensional 2H group V transition-metal dichalcogenides

Layered $2H\text{\ensuremath{-}}T{X}_{2}$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{\ensuremath{-}}T{X}_{2}$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_{2}$, ${\mathrm{TaS}}_{2}$, ${\mathrm{TaSe}}_{2}$, and ${\mathrm{NbS}}_{2}$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_{2}$ and ${\mathrm{TaSe}}_{2}$ than in ${\mathrm{TaS}}_{2}$ and ${\mathrm{NbS}}_{2}$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature ${T}_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of ${T}_{\mathrm{c}}$ in $\mathrm{Nb}{X}_{2}$ and $\mathrm{Ta}{X}_{2}$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.

Intervalley scattering induced significant reduction in lattice thermal conductivities for phosphorene.

The thermal transport properties of buckled phosphorene (β-P) and antimonene (β-Sb) are investigated using first-principles methods. The large acoustic-optical phonon gaps of 3.8 THz and 2.2 THz enable the four-phonon interaction to play an important role in phonon scattering for both β-P and β-Sb. Considering the electron-phonon coupling, the lattice thermal conductivity can further undergo 84% decrease to 4.9 W mK-1 for p-type β-P at n = 5 × 1013 cm-2. By quantitatively describing the scattering probability of electrons in different paths combined with electron-phonon coupling matrix element analysis, it is found that multi-valley features of electronic band structure and strong electron-phonon coupling strength make electrons have strong intervalley scattering behavior in β-P. The former plays an important role in the energy conservation condition of the scattering process, and the latter determines the selection rule. Our work elucidates the contribution of higher-order phonon interactions as well as electron-phonon coupling effects to lattice thermal conductivity, and provides a new idea for finding materials with low lattice thermal conductivity induced by intervalley scattering.

Investigation of superconductivity in ultrahigh pressure phases of yttrium

The superconductivity of yttrium metal under high pressure were systematically investigated by utilizing first-principles calculations. Based on the evolutionary structure searches, we have proposed a new ultrahigh pressure phase of C2/m that is energetically competitive to the previously reported Fmm2. The electron-phonon coupling calculations demonstrated a Tc of 16.97 K at 700 GPa in our proposed C2/m, whereas the Tc in Fmm2 was estimated to be 12.19–9.46 K in the pressure range of 600–800 GPa accompanied by a declining trend upon compression. Further analyses of Fermi surface nesting functions reveal that the shrinking Tc in Fmm2 is dominated by phonon frequencies and N(εF), while the difference of Tc's between C2/m and Fmm2 is mainly attributed to the tremendous difference of electron-phonon matrix element. Our findings would offer fundamental insights for understanding the superconducting mechanism in yttrium and even other rare earth superconductors under BCS framework.

Electron–phonon coupling and superconductivity in an alkaline earth hydride CaH6 at high pressures

Recently, an alkaline earth hydride CaH6 having a sodalitelike clathrate structure has been experimentally synthesized at megabar pressures with a maximum T c of 215 K, comparable to that of a rare earth hydride LaH10. Here, based on first-principles calculations, we find that CaH6 exhibits a huge peak in the Eliashberg spectral function α 2 F around the low-frequency region of H-derived phonon modes, in contrast to LaH10 having a widely spreading spectrum of α 2 F over the whole frequencies of H-derived phonon modes. It is revealed that the huge peak of α 2 F in CaH6 is associated with an effective electron–phonon coupling (EPC) between low-frequency optical phonons and hybridized H 1s and Ca 3d states near the Fermi energy. As pressure increases, the strengthened H–H covalent bonding not only induces a hardening of optical phonon modes but also reduces the electron–phonon matrix elements related to the low-frequency optical modes, thereby leading to a lowering of the EPC constant. It is thus demonstrated that H-derived low-frequency phonon modes play an important role in the pressure-induced variation of T c in CaH6. Furthermore, unlike the presence of two distinct superconducting gaps in LaH10, CaH6 is found to exhibit a single isotropic superconducting gap.

