Download Elec-‐ph. and ph.-‐ph. coupling in semiconductors and bismuth

Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Jelena Sjakste and Nathalie Vast
Ecole Polytechnique, Palaiseau, France
Matteo Calandra and Francesco Mauri
University Paris 6, France
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
1
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Outline :
Materials for the energy: towards a description ab initio of thermoelectricity
1.  Ab initio calculation of the thermal conductivity
2.  Electron-phonon coupling for electron transport
Methods for the calculation of the electron-phonon coupling
3.  Wannier method to interpolate electron-phonon
4.  Extension to polar-optical coupling
Keywords: high performance computing, atomic scale,
density functional theory, Boltzmann’s transport equation
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
2
Materials for the energy: towards a descrip7on ab ini7o of thermoelectricity Thermoelectric effect:
• 
Seebeck effect: a temperature gradient at the boundaries of an open
circuit induces a potential difference: => application: generation of
electrical power
silicium-germanium alloys SiGe
• 
Pelletier effect: reversible production of heat at the junction between
two conductors in which there is an electrical current:
=> application: cooling module
Tellure de bismuth Bi2Te3
• 
Aim at a niche market (no large scale e)
•  Figure of merit : ZT=S2 σ T/ κ S : Seebeck coefficient (µV/K)
σ : electrical onductivity κ : thermal conductivity
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
3
Materials for the energy: towards a descrip7on ab ini7o of thermoelectricity A. Shakouri, Annu. Rev. Mater. Res. 41, 399 (2011)
Figure of Merit ZT
ZT=S2 σ T/ κ
Electrical conductivity
Thermal conductivity
(electron + phonon)
S
Seebeck coefficient
In this talk, mainly S et kLattice
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
4
Aim: descrip7on ab ini7o of transport proper7es, of which thermoelectricity Electronic band structure and low energy excitations like phonons are properly
described by density functional theory for semiconductors and bismuth
Thermoelectric
factor of merit
ZT=S2 σ T/ κ Need to describe electron-phonon and phonon-phonon interaction
without ajustable parameters, based on density functional (perturbation) theory
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
5
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Outline :
Materials for the energy: towards a description ab initio of thermoelectricity
➔  1. Ab initio calculation of the thermal conductivity
2.  Electron-phonon and the Seebeck coefficient of silicon
Methods for the calculation of the electron-phonon coupling
3.  Wannier method to interpolate electron-phonon
4.  Extension to polar-optical coupling
Keywords: high performance computing, atomic scale,
density functional theory, Boltzmann’s transport equation
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
6
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Outline :
Materials for the energy: towards a description ab initio of thermoelectricity
➔  1. Ab initio calculation of the thermal conductivity
2.  Electron-phonon and the Seebeck coefficient of silicon
Methods for the calculation of the electron-phonon coupling
3.  Wannier method to interpolate electron-phonon
4.  Extension to polar-optical coupling
Keywords: high performance computing, atomic scale,
density functional theory, Boltzmann’s transport equation
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
7
Boltzmann transport equa7on (BTE) for phonons Need the phonon distribution function nq
Scattering probabilities
of a phonon by the phonon-phonon interaction
ph-ph
Bords de
l’échantillon
Transport coefficient:
Lattice thermal conductivity κL obtained
Supplementary
material: BTE solution – 1.
