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Non Equilibrium Many-Body Perturbation Theory from first principles - - PowerPoint PPT Presentation

Jan 26, 2023 178 likes •808 views

Non Equilibrium Many-Body Perturbation Theory from first principles D. Sangalli CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Monterotondo Scalo, Italy. MaX conference 2018 29 th 31 st

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Non Equilibrium Many-Body Perturbation Theory from first principles

  • D. Sangalli

CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Monterotondo Scalo, Italy. MaX conference 2018 29th – 31st January 2018, Trieste, Italy

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Higher accuracy Larger systems High throughput

New computational resources make possible to tackle more challenging computational problems from first-principles

New physics Ultra-fast and non equilibrium physics QP vs KS energies BSE vs IP absorption Extend the limits of system size DFT (103 – 104 atoms) - MBPT (102 103 atoms) Surfaces, interfaces, nanostructures ab-initio

yambopy

Yambo and HPC

yambo plugin

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SLIDE 3

Higher accuracy Larger systems High throughput New physics Ultra-fast and non equilibrium physics QP vs KS energies BSE vs IP absorption Extend the limits of system size DFT (103 – 104 atoms) - MBPT (102 103 atoms) Surfaces, interfaces, nanostructures ab-initio

yambopy

Yambo and HPC

yambo plugin

New computational resources make possible to tackle more challenging computational problems from first-principles

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SLIDE 4

Why so fast ?

Spatial resolution of ~0.06 mm = 60 µm Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales

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SLIDE 5

Enlarge space: Telescope, Galileo (1609) Magnification ~ x20 1610 Moons of Jupiter Spatial resolution of ~0.06 mm = 60 µm Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales

Why so fast ?

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SLIDE 6

Spatial resolution of ~0.06 mm = 60 µm Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales Enlarge space: Telescope, Microscope, … , Scanning electron microscopy, Transmissions electron microscopy Resolution ~ 1 Angstrom = 10-10 mt Magnification ~ 106 - 107

Nature Materials 10, 165 (2011) TEM image

Why so fast ?

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SLIDE 7

Nature Materials 10, 165 (2011) TEM image graphene Lattice constant 2 Ang

Enlarge space: Telescope, Microscope, … , Scanning electron microscopy, Transmissions electron microscopy Slow down time ? 1791 George Stubbs (english painter) Spatial resolution of ~0.06 mm = 60 µm Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales Resolution ~ 1 Angstrom = 10-10 mt Magnification ~ 106 - 107

Why so fast ?

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Why so fast ?

1878 “Sallie Gardner at a Gallop” is a series of photographs consisting of a galloping horse

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SLIDE 9

Nature Materials 10, 165 (2011) TEM image Lattice constant 2 Ang

Enlarge space: Telescope, Microscope, … , Scanning electron microscopy, Transmissions electron microscopy Slow down time 1878 “Sallie Gardner at a Gallop” is a series of photographs consisting of a galloping horse ~ 0.5 ms = 500 µm resolution (x80) How fast can we go ? Spatial resolution of ~0.06 mm = 60 µm Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales Resolution ~ 1 Angstrom = 10-10 mt Magnification ~ 106 - 107

Why so fast ?

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SLIDE 10

Why so fast ?

Flash photolysis method 1949

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Flash photolysis method 1949

Why so fast ?

a= Fcoulomb(d) m d=0.5at

2

Breaking of an ICN molecule on the fs time- scale Femto-chemestry Atoms ~ 10-13 s = 100 fs

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SLIDE 12

Flash photolysis method 1949

Why so fast ?

Electrons ~ 10-16 s = 0.1 fs (Bohr model) Atoms ~ 10-13 s = 100 fs

a= Fcoulomb(d) m d=0.5at

2

Breaking of an ICN molecule on the fs time- scale Femto-chemestry

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SLIDE 13

Why so fast ?

5 fs ~ 1013 slow down of time

(1 Ang ~ 106–107 space magnification)

Shortest laser pulses <1 fs (X-Ray) 2003

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10-18 as

Why so fast ?

5 fs ~ 1013 slow down of time

(1 Ang ~ 106–107 space magnification)

2003 Shortest laser pulses <1 fs (X-Ray)

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SLIDE 15

10-18 as

Why so fast ?

5 fs ~ 1013 slow down of time

(1 Ang ~ 106–107 space magnification)

2003 Shortest laser pulses <1 fs (X-Ray)

TDDFT

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SLIDE 16

10-18 as

Why so fast ?