Variational polaron equations applied to the anisotropic Fröhlich model

Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as individual electron, phonon and electron-phonon contributions are obtained. We suggest an efficient gradient-based optimization algorithm and apply these equations to the generalized Fr\"ohlich model with anisotropic non-degenerate electronic bands, both in two- and three-dimensional cases. The effect of the divergence of Fr\"ohlich electron-phonon matrix elements at $\Gamma$-point is treated analytically, improving the convergence with respect to the sampling in reciprocal space. The whole methodology is validated by obtaining the known asymptotic solution of the standard Fr\"ohlich model in isotropic scenario and also by comparing our results with the Gaussian ansatz approach, showing the difference between the numerically exact and Gaussian trial wavefunctions. Additionally, decomposition of the energy into individual terms allows one to recover the Pekar's 1:2:3:4 theorem, which is shown to be valid even in the anisotropic case. We expect that the improvements in the formalism and numerical implementation will be applicable beyond the large polaron hypothesis inherent to Fr\"ohlich model.

First-principles calculations of double resonance Raman spectra for monolayer MoTe2

Since double resonance Raman (DRR) spectra are laser-energy dependent, the first-principles calculations of DRR for two-dimensional materials are challenging. Here, the DRR spectrum of monolayer MoTe$_2$ is calculated by home-made program, in which we combine {\em ab-initio} density-functional-theory calculations with the electron-phonon Wannier (EPW) method. Within the fourth-order perturbation theory, we are able to quantify not only the electron-photon matrix elements within the dipole approximation, but also the electron-phonon matrix elements using the Wannier functions. The reasonable agreement between the calculated and experimental Raman spectra is achieved, in which we reproduce some distinctive features of transition metal dichalcogenides (TMDCs) from graphene (for example, the dominant intervalley process involving an electron or a hole). Furthermore, we perform an analysis of the possible DRR modes over the Brillouin zone, highlighting the role of low-symmetry points. Raman tensors for some DRR modes are given by first principles calculations from which laser polarization dependence is obtained.

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

\textit{Ab initio} calculations of electron-phonon interactions including the polar Fr\"ohlich coupling have advanced considerably in recent years. The Fr\"ohlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fr\"ohlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fr\"ohlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. Here, we generalize previous work on the \textit{ab initio} Fr\"ohlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for 3D and 2D systems when the interlayer separation tends to zero or infinity, respectively. This new expression enables an accurate description of the Fr\"ohlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct \textit{ab initio} density-functional perturbation theory calculations for monolayer BN and MoS$_2$, and we provide a simple expression for the 2D Fr\"ohlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

Deformation potential extraction and computationally efficient mobility calculations in silicon from first principles

We present a first-principles framework to extract deformation potentials in Silicon based on density-functional theory (DFT) and density-functional perturbation theory (DFPT). We compute the electronic band structures, phonon dispersion relations, and electron-phonon matrix elements to extract deformation potentials for acoustic and optical phonons for all possible processes. The matrix elements clearly show the separation between intra- and inter-valley scattering in the conduction band, and quantify the strength of the scattering events in the degenerate bands of the valence band. We then use an advanced numerical Boltzmann transport equation (BTE) simulator that couples DFT electronic structures and energy/momentum-dependent scattering rates to compute the transport properties for electrons and holes. By incorporating ionized impurity scattering as well, we calculate the n-type and p-type mobility versus carrier density and make comparisons to experiments, indicating excellent agreement. The fact that the method we present uses well-established theoretical tools and requires the extraction of only a limited number of matrix elements, makes it generally computationally very attractive, especially for semiconductors with a large unit cell and lower symmetry.

Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands.

