The Allen-Heine-Cardona theory allows us to calculate phonon-induced electron self-energies from first principles without resorting to the adiabatic approximation. However, this theory has not been able to account for the change of the electron wave function, which is crucial if interband energy differences are comparable to the phonon-induced electron self-energy as in temperature-driven topological transitions. Furthermore, for materials without inversion symmetry, even the existence of such topological transitions cannot be investigated using the Allen-Heine-Cardona theory. Here, we generalize this theory to the renormalization of both the electron energies and wave functions. Our theory can describe both the diagonal and off-diagonal components of the Debye-Waller self-energy in a simple, unified framework. For demonstration, we calculate the electron-phonon coupling contribution to the temperature-dependent band structure and hidden spin polarization of BiTlSe2 across a topological transition. These quantities can be directly measured. Our theory opens a door for studying temperature-induced topological phase transitions in materials both with and without inversion symmetry.
We develop a theory for the electron-phonon interaction effects on the electronic properties of graphene. We analytically calculate the electron self-energy, spectral function and band velocity renormalization due to phonon-mediated electron-electron interaction. We find that phonon-mediated electron-electron coupling has a large effect on the graphene band structure renormalization, and our analytic theory successfully captures the essential features of the observed graphene electron spectra in the ARPES experiments, predicting a kink at $\sim 200\mathrm{meV}$ below the Fermi level and a redu…
We measure the temperature dependence of the Raman spectra of metallic and semiconducting nanotubes. We show that the different trend in metallic tubes is due to phonon re-normalization induced by the variation in electronic temperature, which is modeled including non-adiabatic contributions to account for the dynamic, time dependent nature
The physics of mutual interaction of phonon quasiparticles with electronic spin degrees of freedom, leading to unusual transport phenomena of spin and heat, has been a subject of continuing interests for decades. Despite its pivotal role in transport processes, the effect of spin-phonon coupling on the phonon system, especially acoustic phonon properties, has so far been elusive. By means of inelastic neutron scattering and first-principles calculations, anomalous scattering spectral intensity from acoustic phonons was identified in the exemplary collinear antiferromagnetic nickel (II) oxide, …
The renormalization of the band structure at zero temperature due to electron-phonon coupling is investigated in diamond, BN, LiF and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite …
The temperature dependence of the first-order phonon mode of single crystal of Silicon (Si) is determined by Raman scattering in a broad temperature range of 4-623 K. Our studies reveal the anomalous red-shift of the Raman active phonon mode at temperature (~ 50 K) attributed to the anomalous expansion of Si in the low temperature region. Silicon shows negative thermal expansion below 120 K, however, odd behaviour is also observed at very low temperatures i.e., softening of the Si crystal is detected below 40 K. This peculiar behaviour of Si is described by the anomalous phonon anharmonicity o…
We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the …
Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limi…
SrTiO$_3$ has been extensively investigated owing to its abundant degrees of freedom for modulation. However, the microscopic mechanism of thermal transport especially the relationship between phonon scattering and lattice distortion during the phase transition are missing and unclear. Based on deep-potential molecular dynamics and self-consistent \textit{ab initio} lattice dynamics, we explore the lattice anharmonicity-induced tetragonal-to-cubic phase transition and explain this anomalous behavior during the phase transition. Our results indicate the significant role of the renormalization o…
First-principles theory of phonon renormalization from nonlinear electron-phonon interactions
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Theory of Quantum Systems and Complex Systems, Universiteit Antwerpen（安特卫普大学量子系统与复杂系统理论）；Faculty of Physics, Computational Materials Physics, University of Vienna（维也纳大学物理学院计算材料物理系）；Department of Physics and Astronomy “Augusto Righi”, Alma Mater Studiorum - Università di Bologna（博洛尼亚大学阿ugusto Righi物理与天文学系）
We present a novel approach to electron-lattice interaction beyond the linear-coupling regime. Based on the solution of a Holstein-Peierls-type model, we derive explicit analytical expressions for the eigenvalue spectrum of the Hamiltonian, resulting in a narrowing of bands as a function of temperature. Our approach enables the intuitive interpretation in terms of quasiparticles, i.e. polaron bands and dressed-phonon frequencies. Being nonperturbative, the formalism also applies in the strong-coupling case. We apply it to the organic crystal naphthalene, with the coupling strengths obtained by…
We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear bandstructure of graphene and deviates substantially from the usual metallic behavior. The effective band velocity of the Dirac fermions is found to be reduced by 4-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.