5 fs ~ 1013 slow down of time

(1 Ang ~ 106–107 space magnification)

2003 Shortest laser pulses <1 fs (X-Ray)

MBPT

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SLIDE 17

Two photons photo-emission

Pump and Probe experiments

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SLIDE 18

Pump and Probe experiments

Two photons photo-emission

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SLIDE 19

Pump and Probe experiments

Two photons photo-emission

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Transient absorption (reflectivity)

Pump and Probe experiments

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SLIDE 21

2012

Pump and Probe experiments

Transient absorption (reflectivity)

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Pump and Probe experiments

2012

Recent measures perfomed at Politecnico in Milano

Transient absorption (reflectivity)

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SLIDE 23

Strong technological interest

Magnetic field Laser pulses Exchange interaction spin-

  • rbit

Spin precession

Ultra-fast magnetization control

  • Phys. Rev. Lett. 76, 4250 (1996)

Nature 435, 635 (2005)

  • Rev. Mod. Phys. 82, 2731 (2010)

femto-magnetism sub-ps circularly polarized pulses

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SLIDE 24

Time resolved magnetization

New generation magnetic recording devices

  • Phys. Rev. Lett. 99, 047601 (2007)
  • Phys. Rev. Lett. 103, 117201 (2009)

Selected for viewpoint in physics and editor's suggestion

Magnetic field Laser pulses Exchange interaction spin-

  • rbit

Spin precession

Ultra-fast magnetization control

  • Phys. Rev. Lett. 76, 4250 (1996)

Nature 435, 635 (2005)

  • Rev. Mod. Phys. 82, 2731 (2010)
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SLIDE 25

Time resolved magnetization

Theory ? New generation magnetic recording devices

  • Phys. Rev. Lett. 99, 047601 (2007)
  • Phys. Rev. Lett. 103, 117201 (2009)

Selected for viewpoint in physics and editor's suggestion

Magnetic field Laser pulses Exchange interaction spin-

  • rbit

Spin precession

Ultra-fast magnetization control

  • Phys. Rev. Lett. 76, 4250 (1996)

Nature 435, 635 (2005)

  • Rev. Mod. Phys. 82, 2731 (2010)
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SLIDE 26

Strong need of theoretical modelling

No easy interpretation of the data Strong request for theoretical modelling both to describe table top experiments

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SLIDE 27

Strong need of theoretical modelling

No easy interpretation of the data Strong request for theoretical modelling both to describe table top experiments and measures at FEL facilities

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SLIDE 28

Description of pump & probe experiments

Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements

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SLIDE 29

1 - Coherent evolution

Description of pump & probe experiments

Photo-carriers excitations: how are carriers created ? Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements

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1 - Coherent evolution 2 - Scattering term

Photo-carriers excitations: how are carriers created ? carriers relaxation: how is the equilibrium restored?

Description of pump & probe experiments

Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements

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SLIDE 31

Photo-carriers excitations: how are carriers created ? carriers relaxation: how is the equilibrium restored? Measurement process

1 - Coherent evolution 2 - Scattering term 3 - Define the measured physical quantities

Description of pump & probe experiments

Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements

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SLIDE 32

Ab-Initio Many-Body Perturbation Theory

  • G. Onida, L. Reining, and A. Rubio,
  • Rev. Mod. Phys. 74, 601 (2002)

DFT AiMBPT

[

−∇

2

2 +vs(r)]ψnk (r)=ϵnk ψnk(r) v s(r)=vions(r)+vHxc [n](r)

DFT

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SLIDE 33

+

Ab-Initio Many-Body Perturbation Theory

  • G. Onida, L. Reining, and A. Rubio,
  • Rev. Mod. Phys. 74, 601 (2002)

MBPT DFT DFT MBPT

G KS

(r)(r ,r ' ,ω)=∑ nk

ψnk

∗ (r) ψnk(r ')

ω−ϵnk

KS+i η

ϵnk

QP=ϵnk KS +⟨Σ(ϵ QP)−V Hxc⟩

[

−∇

2

2 +vs(r)]ψnk (r)=ϵnk ψnk(r)

Predictive, parameters free and accurate Computationally very demanding

v s(r)=vions(r)+vHxc [n](r)

