Electron-electron and electron-phonon correlation effects on the finite-temperature electronic and optical properties of zinc-blende GaN

Kawai, H.; Yamashita, Koichi; Cannuccia, Elena; Marini, Andrea

doi:10.1103/physrevb.89.085202

Cited by 60 publications

(52 citation statements)

References 34 publications

(48 reference statements)

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“…This result is in line with earlier estimations of many-body effects on the electron-phonon coupling in various systems [40][41][42][43][44][45], As a third approach, the diagrammatic method of manybody perturbation theory, from which AHC originates, allowed Giustino et al [46] to compute the ZPR and the temperature dependence of the diamond band gap with Wannier functions in the density-functional perturbation theory (DFPT) [47,48] framework. Marini et al [49][50][51][52] focused on the dynamical effects, beyond the adiabatic approximation, which are absent from the two previous approaches (MD and FP).…”

Section: Introductionmentioning

confidence: 99%

Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

et al. 2014

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The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g., density-functional theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principles context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the density-functional perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion approximation. For the two different numerical approaches without non-rigid-ion terms, the agreement is better than 7 p t V in the case of diamond, which represent an agreement to five significant digits. The magnitude of the non-rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies.

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Section: Introductionmentioning

confidence: 99%

Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

et al. 2014

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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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confidence: 99%

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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“…The Allen-Heine-Cardona (AHC) theory [2][3][4] is one of the current state-of-the-art methods to study the effect of electron-phonon coupling (EPC) on electronic structures from first-principles density functional theory (DFT) and density functional perturbation theory (DFPT). Zero-point renormalization and temperature dependence of the electronic band gap [5][6][7][8][9][10][11][12][13] , optical responses [14][15][16] , and topological properties 17 are being actively investigated with the AHC theory.…”

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confidence: 99%

Phonon-induced renormalization of electron wave functions

Lihm

Park

2020

Phys. Rev. B

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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 wavefunction, which is crucial if inter-band 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 wavefunctions. Our theory can describe both the diagonal and off-diagonal components of the Debye-Waller selfenergy 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 new door for studying temperature-induced topological phase transitions in materials both with and without inversion symmetry.Interactions between electrons and phonons induce a temperature-dependent renormalization of electronic structures 1 . The Allen-Heine-Cardona (AHC) theory 2-4 is one of the current state-of-the-art methods to study the effect of electron-phonon coupling (EPC) on electronic structures from first-principles density functional theory (DFT) and density functional perturbation theory (DFPT). Zero-point renormalization and temperature dependence of the electronic band gap 5-13 , optical responses 14-16 , and topological properties 17 are being actively investigated with the AHC theory.In the AHC theory 2-4 , the matrix elements of the second-order derivatives of the electron potential is required to compute the Debye-Waller (DW) contribution to the electron self-energy. This matrix element is approximated using the rigid-ion approximation (RIA), which assumes that the potential is a sum of atomcentered contributions. Then, by invoking the translational invariance of the electron eigenvalues, one can calculate the second-order EPC matrix elements from the first-order EPC matrix elements. However, this method is applicable only to the band-diagonal part of the DW self-energy. An approximation scheme for the full DW self-energy matrix including off-diagonal components has been absent.The missing off-diagonal components of the self-energy are essential to describe the hybridization of energy eigenstates 1,[18][19][20][21][22] . Thus, the current scope of the firstprinciples AHC theory is limited in that the EPC-induced change of the electron eigenstate wavefunctions is neglected. This theoretical limitation even precluded a complete study of electronic structures across an EPCinduced topological transition. For example, in Ref. 17 , the renormalized electron energy was calculated only at Γ where the wavefunction hybridization is forbidden due to...

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Electron-electron and electron-phonon correlation effects on the finite-temperature electronic and optical properties of zinc-blende GaN

Cited by 60 publications

References 34 publications

Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

Theory of Thermal Relaxation of Electrons in Semiconductors

Phonon-induced renormalization of electron wave functions

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