In the past five years enormous progress has been made in the ab initio calculations of the optical response of electrons in semiconductors. The calculations include the Coulomb interaction between the excited electron and the hole left behind, as well as local field effects. However, they are performed under the assumption that the atoms occupy fixed equilibrium positions and do not include effects of the interaction of the lattice vibrations with the electronic states (electron-phonon interaction). This interaction shifts and broadens the energies at which structure in the optical spectra is…
Developing a microscopic understanding of spin decoherence is essential to advancing quantum technologies. Electron spin decoherence due to atomic vibrations (phonons) plays a special role as it sets an intrinsic limit to the performance of spin-based quantum devices. Two main sources of phonon-induced spin decoherence - the Elliott-Yafet (EY) and Dyakonov-Perel (DP) mechanisms - have distinct physical origins and theoretical treatments. Here we show calculations that unify their modeling and enable accurate predictions of spin relaxation and precession in semiconductors. We compute the phonon…
We report phonon renormalization induced by an external electric field E in ferroelectric poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] nanofibers through measuring the E-dependent thermal conductivity. Our experimental results are in excellent agreement with the theoretical ones derived from the lattice dynamics. The renormalization is attributed to the anharmonicity that modifies the phonon spectrum when the atoms are pulled away from their equilibrium positions by the electric field. Our finding provides an efficient way to manipulate the thermal conductivity by tuning external …
Amongst the X(Sn,Pb)Y$_3$ perovskites currently under scrutiny for their photovoltaic applications, the cubic B-$α$ phase of CsSnI$_3$ is arguably the best characterized experimentally. Yet, according to the standard harmonic theory of phonons, this deceptively simple phase should not exist at all due to rotational instabilities of the SnI$_6$ octahedra. Here, employing self-consistent phonon theory we show that these soft modes are stabilized at experimental conditions through anharmonic phonon-phonon interactions between the Cs ions and their iodine cages. We further calculate the renormaliz…
Recently, Zacharias et al [Phys. Rev. Lett. 115, 177401 (2015)] developed a new ab initio theory of temperature-dependent optical absorption spectra and band gaps in semiconductors and insulators. In that work the zero-point renormalization and the temperature dependence were obtained by sampling the nuclear wavefunctions using a stochastic approach. In the present work, we show that the stochastic sampling can be replaced by fully deterministic supercell calculations based on a single optimal configuration of the atomic positions. We demonstrate that a single calculation is able to capture th…
With the ever-increasing sophistication of codes, the verification of the implementation of advanced theoretical formalisms becomes critical. In particular, cross comparison between different codes provides a strong hint in favor of the correctness of the implementations, and a measure of the (hopefully small) possible numerical differences. We lead a rigorous and careful study of the quantities that enter in the calculation of the zero-point motion renormalization of the direct band gap of diamond due to electron-phonon coupling, starting from the total energy, and going through the computati…
The energy gap of simple band insulators like GaAs is a strong function of temperature due to the electron-phonon interactions. Interestingly, the perturbation from zero-point phonons is also predicted to cause significant (a few percent) renormalization of the energy gap at absolute zero temperature but its value has been difficult to estimate both theoretically and, of course, experimentally. Given the experimental evidence [Bhattacharya, et al., Phys. Rev. Lett. 114, 047402 (2015)] that strongly supports that the exponential broadening (Urbach tail) of the excitonic absorption edge at low t…
Organic molecular crystals are expected to feature appreciable electron-phonon interactions that influence their electronic properties at zero and finite temperature. In this work, we report first-principles calculations and an analysis of the electron-phonon self-energy in naphthalene crystals. We compute the zero-point renormalization and temperature dependence of the fundamental band gap, and the resulting scattering lifetimes of electronic states near the valence- and conduction-band edges employing density functional theory. Further, our calculated phonon renormalization of the $GW$-corre…
Using first-principles techniques, we calculate the renormalization of the electron Fermi velocity and the vibrational lifetimes arising from electron-phonon interactions in doped bilayer graphene and in graphite and compare the results with the corresponding quantities in graphene. For similar levels of doping, the Fermi velocity renormalization in bilayer graphene and in graphite is found to be approximately 30% larger than that in graphene. In the case of bilayer graphene, this difference is shown to arise from the interlayer interaction. We discuss our findings in the light of recent photo…
We present an ab-initio density-functional-theory approach for calculating electron-phonon interactions within the projector augmented-wave method. The required electron-phonon matrix elements are defined as the second derivative of the one-electron energies in the 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 simple eigenvalue problems and all-electron formulations. We discuss the relation between our definition of the electron-phonon matrix element and other formulations…