AiMBPT

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SLIDE 34

The Kadanoff Baym equation

  • DFT band structure
  • QP corrections
  • DFPT phonons and

el-ph matrix elements

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SLIDE 35

Coherent evolution

i ∂tG nmk

< (t ,t)−[ H eq+ΔV H+Δ Σs+U ext(t ),G <(t ,t)]nmk=Snmk (t)

Scattering term

The Kadanoff Baym equation

Gnmk

< (t)=⟨ψnk|G <(rt ,r ' t )

|ψmk⟩

G nmk

< (0)=δnm f nk eq

  • DFT band structure
  • QP corrections
  • DFPT phonons and

el-ph matrix elements Pump laser pulse Many body effects

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SLIDE 36
  • DFPT phonons and

el-ph matrix elements

Coherent evolution

i ∂tG nmk

< (t ,t)−[ H eq+ΔV H+Δ Σs+U ext(t ),G <(t ,t)]nmk=Snmk (t)

Scattering term

The Kadanoff Baym equation

P(t )=−e∑nmk r nmk ΔGnmk

< (t)

f nk(t)=−iG nnk

< (t)

Gnmk

< (t)=⟨ψnk|G <(rt ,r ' t )

|ψmk⟩

G nmk

< (0)=δnm f nk eq

  • DFT band structure
  • QP corrections

Pump laser pulse Many body effects

χ[ f nk(t)](ω)

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SLIDE 37

Time (ps) Photo-emission intensity

  • 0.2 0 0.2 0.4 0.6 0.8
  • Phys. Rev. B 84, 235230 (2011)
  • Phys. Rev. Lett. 102, 087403 (2009)

Pump and probe experiments

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SLIDE 38

L Γ X W K Γ L'

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Time (ps) Photo-emission intensity

  • 0.2 0 0.2 0.4 0.6 0.8
  • Phys. Rev. B 84, 235230 (2011)
  • Phys. Rev. Lett. 102, 087403 (2009)

Pump and probe experiments

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SLIDE 39

L Γ X W K Γ L' L Γ X W K Γ L'

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Time (ps) Photo-emission intensity

  • 0.2 0 0.2 0.4 0.6 0.8
  • Phys. Rev. B 84, 235230 (2011)
  • Phys. Rev. Lett. 102, 087403 (2009)

Pump and probe experiments

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SLIDE 40

Time (ps) Photo-emission intensity

  • 0.2 0 0.2 0.4 0.6 0.8
  • Phys. Rev. B 84, 235230 (2011)
  • Phys. Rev. Lett. 102, 087403 (2009)
  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Pump and probe experiments

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SLIDE 41

γnk

e ,eq=ℑ[Σnk elph]

f nk

(e )=f nk (e ,0) e −γnk

(e , eq) t

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Non equilibrium qp-lifetimes

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SLIDE 42

∂t f nk

(e)(t )=γnk ( h)f nk (h)−γnk (e) f nk ( e)

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Non equilibrium qp-lifetimes

∂t f nk

(e)(t )=−γnk (e ,eq) f nk (e)

γnk

e ,eq=ℑ[Σnk elph]

f nk

(e )=f nk (e ,0) e −γnk

(e , eq) t

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SLIDE 43

∂t f nk

(e)(t )=−γnk (e )f nk (e)

∂t f nk

(e)(t )= γnk (h) f nk ( h)−γnk (e )f nk (e)

f nk

(e )

f nk

(e)

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Non equilibrium qp-lifetimes

∂t f nk

(e)(t )=−γnk (e ,eq) f nk (e)

γnk

e ,eq=ℑ[Σnk elph]

f nk

(e )=f nk (e ,0) e −γnk

(e , eq) t

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SLIDE 44

∂t f nk

(e)(t )=−γnk (e )f nk (e)

∂t f nk

(e)(t )= γnk (h) f nk ( h)−γnk (e )f nk (e)

f nk

(e )

f nk

(e)

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Non equilibrium qp-lifetimes

∂t f nk

(e)(t )=−γnk (e ,eq) f nk (e)

γnk

e ,eq=ℑ[Σnk elph]

f nk

(e )=f nk (e ,0) e −γnk

(e , eq) t

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SLIDE 45

∂t f nk

(e)(t )=−γnk (e )f nk (e)

∂t f nk

(e)(t )= γnk (h) f nk ( h)−γnk (e )f nk (e)

f nk

(e )

f nk

(e)

  • D. Sangalli, and A.