by Fourier’s
law
Phonon transport proportional
velocitycq
Température
energyħωq
gradient
Distribution phonon nq
Phonon scattering probabilities are computed ab initio
(Monday we have listened to Lorenzo Paulatto’s talk about D3)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
8
Boltzmann transport equa7on for phonons BTE for phonons: on obtains the phonon distribution function nq
ph-ph
Sample boundaries
Phonon-phonon and phonon-interface scattering
… or phonon decay by the
phonon-phononinteraction (anharmonicity)
Phonon creation…
Scattering by sample borders
Phonon scattering probabilities are computed ab initio
(Monday we have listened to Lorenzo Paulatto’s talk about D3)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
9
LaEce thermal conduc7vity in bismuth Trigonal crystal of bismuth : binary direction (perpendicular to the trigonal axis)
Black:
Our ab initio calculation
Bi
Ph-ph scattering
Normal + Umklapp
Scattering
By sample border
100-nm
50-nm
Umklapp 1/T
Green: measurements
Issi, Aust. J. Physics (1979)
Red: Calculations (USA)
Lee, Esfarjani, Mendoza,
Dresselhaus, Gang Chen,
Phys. Rev. B (2014)
Effet of the
nanostructuring:
Decrease of thermal
Conductivity by 50%
in a 100-nmnanostructure
at 100 K
Maksim MARKOV PhD, Ecole Polytechnique
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
10
Phonons scaHering by phonon-­‐phonon coupling (anharmonicity) The three acoustic phonons in bismuth
The longitudinal LA phonon has a short lifetime (>10 ps)
Forte
(high scattering probability
phonon-phonon interaction)
Phonon frequency (cm-1)
Bi
Green, red, blue colors:
scattering probability
by phonon-phonon
interaction
(one color per phonon)
Maksim MARKOV PhD,
Ecole Polytechnique
High symmetry direction in the Brillouin zone
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
11
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Outline :
Materials for the energy: towards a description ab initio of thermoelectricity
1.  Ab initio calculation of the thermal conductivity
➔  2. Electron-phonon coupling for electronic transport
Methods for the calculation of the electron-phonon coupling
3.  Wannier method to interpolate electron-phonon
4.  Extension to polar-optical coupling
Keywords: high performance computing, atomic scale,
density functional theory, Boltzmann’s transport equation
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
12
Input data for Boltzmann transport equa7on (BTE) for electrons Besides electronic energy εk and velocity vk , need sca3ering probabili6es of electrons by phonons through the el-­‐ph interac6on calculated ab ini&o Want the electron distribution function fk e
BTE for electrons
BTE linearized: gk
Transport coefficients:
Electrical conductivity
Seebeck coefficient
S
Need an efficient method to compute electron-phonon coupling matrix elements
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
13
Seebeck coefficient of n-­‐doped silicon (low doping) BTE + ab initio calculations
matrix elements of the e-p interaction
Need
vk
Good agreement by coupling BTE to DFT
G. Kané, M. Markov, J. Sjakste, F. Fugallo, L. Paullatto, M. Lazzeri, F. Mauri and N. Vast (to be submitted)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
14
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Outline :
Materials for the energy: towards a description ab initio of thermoelectricity
1.  Ab initio calculation of the thermal conductivity
2.  Electron-phonon coupling for electron transport
Methods for the calculation of the electron-phonon coupling
➔  3. Wannier method to interpolate electron-phonon
4.  Extension to polar-optical coupling
Keywords: high performance computing, atomic scale,
density functional theory, Boltzmann’s transport equation
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
15
Theore7cal framework to compute electron-­‐phonon coupling 1) Density Functional Theory
&(H 0 − ε 0 ) ψ 0 = 0
(
0
' ρ0 = ψ ψ0
( 0
0
0
v
=
v
(
ρ
)
) eff
eff
ε n,k , ψ n,k ,v eff
Hohenberg, Kohn, Phys. Rev. 1964; Kohn, Sham, ibid 1965"
v eff0 = v eff0 + Δv,
ρ = ρ 0 + Δρ
((H
€ − ε ) Δψ = −P Δv ψ
c
eff
*
) Δρ = ψ Δψ + Δψ ψ
*€€
λ
λ
λ
Δv
=
Δv
(u
eff ,q
eff ,q
q ,Δρ )
+
2) Density Functional Perturbation Theory
ω ,Δv
λ
q
€
λ
eff ,q
0
Baroni, de Gironcoli, Dal Corso, Giannozzi, "
Rev. Mod. Phys. 2001"
€
0
0
0
0
3) Matrix elements for electron-phonon coupling
ψ n,k Δv
λ
eff ,q
elphon.f90
ψ n,k +q
€
Mauri, Zakharov, de Gironcoli, S. Louie PRL 1996"
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
1616
CALC_ISDP op7on Electron-phonon calculation in semiconductors.
Inside Iurii’s dropbox repository
The CALC_ISDP option allows the direct calculation of one single
deformation potential Dk k+q where k is the wave vector of the initial
electronic state and q is the phonon wave vector.
CALC_ISDP is an option of the electron-phonon calculation. It consists
-  in a subroutine calc_isdp.f90 called in ph.x, coming from
elphsum_simple.f90 with no call to symdyn_munu
-  in several modications through the pw.x and ph.x codes.
