We studied the optical properties of antiferromagnetic ZnCr2Se4 by infrared spectroscopy up to 28,000 cm-1 and for temperatures from 5 to 295 K. At the magnetic phase transition at 21 K, one of the four phonon modes reveals a clear splitting of 3 cm-1 as a result of spin-phonon coupling, the other three optical eigenmodes only show shifts of the eigenfrequencies. The antiferromagnetic ordering and the concomitant splitting of the phonon mode can be suppressed in a magnetic field of 7 T. At higher energies we observed a broad excitation band which is dominated by a two-peak-structure at about 18,000 cm-1 and 22,000 cm-1, respectively. These energies are in good agreement with the expected spin-allowed crystal-field transition of the Cr3+ ions. The unexpected strength of these forbidden onsite d-d transitions is attributed to a considerable hybridization of the selenium p with the chromium d orbitals.
We study spin dynamics of a spin-Peierls chain with nearest-neighbor and next-nearest-neighbor Heisenberg spin exchange interactions together with a gapped and dispersionless phonon. The dynamical spin correlation function and phonon excitation spectrum are calculated at zero temperature by using dynamical density-matrix renormalization-group method. We find a new spin excitation assisted by non-softening phonon. The excitation is located above phonon in energy and shows a dispersive feature with strong intensity near the momentum $π$. The phonon excitation spectrum is also influenced by the s…
We study quenches of the interaction and electron-phonon coupling parameter in the Hubbard-Holstein model, using nonequilibrium dynamical mean field theory. The calculations are based on a generalized Lang-Firsov scheme for time-dependent interactions or externally driven phonons, and an approximate strong-coupling impurity solver. The interaction quench calculations reveal the phonon-assisted decay of excess doublons, while the quenches of the electron-phonon coupling lead to persistent oscillations of the phonons and to a phonon-enhanced doublon production.
We analyze the excitation spectra of a spin-phonon coupled chain in the presence of a soliton. This is taken as a microscopic model of a Spin-Peierls material placed in a high magnetic field. We show, by using a semiclassical approximation in the bosonized representation of the spins that a trapped magnetic state obtained in the adiabatic approximation is destroyed by dynamical phonons. Low energy states are phonons trapped by the soliton. When the magnetic gap is smaller than the phonon frequencies the only low energy state is a mixed magneto-phonon state with the energy of the gap. We emphas…
We consider the two-chain Heisenberg ladder with antiferromagnetic interactions. Our approach is based on the description of spin excitations as triplets above a strong-coupling singlet ground state. It is shown that interaction with dynamic phonons drastically changes the dispersion of the elementary triplet excitation (magnon) and the spin structure factor. It is also shown that a new triplet excitation appears in the spectrum: the bound state of a magnon and a phonon.
Elementary excitations of the 4k$_F$ charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological unbound solitons carrying charge $e/2$. Relevance to the 4k$_F$ charge density wave instability in $\rm (DI-DCNQI)_2Ag$ or recently discovered in (TMTTF)$_2$X (X=PF$_6$, AsF$_6$) is discussed.
We report on the optical excitation spectra in Sr$_2$VO$_4$. The phonon modes are assigned and their evolution with temperature is discussed in the frame of the different phase transitions crossed upon cooling. Besides the expected infrared-active phonons we observe two additional excitations at about 290 cm$^{-1}$ and 840 cm$^{-1}$ which could correspond to electronic transitions of the V$^{4+}$ ions. Our experimental results are discussed in the context of recent experimental and theoretical studies of this material with a unique spin-orbital ground state.