Marini, Europhysics Letters 110, 47004 (2015)

Non equilibrium qp-lifetimes

∂t f nk

(e)(t )=−γnk (e ,eq) f nk (e)

γnk

e ,eq=ℑ[Σnk elph]

f nk

(e )=f nk (e ,0) e −γnk

(e , eq) t

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SLIDE 46

Energy [eV]

  • 300 fs

O c c u p a t i

  • n

s

  • 100 fs

100 fs

f nk

(e)(ϵnk)

Time distance from the pump pulse maximum

Formation of Fermi distributions

Snnk

< (t)=γnk (h)f nk (h)(t)−γnk (e)f nk (e)(t)

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SLIDE 47

O c c u p a t i

  • n

s

1 ps 1 ps 500 fs 500 fs 1.5 ps 1.5 ps 1600 K 1600 K 700 fs 700 fs 2 ps 2 ps 1360 K 1360 K 3140 K 3140 K 5400 K 5400 K 7890 K 7890 K

Energy [eV]

  • 300 fs
  • 100 fs

100 fs

f nk

(e)(ϵnk)

300 fs Time distance from the pump pulse maximum

Formation of Fermi distributions

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SLIDE 48

O c c u p a t i

  • n

s

1 ps 1 ps 1.5 ps 1.5 ps 1600 K 1600 K 700 fs 700 fs 2 ps 2 ps 1360 K 1360 K 3140 K 3140 K 5400 K 5400 K

7890 K

Energy [eV]

  • 300 fs
  • 100 fs

100 fs

f nk

(e)(ϵnk)

300 fs 500 fs Time distance from the pump pulse maximum

Formation of Fermi distributions

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SLIDE 49

O c c u p a t i

  • n

s

1 ps 1.5 ps 1600 K 700 fs 2 ps 1360 K 3140 K 5400 K

Energy [eV]

  • 300 fs
  • 100 fs

100 fs

f nk

(e)(ϵnk)

300 fs 500 fs Time distance from the pump pulse maximum 7890 K

Formation of Fermi distributions

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SLIDE 50

O c c u p a t i

  • n

s

1 ps 1.5 ps 1600 K 700 fs 2 ps 1360 K 3140 K 5400 K

Energy [eV]

  • 300 fs
  • 100 fs

100 fs

f nk

(e)(ϵnk)

300 fs 500 fs Time distance from the pump pulse maximum 7890 K

Formation of Fermi distributions

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SLIDE 51

Transient reflectivity Silicon

  • D. Sangalli, S. Dal Conte, C. Manzoni,
  • G. Cerullo and A. Marini,

Editor's suggestion

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SLIDE 52

White Probe 1.7 – 3.1 eV

Transient reflectivity Silicon

Measured region

Pump Energy 3.1 eV Fluence 12 nJ – 200 nJ

  • D. Sangalli, S. Dal Conte, C. Manzoni,
  • G. Cerullo and A. Marini,

Editor's suggestion

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SLIDE 53

Transient reflectivity Silicon

  • D. Sangalli, S. Dal Conte, C. Manzoni,
  • G. Cerullo and A. Marini,

Bleaching, photo-induced absorption, stimulated emission

Editor's suggestion

ϵ(ω, τ)=1−4 π Σλ Rλ

∗(τ)Lλ λ exc(ω)Rλ(τ)−4 π Σij Rij ∗(τ)Lij ,ij qp (ω)Rij(τ)

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SLIDE 54
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SLIDE 55

Transient reflectivity Silicon

  • D. Sangalli, S. Dal Conte, C. Manzoni,
  • G. Cerullo and A. Marini,

Screening effects

Editor's suggestion

ϵ(ω, τ)=1−4π Σλ Rλ

∗Lλλ exc(ω, τ)Rλ

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SLIDE 56

Transient reflectivity Silicon

17

  • D. Sangalli, S. Dal Conte, C. Manzoni,
  • G. Cerullo and A. Marini,

Screening effects Bleaching, stimulated emission, photo-induced absorption

+

Editor's suggestion

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SLIDE 57

CNR-ISM, Division of Ultrafast Processes in Materials, Area della Ricerca di Roma 1, Monterotondo Scalo, Italy Code, theory developments, application to bulk systems: www.yambo-code.org (part GPL / part “pre-GPL”) https://github.com/yambo-code

