EPW: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions

Poncé, Samuel; Margine, E. R.; Verdi, Carla; Giustino, Feliciano

doi:10.1016/j.cpc.2016.07.028

Cited by 1,032 publications

(859 citation statements)

References 168 publications

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“…In semiconductors, the highly heterogeneous electron-phonon interactions (e.g. in polar semiconductors with Fröhlich interactions [9]) and, in some cases, the higher lattice thermal conductivity in comparison to metals weaken the hypothesis of a thermalized phononic subsystem [10,11], hence calling for the reexamination of the 2T physical picture in semiconductors.In this context, the advent of first-principles techniques able to predict the mode-and energy-resolved electronphonon [12][13][14] and phonon-phonon interactions [15,16] provides an important opportunity: In their modern implementations [13,16,17], these methods have been able to predict lattice thermal conductivities [18][19][20][21], the temperature-and pressure-dependence of the electronic bandgap [22][23][24][25][26][27][28], electrical conductivities [29,30], and hot carrier dynamics [31,32]. However, to the best of our knowledge and despite these early successes, these approaches have yet to be applied to the computation of electron-induced, non-equilibrium phonon distributions and their effects on thermal relaxation of electrons.…”

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“…Hence, we expect our simulation method and the approximation of f nk (t) to be quantitative at subsequent times. Specifically, we define the EPI scattering potential as an explicit functional of the phonon and electron occupation functions at time t, and compute it using Fermi's golden rule:, in which |g qν (mk + q, nk)| is the time-independent electron-phonon matrix elements involving electronic states |nk and |mk + q and vibrational state |qν evaluated using Wannier interpolation with the EPW code [13]. M mnνkq (t) is the timedependent joint density of states computed from n qν (t), f nk (t), f mk+q (t), and the electron and phonon spectral densities (detailed formulas are given in Supplemental Material).…”

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confidence: 99%

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Theory of Thermal Relaxation of Electrons in Semiconductors

Sridhar¹,

Chan²,

Darancet³

2017

Phys. Rev. Lett.

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We compute the transient dynamics of phonons in contact with high energy "hot" charge carriers in 12 polar and non-polar semiconductors, using a first-principles Boltzmann transport framework. For most materials, we find that the decay in electronic temperature departs significantly from a single-exponential model at times ranging from 1 ps to 15 ps after electronic excitation, a phenomenon concomitant with the appearance of non-thermal vibrational modes. We demonstrate that these effects result from the slow thermalization within the phonon subsystem, caused by the large heterogeneity in the timescales of electron-phonon and phonon-phonon interactions in these materials. We propose a generalized 2-temperature model accounting for the phonon thermalization as a limiting step of electron-phonon thermalization, which captures the full thermal relaxation of hot electrons and holes in semiconductors. A direct consequence of our findings is that, for semiconductors, information about the spectral distribution of electron-phonon and phonon-phonon coupling can be extracted from the multi-exponential behavior of the electronic temperature.Following the seminal works of Kaganov et al. [1] and Allen [2], the thermalization of a system of highly energetic charge carriers with a lattice is frequently understood as an electron-phonon mediated, temperature equilibration process with a single characteristic timescale τ el-ph . Such description, referred to as the two temperature (2T) model, relies on the central assumption that both electrons and phonons remain in distinct thermal equilibria and can therefore be described by timedependent temperatures T el (t) and T ph (t) during the thermal equilibration process. In metals, due to the relative homogeneity of the electron-phonon interactions and the rates of thermalization within the electronic and phononic subsystems, the hypothesis of subsystem-wide thermal equilibrium is generally accurate, and the 2T model has been successful in modeling ultra-fast laser heating [3][4][5], despite some notable deviations from the 2T predictions in graphene and aluminum [6][7][8]. In semiconductors, the highly heterogeneous electron-phonon interactions (e.g. in polar semiconductors with Fröhlich interactions [9]) and, in some cases, the higher lattice thermal conductivity in comparison to metals weaken the hypothesis of a thermalized phononic subsystem [10,11], hence calling for the reexamination of the 2T physical picture in semiconductors.In this context, the advent of first-principles techniques able to predict the mode-and energy-resolved electronphonon [12][13][14] and phonon-phonon interactions [15,16] provides an important opportunity: In their modern implementations [13,16,17], these methods have been able to predict lattice thermal conductivities [18][19][20][21], the temperature-and pressure-dependence of the electronic bandgap [22][23][24][25][26][27][28], electrical conductivities [29,30], and hot carrier dynamics [31,32]. However, to the best of our knowledge and despite these ...

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confidence: 99%

mentioning

confidence: 99%

Theory of Thermal Relaxation of Electrons in Semiconductors

Sridhar¹,

Chan²,

Darancet³

2017

Phys. Rev. Lett.