The calc isdp subroutine is called in the ph.x program when the
CALC_ISDP is set to true in the inputph namelist for electron-phonon
calculation. The ph.x/calc isdp call must come after an scf (pw.x) , then
a PHonon (ph.x) and a then non-scf calculation with the flag calc isdp
set to true (pw.x).
Jelena
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE,
Matteo CALANDRA,
MAURI
Sjakste, Nathalie
Vast andNathalie
ValeriyVAST,
Tyuterev,
Phys. Rev.Francesco
Lett. 99,
236405 (2007).
17
Electron-­‐phonon scaHering 7me 3) Matrix elements for el-ph coupling :
λ
ψ n,k Δv eff
,q ψ n,k +q
calc_isdp.f90
4) TAU-ISDP programme tau_isdp.f90
Probability of the transition from |n;k> to |n’;k+q>
2
€
2π
n,n'
Pk,k +q =
!
n,k Δv eff n',k + q
δ (ε nk − ε n',k +q )
Integration of all possible final valleys
9
Electron-phonon scattering time
!
"
Γn",""k" = "
<"τn" ,""k" >"
Energy eV
€
d 3q n,n '
1
Γn ,k (T ) = 2∑ ∫ 3 Pk ,k + q ( N q (ωq , T ) + )
8π
2
8
n'
Nq – Bose-Einstein
phonon distribution
Ψ n,k+q
Ψ n,k D
7
6
X1
L1
X3
GaAs
Γ1
Sjakste, Vast, Tyuterev, PRL (2007)
Γ
15
5 meeting : linear
Advanced Quantum ESPRESSO developer’s
response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
18
TAU_ISDP programme Inside Iurii’s dropbox repository
The tau_isdp program contains the calculation of the electron-phonon
scattering rate/time for a given initial electronic state according to the
Fermi Golden Rule.
Use: the tau_isdp can be used independently,
after a set of direct calculations performed with the calc_isdp, or
after a Wannier interpolation of the electron-phonon matrix elements.
If compiled inside the Quantum ESPRESSO package it could make use
of refold_q_ws.f90 subroutine in D3Q subroutine and w0gauss.f90
subroutine in PW.
Jelena Sjakste, Nathalie Vast and Valeriy Tyuterev, Phys. Rev. Lett. 99, 236405 (2007).
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
19
Wannier method to interpolate electron-­‐phonon matrix elements (1) Maximally localized Wannier functions (MLWF) are defined as:
QE Bloch functions
The matrix U is obtained at the end of the Wannierization procedure.
The converse transformation is
The deformation potential is defined as
Fourier transform of the phonon
displacement, s=(A,α)
Bloch-function periodic-part
Nkw= number of k-points used in the wannierization.
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
20
Wannier method to interpolate electron-­‐phonon matrix elements (2) The calculation of
is very expensive as it requires one ph.x calculation for each q.
Thus obtaining d on ultradense phonon and electron momentum grids
brute force is difficult (impossible).
The solution is to use maximally localized Wannier function.
We first calculate dsmn (k+q,k) on a coarse k and q point grid with ph.x
(we assume Nq=Nkw)
Then we write the deformation potential in the Wannier function basis using MLWF
where the R are on a supercell compatible with Nkw and translational invariance has been used.
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
21
Wannier method to interpolate electron-­‐phonon matrix elements (3) s
If dmn (R,RL) is localized, then we can go back in k, q space
where now q and k are any point (and not necessary points of the initial coarse grid).
The localization of the deformation potential in real space is the key property.
It depends on:
1. The localization of Wannier functions (for k vectors)
2. How much the force constants are short range (for q vectors)
In metals, despite the presence of Kohn anomalies, the method works very well.
In polar insulators special care is needed to treat the q->0 limit.