The “ultra-fast” team

  • D. Sangalli
  • E. Perfetto
  • G. Stefanucci

University of Tor Vergata, Roma, Italy Code, theory development, applications to models and isolated systems

  • A. Marini

(project leader)

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SLIDE 58

Nano Letters, 17, 4549 (2017): Ab Initio Calculations of Ultrashort Carrier Dynamics in Two-Dimensional Materials: Valley Depolarization in Single-Layer WSe2 CNR-ISM, Division of Ultrafast Processes in Materials, Area della Ricerca di Roma 1, Monterotondo Scalo, Italy

The “ultra-fast” team

  • D. Sangalli
  • E. Perfetto
  • G. Stefanucci

University of Tor Vergata, Roma, Italy

  • A. Molina-Sanchez
  • M. Marsili

Institute of Materials Science, University of Valencia, Valencia, Spain ACS nano 10, 1182 (2016) Photo-Induced Bandgap Renormalization Governs the Ultrafast Response of Single-Layer MoS2

  • A. Marini

(project leader) Applications to transition metal dicalcogenides Teaching Code, theory developments, application to bulk systems: www.yambo-code.org (part GPL / part “pre-GPL”) https://github.com/yambo-code Code, theory development, applications to models and isolated systems

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SLIDE 59

References

Development of the theoretical and numerical method:

  • C. Attaccalite, M. Gruning, A. Marini, Phys. Rev. B 84, 245110 (2011)
  • D. Sangalli, A. Marini, A. Debernardi, Phys. Rev. B 86, 125139 (2012)
  • A. Marini, J. of Phys: Conf. Ser. 427, 012003 (2013)
  • D. Sangalli and A. Marini, J. of Phys: Conf. Ser. 609, 012006 (2015)
  • E. Perfetto, D. Sangalli, A. Marini, G. Stefanucci, Phys. Rev. B 92, 205304 (2015)
  • E. Perfetto, D. Sangalli, A. Marini, G. Stefanucci, Phys. Rev. B 94, 245303 (2016)

Applications to bulk silicon:

  • D. Sangalli, and A. Marini, Europhysics Letters 110, 47004 (2015)
  • D. Sangalli, S. Dal Conte, C. Manzoni, G. Cerullo and A. Marini, Phys. Rev B 93, 195205 (2016)

Applications to TMDs:

  • A. Molina Sanchez, D. Sangalli, K. Hummer, A. Marini, L. Wirtz, Phys. Rev. B 88, 045412 (2013)
  • E. Pogna, M. Marsili, D. De Fazio, S. Dal Conte, C. Manzoni, D. Sangalli,
  • D. Yoon, A. Lombardo, A. Ferrari, A. Marini, G. Cerullo, D. Prezzi, ACS nano 10, 1182 (2016)
  • A. Molina Sanchez, D. Sangalli, L. Wirtz, and A. Marini, Nano Letters 17, 4549 (2017)

Thank you for your attention

Applications molecules:

  • E. Perfetto, D. Sangalli, A. Marini, and G. Stefanucci, submitted to Journal of Physical Chemistry Letters (2018)
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SLIDE 60
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SLIDE 61

Propagate a group of small matricies, one for each k-point, "N x N". Silicon case: N = 8; 743 matricies on a double grid in the IBZ (4x4x4 + 15x15x15) (6x6x6 + 25x25x25) All EOM are coupled via a) The calculation of the density matrix (easy part) b) The scattering processes from k -> k+q which need to be updated Some timing on bulk silicon @(4x4x4+15x15x15): DFT: (i) scf: ~1s serial (coarse grid) (ii) nscf: 33s serial (coarse grid, 100 bands) 5m 6s 4 cores (fine grid) DFPT: (i) phonons and elph: 1m 4 cores (coarse grid, 10 bands) GW: 9h 8m 4 cores (fine grid) BSE: 1h30m 4 cores (fine grid) SEX Kernel: 2m48s 4 cores (coarse grid) NEGF: (t=0.01 fs) 14h38m 4 cores (double grid, scatt. 2.5 fs, 11h1m ) NEQ COHSEX: 1h51m 4 cores (fine grid) NEQ BSE: 2h40m 4 cores (fine grid)

The Kadanoff Baym equation

Coherent evolution

i ∂tG nmk

< (t ,t)−[ H eq+ΔV H+Δ Σs+U ext(t ),G <(t ,t)]nmk=Snmk (t)

Scattering term