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“…4(a)], leading to a weak occupation of the conduction bands while retaining full occupation of the valence bands. We use the EPW [29,30] code of the QUANTUM ESPRESSO [31] package to evaluate Eq. (1) on a fine mesh in the BZ.…”

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confidence: 99%

Momentum-Resolved View of Electron-Phonon Coupling in Multilayer WSe2

et al. 2017

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We investigate the interactions of photoexcited carriers with lattice vibrations in thin films of the layered transition metal dichalcogenide (TMDC) WSe 2 . Employing femtosecond electron diffraction with monocrystalline samples and first-principles density functional theory calculations, we obtain a momentumresolved picture of the energy transfer from excited electrons to phonons. The measured momentumdependent phonon population dynamics are compared to first-principles calculations of the phonon linewidth and can be rationalized in terms of electronic phase-space arguments. The relaxation of excited states in the conduction band is dominated by intervalley scattering between Σ valleys and the emission of zone boundary phonons. Transiently, the momentum-dependent electron-phonon coupling leads to a nonthermal phonon distribution, which, on longer time scales, relaxes to a thermal distribution via electron-phonon and phononphonon collisions. Our results constitute a basis for monitoring and predicting out of equilibrium electrical and thermal transport properties for nanoscale applications of TMDCs. DOI: 10.1103/PhysRevLett.119.036803 Semiconducting transition metal dichalcogenides combine crystal structures of chemically stable twodimensional layers with indirect band gaps in the visible and near infrared optical range. Their intrinsic stability down to monolayer thicknesses [1,2] in combination with the possibility to create artificial stacks [3,4] suggests them for electronic and optoelectronic applications like nanoscale transistors or photodetectors with atomically sharp p-n junctions [5][6][7]. In such devices, the electronic mobilities, electronic coupling, and heat conductivities within the layers and across interfaces are of central interest. Whereas macroscopic heat and electrical transport properties can be measured directly, the observation of the underlying microscopic processes, i.e., the scattering processes of carriers and of phonons, requires methods with time, momentum, and energy resolution to be understood in detail. Such information can be decisive in the correct determination of transport properties [8,9] or energy relaxation [10][11][12]. A momentum-resolved view of scattering processes will in addition be of uttermost importance in conceiving novel quantum technologies harnessing spin and valley degrees of freedom [13][14][15], as they utilize carrier populations at specific positions in momentum space. While time-and angle-resolved photoemission spectroscopy provides this level of detail for electron dynamics, see, for instance, Refs. [16,17], techniques for studying ultrafast structural dynamics have not yet reached the equivalent level of resolution. Recently, the investigation of the time-and momentum-resolved phonon population has been demonstrated with ultrafast x-ray and electron diffraction [18][19][20][21].This work reports a momentum-resolved study of scattering processes and the resulting energy transfer between photoexcited electrons and phonons in thin bulklike films of WS...

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“…The Wannier interpolation method was used to obtain ultradense electronic structure, phonon dispersion, and el-ph couplings matrix as implemented in the Wannier90 [44] and EPW code. [45,46] The el-ph coupling matrix was interpolated from 10 × 10 × 1 coarse k-mesh and 5 × 5 × 1 coarse q-mesh into 120 × 120 × 1 k-and q-meshes for stanene. In graphene, the el-ph coupling matrix was interpolated from 6 × 6 × 1 coarse k-and q-mesh into 120 × 120 × 1 k-and q-meshes.…”

Section: Charge Carrier Mobility and Electron-phonon Couplingsmentioning

confidence: 99%

“…[40] In this work, we consider all the el-ph scattering processes in stanene to calculate the carrier mobility. The state-of-the-art DFPT [41] coupled with a Wannier interpolation scheme [42] as implemented in the Quantum ESPRESSO, [43] Wannier90, [44] and EPW packages [45,46] was employed to obtain the ultradense electronic band structures, phonon dispersion, and el-ph coupling matrix elements. With all these ingredients, the Boltzmann transport theory with relaxation time approximation was used to determine the intrinsic charge carrier mobilities.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Charge Transport in Stanene: Roles of Bucklings and Electron–Phonon Couplings

Nakamura

Zhao

et al. 2017

Adv Elect Materials

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The intrinsic charge transport of stanene is investigated by using density functional theory and density functional perturbation theory coupled with Boltzmann transport equations at the first‐principles level. The Wannier interpolation scheme is applied to calculate the charge carrier scatterings with all branches of phonons considering dispersion for the whole range of the first Brillouin zone. The intrinsic electron and hole mobilities are calculated to be (2–3) × 103 cm2 V−1 s−1 at 300 K. It is found that the intervalley scatterings from the out‐of‐plane and the transverse acoustic phonon modes dominate the carrier transport process. By contrast, the mobilities obtained by the conventional deformation potential approach are found to be as large as (2–3) × 106 cm2 V−1 s−1 at 300 K, in which the longitudinal acoustic phonon scattering in the long wavelength limit is assumed to be the dominant scattering mechanism. The inadequacy of the deformation potential approximation in stanene is attributed to the buckling in its honeycomb structure, which originates from the sp2–sp3 orbital hybridization and breaks the planar symmetry. This paper further proposes a strategy to enhance carrier mobilities by suppressing the out‐of‐plane vibrations through clamping by a substrate.

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EPW: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions

Cited by 1,032 publications

References 168 publications

Theory of Thermal Relaxation of Electrons in Semiconductors

Theory of Thermal Relaxation of Electrons in Semiconductors

Momentum-Resolved View of Electron-Phonon Coupling in Multilayer WSe2

Intrinsic Charge Transport in Stanene: Roles of Bucklings and Electron–Phonon Couplings

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