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
22
How it works in prac7ce (1) 1. Obtain matrices U and functions ψkn on a Nkw k-point grid from Wannier90
2. Calculate the dynamical matrices and derivatives of VSCF on the Nkw q-point
grid reduced by symmetries (ph.x)
3. Use symmetries to obtain the derivatives of VSCF on the full Nkw q-point
(dfile_star.f90 already included in ph.x – used also by D3 L. Paulatto)
4. Calculate dmns(k+q,k) on for k in the full Nkw k-point and q in the full Nkw
q-point grid using the same wavefunctions saved in step 1:
this implies assuming that both k and k+q belongs to the Nkw grid a part from
trivial refoldings)
( ph.x, routine ep_matrix_element_wannier.f90 included in Phonon/PH)
5. Obtain first dmns(R,RL) and then dmns(k+q,k) at any k and q by using U from
step 1 and dmns(k+q,k) from step 4 (independent code epiq.f90/epik.f90 ,
not yet included in qe-forge)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
23
How it works in prac7ce (2) Note that in Step 4 :
the use of the same wavefunction used in step 1 is crucial as
any spurious phase (e.g. random phase from the diagonalization procedure)
kills the localization of Wannier functions and of dmns(R,RL)
Step 1 Wannier90 package
Step 2 ph.x
Steps 3 and 4 are already included in SVN version of ph.x
Step 3 dfile_star.f90 already included in ph.x
Step 4 ph.x, routine ep_matrix_element_wannier.f90
They will be probably extracted into a separate program soon.
Step 5: independent code epiq.f90/epik.f90 will be included soon
M. Calandra, G. Profeta, and F. Mauri, PRB 82, 165111 (2010)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
24
Electron-­‐phonon coupling in metal : phonon linewidth, λ Adiabatic and nonadiabatic phonon idspersion In a Wannier approach
M. Calandra, G. Profeta, and F. Mauri, PRB 82, 165111 (2010)
High pressure hydrogen sulfide from first-principles: a strongly anharmonic phonon-mediated
superconductor
I. Errea, M. Calandra, C. J. Pickard, J. Nelson, R. J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, and
F. Mauri, PRL 114, 157004 (2015)
Quantum hydrogen-bond symmetrization and high-temperature superconductivity in hydrogen
sulfide,
I. Errea, M. Calandra, C. J. Pickard, J. Nelson, R. J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, and
F. Mauri, arXiv:1512.02933, to Appear in Nature
Universal increase in the superconducting critical temperature of two-dimensional
semiconductors at low doping by the electron-electron interaction
M. Calandra, P. Zoccante, and F. Mauri, PRL 114, 077001 (2015)
Intercalant and intermolecular phonon assisted superconductivity in K-doped picene
M. Casula, M. Calandra, G. Profeta, and F. Mauri, PRL 107, 137006 (2011)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
25
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches Outline :
Materials for the energy: towards a description ab initio of thermoelectricity
1.  Ab initio calculation of the thermal conductivity
2.  Electron-phonon coupling for electron transport
Methods for the calculation of the electron-phonon coupling
3.  Extension to polar-optical coupling
➔  4. Extension to polar-optical coupling
Keywords: high performance computing, atomic scale,
density functional theory, Boltzmann’s transport equation
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
26
Electron-­‐phonon coupling in a polar materials: troubles with Fröhlich’s interac7on •  Need to interpolate DFT matrix elements:
Ψn,k ΔW qλ Ψn',k +q
Vast, Sjakste, Kane, Trinite, Book Chapter, Simulation of transport in nanodevices, ed. Dollfus/Triozon (exp. 2016)
Sjakste, Timrov, Gava, Mingo, Vast, Annual Reviews of Heat Transfer 17, 333 (2014)
•  But LO phonon generates macroscopic electric field
Matrix element (eV/A)
€
GaAs
Non-local part from Vogl’s exact theory
4π ie
q
Z (α )eλ (αq̂)
2 µ ∑ µλ
ε∞ q
α
Vogl, PRB 13 (1976)
The Fröhlich coupling is
not localised in real space!
Usual methods fail !