We consider a model Hamiltonian for a dimer including all the electronic one- and two-body terms consistent with a single orbital per site, a free Einstein phonon term, and an electron-phonon coupling of the Holstein type. The bare electronic interaction parameters were evaluated in terms of Wannier functions built from Gaussian atomic orbitals. An effective polaronic Hamiltonian was obtained by an unrestricted displaced-oscillator transformation, followed by evaluation of the phononic terms over a squeezed-phonon variational wave function. For the cases of quarter-filled and half-filled orbit…
We examined the temperature (T) evolution of the optical conductivity spectra of Sr$_3$Ir$_2$O$_7$ over a wide range of 10-400 K. The system was barely insulating, exhibiting a small indirect bandgap of $\sim$0.1 eV. The low-energy features of the optical d-d excitation (${\hbar}ω$ $<$ 0.3 eV) evolved drastically, whereas such evolution was not observed for the O K-edge X-ray absorption spectra. This suggests that the T evolution in optical spectra is not caused by a change in the bare (undressed) electronic structure, but instead, presumably originates from an abundance of phonon-assisted ind…
A systematic analysis of phonon-plasmon coupled excitations in three-dimensional (3D) polar systems is provided through the prism of both raw and integrated electron energy loss spectroscopy (EELS) and phonon spectra in the whole relevant parametric space, spanned by the adiabaticity parameter and the electron-phonon interaction (EPI) strength. We show that the EPI strength plays a prominent role in distributing spectral weights among excitations, providing an experimentally convenient way to estimate it from integrated spectra. By projecting the excitations onto the phonon degree of freedom, …
Nonlinear processes involving frequency-mixing of light fields set the basis for ultrafast coherent spectroscopy of collective modes in solids. In certain semimetals and semiconductors, generation of coherent phonon modes can occur by a displacive force on the lattice at the difference-frequency mixing of a laser pulse excitation on the electronic system. Here, as a low-frequency counterpart of this process, we demonstrate that coherent phonon excitations can be induced by the sum-frequency components of an intense terahertz light field, coupled to intraband electronic transitions. This nonlin…
Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations
Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）；I. Institute for Theoretical Physics, Universität Hamburg（汉堡大学第一理论物理研究所）；Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg（维尔茨堡大学理论物理与天体物理研究所及维尔茨堡-德累斯顿卓越集群ct.qmat）；Dipartimento di Scienze Fisiche e Chimiche, Università dell’Aquila（阿奎拉大学物理与化学系）
We show how the coupling between the phonons and electrons in a strongly correlated metal can result in phonon frequencies which have a non-monotonic temperature dependence. Dynamical mean-field theory is used to study the Hubbard-Holstein model that describes the κ-(BEDT-TTF)_2 X family of superconducting molecular crystals. The crossover with increasing temperature from a Fermi liquid to a bad metal produces phonon anomalies that are consistent with recent Raman scattering and acoustic experiments.
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $α$-RuCl3 using inelastic X-ray scattering with meV resolut…
The possibility of magnetic-order induced phonon anisotropy in single crystals of MnO and NiO is investigated using inelastic neutron scattering. Below Tn both compounds exhibit a splitting in their transverse optical phonon spectra of approximately 10%. This behavior illustrates that, contrary to general assumption, the dynamic properties of MnO and NiO are substantially non-cubic.