Graphene moiré superlattices are outstanding platforms to study correlated electron physics and superconductivity with exceptional tunability. However, robust superconductivity has been measured only in magic-angle twisted bilayer graphene (MA-TBG) and magic-angle twisted trilayer graphene (MA-TTG). The absence of a superconducting phase in certain moiré flat bands raises a question on the superconducting mechanism. In this work, we investigate electronic structure and electron-phonon coupling in graphene moiré superlattices based on atomistic calculations. We show that electron-phonon coupling strength λ is dramatically different among graphene moiré flat bands. The total strength λ is very large (λ>1) for MA-TBG and MA-TTG, both of which display robust superconductivity in experiments. However, λ is an order of magnitude smaller in twisted double bilayer graphene (TDBG) and twisted monolayer-bilayer graphene (TMBG) where superconductivity is reportedly rather weak or absent. We find that the Bernal-stacked layers in TDBG and TMBG induce sublattice polarization in the flat-band states, suppressing intersublattice electron-phonon matrix elements. We also obtain the nonadiabatic superconducting transition temperature T_{c} that matches well with the experimental results. Our results clearly show a correlation between strong electron-phonon coupling and experimental observations of robust superconductivity.

First-principles predictions of Hall and drift mobilities in semiconductors

Significant progress on parameter-free calculations of carrier mobilities in real materials has been made during the past decade; however, the role of various approximations remains unclear and a unified methodology is lacking. Here, we present and analyse a comprehensive and efficient approach to compute the intrinsic, phonon-limited drift and Hall carrier mobilities of semiconductors, within the framework of the first-principles Boltzmann transport equation. The methodology exploits a novel approach for estimating quadrupole tensors and including them in the electron-phonon interactions, and capitalises on a rigorous and efficient procedure for numerical convergence. The accuracy reached in this work allows to assess common approximations, including the role of exchange and correlation functionals, spin-orbit coupling, pseudopotentials, Wannier interpolation, Brillouin-zone sampling, dipole and quadrupole corrections, and the relaxation-time approximation. A detailed analysis is showcased on ten prototypical semiconductors, namely diamond, silicon, GaAs, 3C-SiC, AlP, GaP, c-BN, AlAs, AlSb, and SrO. By comparing this extensive dataset with available experimental data, we explore the intrinsic nature of phonon-limited carrier transport and magnetotransport phenomena in these compounds. We find that the most accurate calculations predict Hall mobilities up to a factor of two larger than experimental data; this could point to promising experimental improvements in the samples quality, or to the limitations of density-function theory in predicting the carrier effective masses and overscreening the electron-phonon matrix elements. By setting tight standards for reliability and reproducibility, the present work aims to facilitate validation and verification of data and software towards predictive calculations of transport phenomena in semiconductors.

Carrier transport theory for twisted bilayer graphene in the metallic regime

Understanding the normal-metal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonon-dominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electron-phonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finite-temperature dynamical screening of the electron-phonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments.

First-principles study of electron transport in ScN

We investigate the conduction-band structure and electron mobility in rocksalt ScN based on density functional theory. The first-principles band structure allows us to obtain band velocities and effective masses as a function of energy. Electron-phonon scattering is assessed by explicitly computing the $q$-dependent electron-phonon matrix elements, with the inclusion of the long-range electrostatic interaction. The influence of free-carrier screening on the electron transport is assessed using the random-phase approximation. We find a notable enhancement of electron mobility when the carrier concentration exceeds ${10}^{20}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. We calculate the room-temperature electron mobility in ScN to be 587 ${\mathrm{cm}}^{2}/\mathrm{Vs}$ at low carrier concentrations. When the carrier concentration is increased, the electron mobility starts to decrease significantly around $n={10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ and drops to 240 ${\mathrm{cm}}^{2}/\mathrm{Vs}$ at $n={10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. We also explore the influence of strain in (111)- and (100)-oriented ScN films. For (111) films, we find that a 1.0% compressive epitaxial strain increases the in-plane mobility by 72 ${\mathrm{cm}}^{2}/\mathrm{Vs}$ and the out-of-plane mobility by 50 ${\mathrm{cm}}^{2}/\mathrm{Vs}$. For (100) films, a 1.0% compressive epitaxial strain increases the out-of-plane mobility by as much as 172 ${\mathrm{cm}}^{2}/\mathrm{Vs}$, but has a weak impact on the in-plane mobility. Our study sheds light on electron transport in ScN at different electron concentrations and shows how strain engineering could increase the electron mobility.