Strong electron-phonon interaction which limits electronic mobility of semiconductors can also have significant effects on phonon frequencies. The latter is the key to the use of Raman spectroscopy for nondestructive characterization of doping in graphene-based devices. Using in-situ Raman scattering from single layer MoS$_2$ electrochemically top-gated field effect transistor (FET), we show softening and broadening of A$_{1g}$ phonon with electron doping whereas the other Raman active E$_{2g}^{1}$ mode remains essentially inert. Confirming these results with first-principles density functiona…
We employ quasiparticle path integral molecular dynamics to study how the excitonic properties of model semiconductors are altered by electron-phonon coupling. We describe ways within a path integral representation of the system to evaluate the renormalized mass, binding energy, and radiative recombination rate of excitons in the presence of a fluctuating lattice. To illustrate this approach, we consider Fröhlich-type electron-phonon interactions and employ an imaginary time influence functional to incorporate phonon-induced effects nonperturbatively. The effective mass and binding energies ar…
We develop techniques to study the temperature dependent localization, thermalization, and the effects of phonon scattering on the excitons in halide perovskites from the analysis of the emission spectra. The excitonic Urbach edge, when inferred from the low energy tails of the temperature dependent luminescence spectra, is shown to be sensitive to the electron distribution and thermalization. A method to observe the Urbach focus is devised for halide perovskites where the temperature dependence of the excitonic gap is anomalous. The value of the zero-point bandgap renormalization is inferred …
The adiabatic Born-Oppenheimer approximation is considered to be a robust approach that very rarely breaks down. Consequently, it is predominantly utilized to address various electron-phonon properties in condensed matter physics. By combining many-body perturbation and density functional theories we demonstrate the importance of dynamical (nonadiabatic) effects in estimating superconducting properties in various bulk and two-dimensional materials. Apart from the expected long-wavelength nonadiabatic effects, we found sizable nonadiabatic Kohn anomalies away from the Brillouin zone center for …
We investigate the temperature effect on the electronic band structure and optical absorption property of wide-band-gap ternary nitride MgSiN$_2$ using first-principles calculations. We find that electron-phonon coupling leads to a sizable reduction in the indirect gap of MgSiN$_2$, which is indispensable in understanding the optoelectronic properties of this material. Taking the band gap renormalization into account, the band gap of MgSiN$_2$ determined by the quasiparticle GW0 calculations shows good agreement with recent experimental result. The predicted phonon-assisted indirect optical ab…
The unusual Raman spectrum of MgB$_2$ and its formidable temperature dependence are successfully reproduced by means of a parameter-free \emph{ab initio} nonadiabatic theory that accounts for the electron-hole pair scattering mechanisms with the system phonons. This example turns out to be a prototypical case where a strong nonadiabatic renormalization of the phonon frequency is partially washed out by the aforementioned scattering events, bringing along a characteristic temperature dependence. Both electron-hole pair lifetime and energy renormalization effects due to dynamical electron-phonon…
We investigate the interplay of the electron-electron and electron-phonon interactions in the electronic structure of an exotic insulating state in the layered dichalcogenide 1T-TaS2, where the charge-density-wave (CDW) order coexists with a Mott correlation gap. Scanning tunneling microscopy and spectroscopy measurements with high spatial and energy resolution determine unambiguously the CDW and the Mott gap as 0.20-0.24 eV and 0.32 eV, respectively, through the real space electron phases measured across the multiply formed energy gaps. An unusual local reduction of the Mott gap is observed o…
Compared to most tetrahedral semiconductors, the temperature dependence of the absorption edges of the cuprous halides (CuCl, CuBr, CuI) is very small. CuCl and CuBr show a small increase of the gap $E_0$ with increasing temperature, with a change in the slope of $E_0$ vs. $T$ at around 150 K: above this temperature, the variation of $E_0$ with $T$ becomes even smaller. This unusual behavior has been clarified for CuCl by measurements of the low temperature gap vs. the isotopic masses of both constituents, yielding an anomalous negative shift with increasing copper mass. Here we report the iso…
Influence Functional Approach to Non-Perturbative Exciton Binding Renormalization from Phonons
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；Kavli Energy NanoScience Institute（卡弗里能源纳米科学研究所）
We have studied the influence of magnetic order on the optical phonons of the geometrically frustrated spinel ZnCr$_2$O$_4$ from first-principles. By mapping the first-principles phonon calculations onto a Heisenberg-like model, we developed a method to calculate exchange derivatives and subsequently the spin-phonon couping parameter from first-principles. All calculations were performed within LSDA+U.
We study the thermal distribution of phonons in a graphene sheet. Due to the two electronic bands there are two out-of-plane phonon modes with respect to the two sublattices. One of these modes undergoes an Ising transition by spontaneously breaking the sublattice symmetry. We calculate the critical point, the renormalization of the phonon frequency and the average lattice distortion. This transition might be observable in Raman scattering and in transport properties.