M. Calandra, G. Profeta, F. Mauri, PRB 82, 165111 (2010)
F. Giustino, M.L. Cohen, S.G. Louie, PRB 76, 165108 (2007)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
27
Electron-­‐phonon coupling for polar materials Reciprocal space
Bloch functions
Initial grid
Ψn,k ΔW qλ Ψn',k + q
- Non-local part
GaAs
Real space
Maximally localized Wannier functions
€
Interpolation on dense grid
Reciprocal space
Bloch functions
Dense grid
Ψn,k ΔW qλ Ψn',k + q
+ Non-local part
More accurate description of the electron-phonon matrix elements
J. Sjakste, N. Vast, M. Calandra, F. Mauri, PRB 92, 054307 (2015)
Verdi and Giustino, PRL 115, 176401 (2015)
€Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
28
Time-­‐, angle-­‐ and energy-­‐ resolved spectroscopy in photoexcited GaAs
J. Kanasaki, H. Tanimura, K. Tanimura, PRL 113, 237401 (2014)
H. Tanimura, J. Kanasaki, K. Tanimura, J. Sjakste, N. Vast, M. Calandra, F. Mauri, submitted (2015)
GaAs
Pump:
2.3 eV
Probe:
at 0.75 –to
0.55 eV
Above
Conduction
Band
minimum
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
29
Dynamics of hot electrons en7rely governed by electron-­‐phonon scaHering Solid line: our interpolation of matrix elements
GaAs
n,n', λ
k,k ± q
P
2π
=
Ψn,k ΔW qλ Ψn',k ± q
!
!
Relaxation time (ps)
τ nk =
€
2
δ (ε n',k ± q − ε n,k ∓ !ω qλ )
Γnk
Symbols: relaxation times from expt.
€
« Slow » time: energy relaxation
all phonons are involved
« Fast » time: momentum relaxation
Wavepacket spreads over Brillouin zone
Tanimura, Kanasaki, Tanimura, Sjakste, Vast, Calandra, Mauri, submitted (2015)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
30
What can the code epiq calculate ? 1.  Electron-phonon coupling in metals (phonon linewidth , λ)
2.  Electron-phonon coupling in polar and non polar semiconductors
3.  Lifetimes of excited states in semiconductors
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
31
Life7me of « excited states » due to electron-­‐phonon coupling GaAs
BC
Band structure
and broadening
BV
Broadening
due to el-ph
BC: conduction band
BC
BV: valence band
BV
DOS of final
states restricted
by ε- and kconservation
rules
Minor role of matrix elements
BC
BV
BC
Proportion of
Fröhlich
interaction
BV
Non-vanishing Fröhlich
Interaction through BZ
J. Sjakste, N. Vast, M. Calandra, F. Mauri, PRB 92, 054307 (2015)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
32
What can the code epiq calculate ? 1.  Electron-phonon coupling in metals (phonon linewidth , λ)
2.  Electron-phonon coupling in polar and non polar semiconductors
3.  Lifetimes of excited states in semiconductors
4.  Phonon frequencies in metals with ultradense k- and q-points grids
but no Acoustic Sum Rule (ASR)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
33
Phonon frequencies on ultradense grids (1) MgB2
Phonon dispersion
s
Substantial enhancement of the
in-plane E2g Kohn anomaly related
to the inter-cylinder nesting
Kortus et al. PRL 86, 4656 (2001)
M. Calandra, G. Profeta and F. Mauri, PRB 82, 165111 (2010)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
Phonon frequencies on ultradense grids (2) MgB2
Phonon dispersion
Substantial enhancement of the
in-plane E2g Kohn anomaly related
to the inter-cylinder nesting
A Kohn-anomaly appears on E2g
and B1g branches along ΓA
s
Kortus et al. PRL 86, 4656 (2001)
M. Calandra, G. Profeta and F. Mauri, PRB 82, 165111 (2010)
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
What can the code epiq calculate ? 1.  Electron-phonon coupling in polar and non polar semiconductors
2.  Lifetimes of excited states in semiconductors
3.  Phonon frequencies in metals with ultradense k and q points grids (no AS
rule yet)
4.  Electron-phonon coupling in metals (phonon linewidth , λ)
5.  Double resonant Raman (Herziger et al., PRL 113,187401 (2014) )
6.  Multiband Migdal Eliashberg
Part of these developments will be public very soon
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
Jelena SJAKSTE, Nathalie VAST, Matteo CALANDRA, Francesco MAURI
36
Elec-­‐ph. and ph.-­‐ph. coupling in semiconductors and bismuth, theore7cal approaches J.Sjakste, G. Kane, M. Markov, G. Fugallo, N. Vast Univ. Paris 6 (F. Mauri, M. Lazzeri, M. Calandra) Maksim Markov Gaston Kané
Jelena Sjaskte
Advanced Quantum ESPRESSO developer’s meeting : linear response, TRIESTE 2016
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