We have investigated the phonon and the magnetic excitations in LaCoO3 by inelastic neutron scattering measurements. The acoustic phonon dispersions show some characteristic features of the folded Brillouin zone (BZ) for the rhombohedrally distorted perovskite structure containing two chemical formula units of LaCoO3 in the unit cell. We observed two transverse optical (TO) phonon branches along (delta, delta, delta), consistent with previously reported Raman active Eg modes which show remarkable softening associated with the spin-state transition [Ishikawa et al., (Phys. Rev. Lett. 93 (2004) …
We report an inelastic light scattering study of single-crystalline NaCu$_2$O$_2$, a spin-chain compound known to exhibit a phase with helical magnetic order at low temperatures. Phonon excitations were studied as a function of temperature and light polarization, and the phonon frequencies are compared to the results of ab-initio lattice dynamical calculations, which are also reported here. The good agreement between the observed and calculated modes allows an assignment of the phonon eigenvectors. Two distinct high-energy two-magnon features as well as a sharp low-energy one-magnon peak were …
We study the recently observed orbital excitations, orbitons, and treat electron-electron correlations and lattice dynamics on equal footing. It is shown that the orbiton energy and dispersion are determined by both correlations and lattice-vibrations. The electron-phonon coupling causes satellite structures in the orbiton spectral function and the elementary excitations of the system are mixed modes with both orbital and phonon character. It is proposed that the satellite structures observed in recent Raman-scattering experiments on LaMnO$_3$ are actually orbiton derived satellites in the pho…
We investigate the temperature evolution of the electronic states in the vicinity of the Fermi level of a non-Fermi liquid (NFL) system, CaRuO3 using ultra high-resolution photoemission spectroscopy; isostructural SrRuO3 exhibiting Fermi liquid behavior despite similar electron interaction parameters as that of CaRuO3, is used as a reference. High-energy resolution in this study helps to reveal particle-hole asymmetry in the excitation spectra of CaRuO3 in contrast to that in SrRuO3. In addition, we observe signature of phonon excitations in the photoemission spectra of CaRuO3 at finite temper…
We have performed Raman measurements on TbMnO3 single crystal under magnetic field along the three crystallographic directions. The flip of the spin spiral plane creates an electromagnon excitation. In addition to the electromagnons induced by the Heisenberg coupling, we have detected the electromagnon created by the Dzyaloshinskii-Moriya interaction along the c axis. We have identified all the vibrational modes of TbMnO3. Their temperature dependences show that only one phonon observed along the polarization axis is sensitive to the ferroelectric transition. This mode is tied to the Tb3+ ion …
Photodetection is an indispensable function of optoelectronic devices in modern communication and sensing systems. Contrary to the near-infrared/visible regions, the fast and sensitive photodetectors operated at room temperature for the far-infrared/terahertz regions are not well developed despite a possibly vast range of applications. The bulk photovoltaic effect (BPVE) in single-phase noncentrosymmetric materials based on the shift current mechanism enables less-dissipative energy conversion endowed with instantaneous responsivity owing to the quantum-mechanical geometric phase of electronic…
Both the Dzyaloshiskii-Moriya interaction and the exchange-striction are shown to affect dynamically the magnetoelectric excitations in the perovskite multiferroic RMnO3. The exchange-striction results in a biquadratic interaction between the spins and the transverse phonons, giving rise to quantum fluctuations of the ferroelectric polarization P. This leads to low-lying phonon modes that are perpendicular to P and to the helical spins at small wave vector but are parallel to P at a wave vector close to the magnetic modulation vector. For spin-1/2 helimagnet, the local polarization can be comp…
Interplay of Spin Waves, Crystal-Field Excitations, and Phonons in Multiferroic Ba3HoRu2O9 revealed by Inelastic Neutron Scattering, Crystal-Field Analysis, and Machine-Learned Phonon Calculations
Rajiv Gandhi Institute of Petroleum Technology（Rajiv Gandhi石油技术学院）；ISIS Neutron and Muon Source, STFC, Rutherford Appleton Laboratory（ISIS中子与缪子源，STFC，卢瑟福阿普顿实验室）；School of Physical Sciences, Indian Institute of Technology Goa（印度理工学院果阿分校物理科学学院）；UGC - DAE Consortium for Scientific Research Mumbai Centre, Bhabha Atomic Research Centre（UGC-DAE科学研究中心孟买中心，巴哈原子研究中心）；Highly Correlated Matter Research Group, Physics Department, University of Johannesburg（约翰内斯堡大学高度关联物质研究组物理系）
Raman scattering experiments on stoichiometric, Mott-insulating LaTiO$_3$ over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of $\sim 800$ cm$^{-1}$ upon cooling below the Néel temperature $T_N = 146$ K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for $T > T_N$, but become sharp and symm…