"Quasi-harmonic" (QH) theory should not be considered a low-order theory of anharmonic effects in crystals, but should be recognized as an important effect separate from "true" anharmonicity. The original and widely used meaning of QH theory is to put T=0 volume-dependent harmonic phonon energies omega_Q(V) into the non-interacting phonon free energy. This paper uses that meaning, but extends it to include the use of T=0 V-dependent single-particle electron energies epsilon_K(V). It is demonstrated that the "bare" quasiparticle (QP) energies omega_Q(V) and epsilon_K(V) correctly give the first…
Electronic and optical properties of materials are affected by atomic motion through the electron-phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, globa…
The electron-phonon coupling in potassium-doped graphene on Ir(111) is studied via the renormalization of the pi* band near the Fermi level, using angle-resolved photoemission spectroscopy. The renormalization is found to be fairly weak and almost isotropic, with a mass enhancement parameter of lambda= 0.28(6) for both the K-M and the K-G direction. These results are found to agree well with recent first principles calculations.
On the basis of first-principles calculations and the special displacement method, we demonstrate the quantum confinement scaling law of the phonon-induced gap renormalization of graphene quantum dots (GQDs). We employ zigzag-edged GQDs with hydrogen passivation and embedded in hexagonal boron nitride. Our calculations for GQDs in the sub-10 nm region reveal strong quantum confinement of the zero-point renormalization ranging from 20 to 250 meV. To obtain these values we introduce a correction to the Allen-Heine theory of temperature-dependent energy levels that arises from the phonon-induced …
Polarized Raman scattering spectra of superconducting K$_x$Fe$_{2-y}$Se$_2$ and nonsuperconducting K$_{0.8}$Fe$_{1.8}$Co$_{0.2}$Se$_2$ single crystals were measured in a temperature range from 10 K up to 300 K. Two Raman active modes from the $I4/mmm$ phase and seven from the $I4/m$ phase are observed in frequency range from 150 to 325 cm$^{-1}$ in both compounds, suggesting that K$_{0.8}$Fe$_{1.8}$Co$_{0.2}$Se$_2$ single crystal also has two-phase nature. Temperature dependence of Raman mode energy is analyzed in terms of lattice thermal expansion and phonon-phonon interaction. Temperature de…
The frozen-phonon method, used to calculate electron-phonon coupling effects, requires calculations of the investigated structure using atomic coordinates displaced according to a certain phonon eigenmode. The process of "freezing-in" the specific phonon can bring electronic eigenstates that are energetically close in energy into an anticrossing. This electronic anticrossing effect is, however, unrelated to the wanted electron-phonon coupling, and needs to be removed. We present a procedure how to deal with these problematic anticrossing situations and apply it to the band gap zero-point motio…
This study of the one dimensional Su-Schrieffer-Heeger model in a weak coupling perturbative regime points out the effective mass behavior as a function of the adiabatic parameter $ω_π/J$, $ω_π$ is the zone boundary phonon energy and $J$ is the electron band hopping integral. Computation of low order diagrams shows that two phonons scattering processes become appreciable in the intermediate regime in which zone boundary phonons energetically compete with band electrons. Consistently, in the intermediate (and also moderately antiadiabatic) range the relevant mass renormalization signals the ons…
We consider mutual effect of the electron-phonon and strong Coulomb interactions on each other by summing up leading logarithmic corrections via the renormalization group approach. We find that the Coulomb interaction enhances electron coupling to the intervalley A1 optical phonons, but not to the intravalley E2 phonons.
In this paper, we investigate renormalization of charge carrier effective masses and bandgap narrowing in n-GaAs and wurtzite-type n-GaN over a wide range of temperatures and dopant concentrations. The calculations are based on the Green's function formalism. Contrary to the previous works, we consider the regions below as well as above the Mott transition. Special attention is paid to formation of donor subband and condition for the Mott transition. We also take into account the effects caused by optical phonons. The latter strongly depend on the doping level because of dynamic screening. It …
We explore manifestations of electron-phonon coupling on the electron spectral function for two phonon modes in the cuprates exhibiting strong renormalizations with temperature and doping. Applying simple symmetry considerations and kinematic constraints, we find that the out-of-plane, out-of-phase O buckling mode (B_1g) involves small momentum transfers and couples strongly to electronic states near the anti-node while the in-plane Cu-O breathing modes involve large momentum transfers and couples strongly to nodal electronic states. Band renormalization effects are found to be strongest in th…
Tuning Thermal Conductivity and Electron-Phonon Interactions in Carbon and Boron Nitride Moiré Diamanes via Twist Angle Manipulation
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Digital Materials LLC（数字材料有限责任公司）；Emanuel Institute of Biochemical Physics RAS（俄罗斯科学院埃马纽埃尔生物物理化学研究所）
