First-principles dynamics of electrons and phonons*

Question

1. What contributions have the authors mentioned in the paper "First-principles dynamics of electrons and phonons" ?

2. What is the effect of the narrow width of the electronic bands on the carrier?

3. How can the authors compute the MFPs along different crystallographic directions?

4. How many q-points are needed to converge the e-ph matrix?

Accepted Answer

The authors review this theoretical and computational framework, focusing on perturbative treatments of scattering, dynamics and transport of coupled electrons and phonons.. The authors discuss application of these first-principles calculations to electronics, lighting, spectroscopy and renewable energy.

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The narrow width of the electronic bands induces strong e-ph coupling, and the carriers in these materials, also known as polarons, become localized and strongly coupled with the lattice.

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The MFPs along different crystallographic directions can be computed by multiplying the band velocity by the RT, namely, Lnk = (vnk · k̂) τnk, where the unit crystal momentum vector k̂ is oriented along the ballistic propagation direction.

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To converge the e-ph RTs, interpolation of the e-ph matrix elements is necessary since the sum in eq. 12 requires 104−106 q-points to converge [32–34,36], an unrealistic task for direct DFPT calculations due to computational cost.

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The key contributions of first-principles calculations in this area include understanding dynamical and excited state processes with unprecedented microscopic detail − thus both complementing experiment and providing deeper understanding − as well as guiding the development of novel technologies in electronics, lighting, and energy conversion and storage.

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Due to computational cost, transport calculations employing ab initio RTs have so far been carried out mainly on materials with simple unit cells; research efforts to compute RTs in larger system are underway.

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Scattering with defects, either elastic [74] or inelastic [75], is important in many cases of practical relevance and has also been computed from first principles, though work in this area is still in its nascent stage.

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Transport in organic materials and correlated oxides is typically described as a hopping process of localized polarons, leading to a peculiar temperature dependence of the mobility.

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Expanding the equation of motion in component Green’s functions for different parts of the contour, and employing the Langreth rules [30] to convert integrals containing the product of functions on the contour to integrals on the real time axis, eq. 43 is converted to multiple dynamical equations, called the KBEs.

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The Auger rate (AR) can be computed using the FGR, by obtaining the square e-e matrix elements |M1234|2 forAuger scattering among four given electronic states.

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In particular, Auger scattering limits the efficiency of electronic, optoelectronic and photovoltaic devices through carrier recombination.

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The MFPs computed for noble metals such as Au and Ag show a volcano shape with maximum MFPs of 15−30 nm, which rapidly degrade to ∼5 nm for HCs with energies a few eV away from the Fermi energy.

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Solving such a large set of coupled differential equations would be challenging, but it may enable dramatic advances in understanding coupled carrier and phonon dynamics, a holy grail in solid state physics.

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Boltzmann transport theory (e.g., eq. 45) cannot be applied to compute the conductivity due to the localized nature of the carriers, and the e-ph interaction often cannot be treated perturbatively.

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such diffusion length calculations are still nearly absent in the literature, mainly due to the challenge of including multiple recombination processes.

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Summing over the Matsubara frequencies ωj and performing the Wick rotation to the real frequency axis [37], the imaginary part of the GD diagram gives the e-ph scattering rate in eq.

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For the past few decades, first-principles calculations have focused on computing the energetics of electrons, phonons and excited states.

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A rigorous and general approach to derive eq. 12 consists of treating the e-ph interaction perturbatively, using the Feynman-diagram technique.

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The interactions to include in these calculations are challenging to establish a priori, and since measuring Auger rates experimentally is difficult, validation of the computed results is still non-trivial.

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By computing the scattering rate due to different phonon modes, their work showed that, contrary to common notions, all optical and acoustic modes contribute substantially to excited electron energy loss, with a dominant contribution from transverse acoustic phonons.

Accepted Answer

The authors demonstrated that a HC distribution characteristic of Si under solar illumination thermalizes within 350 fs, in excellent agreement with pump-probe experiments [32].

First-principles dynamics of electrons and phonons*

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Most frequently asked questions

1. What contributions have the authors mentioned in the paper "First-principles dynamics of electrons and phonons" ?

2. What is the effect of the narrow width of the electronic bands on the carrier?

3. How can the authors compute the MFPs along different crystallographic directions?

4. How many q-points are needed to converge the e-ph matrix?

5. What are the key contributions of first principles calculations in materials?

6. Why have mainly been carried out transport calculations on materials with simple unit cells?

7. What is the nascent stage of the BTE formalism?

8. What is the common description of transport in organic materials?

9. What is the simplest way to convert the equation of motion in component Green’s functions?

10. How can the Auger rate be computed using the FGR?

11. What is the effect of Auger scattering on the efficiency of electronic, optoelect?

12. How do the authors compute the MFPs for noble metals?

13. What is the way to solve a large set of coupled differential equations?

14. Why can't eq. 45 be applied to compute the conductivity?

15. Why are diffusion length calculations still scarce in the literature?

16. What is the e-ph scattering rate in eq. 12?

17. What is the main focus of the first-principles calculations?

18. What is the common method of derive eq. 12?

19. What are the main problems of the Auger calculations?

20. What is the contribution of different modes to excited electron energy loss?

21. How does the HC distribution of Si thermalize?

Figures

Citations

Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO 3

Combining Electron-Phonon and Dynamical Mean-Field Theory Calculations of Correlated Materials: Transport in the Correlated Metal Sr$_2$RuO$_4$

Machine learning approach for vibronically renormalized electronic band structures

Predicting Phonon-Induced Spin Decoherence from First Principles: Colossal Spin Renormalization in Condensed Matter.

References

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

Quantum Computation and Quantum Information

Quantum computation and quantum information

Spintronics: Fundamentals and applications

Quantum Computation and Quantum Information

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