We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both ap…
Typical density-functional theory calculations that wrongly predict undoped cuprates to be metallic also predict Cu-O half- and full-breathing phonon energies that are significantly softer than observed, presumably because of weak on-site Coulomb repulsion on the Cu 3d orbitals. We used DFT+U calculations with antiferromagnetic supercells of La$_2$CuO$_4$ to establish correlation between the on-site repulsion strength, tuned via adjusting the value of U, and phonon dispersions. We find that breathing and half-breathing phonons reach experimental values when U is tuned to obtain the correct opt…
A remarkable hardening (~ 30 cm-1) of the normal mode of vibration associated with the symmetric stretching of the oxygen octahedra for the Ba2FeReO6 and Sr2CrReO6 double perovskites is observed below the corresponding magnetic ordering temperatures. The very large magnitude of this effect and its absence for the anti-symmetric stretching mode provide evidence against a conventional spin-phonon coupling mechanism. Our observations are consistent with a collective excitation formed by the combination of the vibrational mode with oscillations of local Fe or Cr 3d and Re 5d occupations and spin m…
The ordered adsorbate layer Sn/Si(111) $(\sqrt 3 \times \sqrt 3)$ with coverage of one third of a monolayer is considered as a realization of strong electronic correlation in surface physics. Our theoretical analysis shows that electron-hole pair excitations in this system can be long-lived, up to several hundred nanoseconds, since the decay into surface phonons is found to be a highly non-linear process. We combine first-principles calculations with help of a hybrid functional (HSE06) with modeling by a Mott-Hubbard Hamiltonian coupled to phononic degrees of freedom. The calculations show tha…
We address the problem of Dirac fermions interacting with longitudinal phonons. A gap in the spectrum of fermions leads to the emergence of the Chern--Simons excitations in the spectrum of phonons. We study the effect of those excitations on observable quantities: the phonon dispersion, the phonon spectral density, and the Hall conductivity.
We make the case for an electronic origin of the strong mode, recently seen in ARPES experiments, and, in this regard, further discuss the physics of the spin resonance peak.
We report first principles calculations of the structural parameters and phonon dispersion of the tetragonal non-centrosymmetric heavy fermion compound CeAuAl$_3$. Taking into account weak magnetoelastic interactions of the rare-earth (RE) ions with the spectrum of phonons, we obtain an analytical expression for the hybridization of quadrupole excitations and phonons from the poles of the one-phonon Green-function. In the paramagnetic phase, we predict the formation of mixed modes that may be observed by inelastic neutron scattering. Our results show that magnetoelastic interactions, albeit be…
The polaron concept captures physical situations involving an itinerant quantum particle (excitation) that interacts strongly with bosonic degrees of freedom and becomes heavily boson-dressed. While the Gerlach-Löwen theorem rules out the occurrence of nonanalyticities of ground-state-related quantities for a broad class of polaron models, examples were found in recent years of sharp transitions pertaining to strongly momentum-dependent interactions of an excitation with dispersionless (zero-dimensional) phonons. On the example of a lattice model with Peierls-type excitation-phonon interaction…
Raman scattering measurements on BiFeO3 single crystals show an important coupling between the magnetic order and lattice vibrations. The temperature evolution of phonons shows that the lowest energy E and A1 phonon modes are coupled to the spin order up to the Neel temperature. Furthermore, low temperature anomalies associated with the spin re-orientation are observed simultaneously in both the E phonon and the magnon. These results suggest that magnetostriction plays an important role in BiFeO3.
We present time-resolved photoemission experiments from a peculiar bismuth surface, Bi(114). The strong one-dimensional character of this surface is reflected in the Fermi surface, which consists of spin-polarized straight lines. Our results show that the depletion of the surface state and the population of the bulk conduction band after the initial optical excitation persist for very long times. The disequilibrium within the hot electron gas along with strong electron-phonon coupling cause a displacive excitation of coherent phonons, which in turn are reflected in coherent modulations of the …
We investigate the electronic dispersion of high-Tc superconductor on the basis of the two-dimensional three-band Hubbard model with the electron-phonon interaction together with the strong electron-electron interaction. In our model, it is shown across the hole-doped region of high-Tc superconductor that the electron-phonon interaction makes a dispersion kink, observed along the nodal direction, and that the small isotope effect appears on the electronic dispersion.
We theoretically investigate magnon-phonon hybrid excitations in two-dimensional ferromagnets. The bulk bands of hybrid excitations, which are referred to as magnon-polarons, are analytically shown to be topologically nontrivial, possessing finite Chern numbers. We also show that the Chern numbers of magnon-polaron bands and the number of band-crossing lines can be manipulated by an external magnetic field. For experiments, we propose to use the thermal Hall conductivity as a probe of the finite Berry curvatures of magnon-polarons. Our results show that a simple ferromagnet on a square lattice…
I construct a simple model to demonstrate that when the many-electron quantum state of a material is near a quantum phase transition and the vibrational motion of a phonon explores the potential energy surface near the transition point, then an impenetrable barrier appears at the potential energy surface which restricts the phonon from crossing the transition point and abnormally increases the phonon frequency. The ensuing anomalous enhancement of the electron phonon coupling is general and independent of the specific nature of the electronic quantum phase transition. Understanding and modelli…
We propose that unconventional superconductivity in hydrated sodium cobaltate $Na_xCoO_2$ results from an interplay of electronic correlations and electron-phonon interactions. On the basis of the $t-V$ model plus phonons we found evidences for a) unconventional superconductivity, b) realistic values of $T_c$ and c) the dome shape existing near $x \sim 0.35$. This picture is obtained for $V$ close to the critical Coulomb repulsion $V_c$ which separates the uniform Fermi liquid from $\sqrt{3} \times \sqrt{3}$ CDW ordered phase.
Electron-phonon-driven charge density waves can in some circumstances allow electronic correlations to become predominant, driving a system into a Mott insulating state. New insights into both the Mott state and preceding charge density wave may result from observations of the coupled dynamics of their underlying degrees of freedom. Here, tunneling injection of single electrons into the upper Hubbard band of the Mott charge-density-wave material 1T-TaS2 reveals extraordinarily narrow electronic excitations which couple to amplitude mode phonons associated with the charge density wave's periodi…
Measurements of the thermal conductivity as a function of temperature and magnetic field in the 2D dimer spin system SrCu$_2$(BO$_3$)$_2$ are presented. In zero magnetic field the thermal conductivity along and perpendicular to the magnetic planes shows a pronounced double-peak structure as a function of temperature. The low-temperature maximum is drastically suppressed with increasing magnetic field. Our quantitative analysis reveals that the heat current is due to phonons and that the double-peak structure arises from pronounced resonant scattering of phonons by magnetic excitations.
Ultrafast perturbations offer a unique tool to manipulate correlated systems due to their ability to promote transient behaviors with no equilibrium counterpart. A widely employed strategy is the excitation of coherent optical phonons, as they can cause significant changes in the electronic structure and interactions on short time scales. Here, we explore a promising alternative route: the non-equilibrium excitation of acoustic phonons. We demonstrate that it leads to the remarkable phenomenon of a momentum-dependent temperature, by which electronic states at different regions of the Fermi sur…
The electronic structure, phonons, electron-phonon coupling, and superconductivity are theoretically studied in noncentrosymmetric superconductor ThCoC$_2$ as a function of pressure, in the pressure range 0 - 20 GPa. We found that the electronic band splitting induced by the spin-orbit coupling is enhanced under pressure. In spite of the overall stiffening of the crystal lattice, the electron-phonon coupling constant $λ$ increases with pressure, from 0.583 at 0 GPa to 0.652 at 20 GPa. If the isotropic Eliashberg electron-phonon coupling theory is used to simulate the effect on the critical tem…
Unlike in ordinary metals, in graphene, phonon structure can be seen in the quasiparticle electronic density of states, because the latter varies on the scale of the phonon energy. In a magnetic field, quantization into Landau levels creates even more significant variations. We calculate the density of states incorporating electron-phonon coupling in this case and find that the coupling has pronounced new effects: shifting and broadening of Landau levels, creation of new peaks, and splitting of any Landau levels falling near one of the new peaks. Comparing our calculations with a recent experi…
We study the electron and phonon spectral functions as well as superconductivity for a two dimensional electron gas couped to dipolar phonons via small-momentum transfer scattering. The results reported here are obtained through sign-problem-free quantum Monte-Carlo simulation. Hence aside from modeling there is no further approximations. Our results can be relevant to the high-temperature superconductor at the interface between a unit-cell-thick FeSe and SrTiO3.
This treatise reviews latest results obtained from angle-resolved photoemission spectroscopy (ARPES) on cuprate superconductors, with a special focus on the electron-phonon interaction. What has emerged is rich information about the anomalous electron-phonon interaction well beyond the traditional views of the subject. It exhibits strong doping, momentum and phonon symmetry dependence, and shows complex interplay with the strong electron-electron interaction in these materials.
Advances in light sources and time resolved spectroscopy have made it possible to excite specific atomic vibrations in solids and to observe the resulting changes in electronic properties but the mechanism by which phonon excitation causes qualitative changes in electronic properties, has remained unclear. Here we show that the dominant symmetry-allowed coupling between electron density and dipole active modes implies an electron density-dependent squeezing of the phonon state which provides an attractive contribution to the electron-electron interaction, independent of the sign of the bare el…
We present a dynamical study on the nonlinear conduction behaviour in the commensurate charge-density-wave phase of the quasi-one-dimensional conductor DCNQI$_2$Cu below 75 K. We can accurately simulate magnitude and time-dependence of the measured conductivity in response to large voltage pulses by accounting for the energy exchange between the phononic and electronic subsystems by means of an electrothermal model. Our simulations reveal a distinct non-equilibrium population of optical phonon states with an average energy of E$_{ph}$ = 19 meV being half the activation energy of about $Δ$E$_a$…
We determine the nature of coupled phonons and magnetic excitations in AlFeO3 using inelastic light scattering from 5 K to 315 K covering a spectral range from 100-2200 cm-1 and complementary first-principles density functional theory-based calculations. A strong spin-phonon coupling and magnetic ordering induced phonon renormalization are evident in (a) anomalous temperature dependence of many modes with frequencies below 850 cm-1, particularly near the magnetic transition temperature Tc ~ 250 K, (b) distinct changes in band positions of high frequency Raman bands between 1100-1800 cm-1, in p…
In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero local Berry curvature of low-energy massive Dirac fermions can give rise to nontrivial spin and charge responses, even though the integral of the Berry curvature over all occupied states is zero. In this work, we present a new effect induced by the electronic Berry curvature. By studying electron-phonon interactions in BaMnSb$_2$, a prototype two-dimensional Dirac material possessing two TR-related massive Dirac cones, we find that the nonzero local Berry curvature of electrons can induce a phonon angular momentum. The d…
Unveiling the nature of the bosonic excitations that mediate the formation of Cooper pairs is a key issue for understanding unconventional superconductivity. A fundamen- tal step toward this goal would be to identify the relative weight of the electronic and phononic contributions to the overall frequency (Ω) dependent bosonic function, Π(Ω). We perform optical spectroscopy on Bi2212 crystals with simultaneous time- and frequency-resolution; this technique allows us to disentangle the electronic and phononic contributions by their different temporal evolution. The strength of the interaction (…
Pump-probe experiments have suggested the possibility to control electronic correlations by driving infrared-active phonons with resonant midinfrared laser pulses. In this work we study two possible microscopic nonlinear electron-phonon interactions behind these observations, namely coupling of the squared lattice displacement either to the electronic density or to the double occupancy. We investigate whether photon-phonon coupling to quantized light in an optical cavity enables similar control over electronic correlations. We first show that inside a dark cavity electronic interactions increa…
We report the first systematic measurements of the Raman scattering by electrons in elemental metals of Al, Mo, Nb, Os, Pb, Re, Ta, Ti, V, W and metallic compound La$B_6$. Experimental spectra are modelled on the base of the band structures, calculated within the density functional theory, taking properly into account the effects of electron-phonon scattering. The agreement between our measured and calculated spectra is excellent for the variety of metals, thus providing estimates for the electron-phonon coupling constants and temperature-dependent relaxation rates. The method can be applied f…
