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 January 2018, Trieste, Italy
Yambo and HPC New computational resources make possible to tackle more challenging computational problems from first-principles QP vs KS energies Higher BSE vs IP absorption accuracy High throughput Ultra-fast and non equilibrium physics New physics yambo plugin Larger Surfaces, interfaces, yambopy systems nanostructures ab-initio Extend the limits of system size DFT (10 3 – 10 4 atoms) - MBPT (10 2 10 3 atoms)
Yambo and HPC New computational resources make possible to tackle more challenging computational problems from first-principles QP vs KS energies Higher BSE vs IP absorption accuracy High throughput Ultra-fast and non equilibrium physics New physics yambo plugin Larger Surfaces, interfaces, yambopy systems nanostructures ab-initio Extend the limits of system size DFT (10 3 – 10 4 atoms) - MBPT (10 2 10 3 atoms)
Why so fast ? Spatial resolution of ~0.06 mm = 60 µ m Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales
Why so fast ? Spatial resolution of ~0.06 mm = 60 µ m Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales Enlarge space: 1610 Telescope, Galileo (1609) Moons of Jupiter Magnification ~ x20
Why so fast ? Spatial resolution of ~0.06 mm = 60 µ m 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 Nature Materials 10, 165 (2011) TEM image Resolution ~ 1 Angstrom = 10 -10 mt Magnification ~ 10 6 - 10 7
Why so fast ? Spatial resolution of ~0.06 mm = 60 µ m Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales Enlarge space: Slow down time ? Telescope, Microscope, … , 1791 George Stubbs (english painter) Scanning electron microscopy, Transmissions electron microscopy Nature Materials 10, 165 (2011) TEM image graphene Lattice constant 2 Ang Resolution ~ 1 Angstrom = 10 -10 mt Magnification ~ 10 6 - 10 7
1878 “Sallie Gardner at a Gallop” is a series of photographs Why so fast ? consisting of a galloping horse
Why so fast ? Spatial resolution of ~0.06 mm = 60 µ m Time resolution of ~0.04 s = 40 ms We can use technology to explore shorter space and time scales Enlarge space: Slow down time Telescope, Microscope, … , 1878 “Sallie Gardner at a Gallop” is Scanning electron microscopy, a series of photographs consisting of Transmissions electron microscopy a galloping horse ~ 0.5 ms = 500 µ m resolution (x80) Nature Materials 10, 165 (2011) TEM image Lattice constant 2 Ang Resolution ~ 1 Angstrom = 10 -10 mt Magnification ~ 10 6 - 10 7 How fast can we go ?
Why so fast ? Flash photolysis method 1949
Why so fast ? Flash photolysis method 1949 a = F coulomb ( d ) 2 d = 0.5 at m Atoms ~ 10 -13 s = 100 fs Femto-chemestry Breaking of an ICN molecule on the fs time- scale
Why so fast ? Flash photolysis method 1949 a = F coulomb ( d ) 2 d = 0.5 at m Atoms ~ 10 -13 s = 100 fs Femto-chemestry Breaking of an ICN molecule on the fs time- scale Electrons ~ 10 -16 s = 0.1 fs (Bohr model)
Why so fast ? 5 fs ~ 10 13 slow down of time (1 Ang ~ 10 6 –10 7 space magnification) Shortest laser pulses <1 fs (X-Ray) 2003
Why so fast ? 5 fs ~ 10 13 slow down of time (1 Ang ~ 10 6 –10 7 space magnification) Shortest laser pulses <1 fs (X-Ray) 2003 10 -18 as
Why so fast ? 5 fs ~ 10 13 slow down of time (1 Ang ~ 10 6 –10 7 space magnification) Shortest laser pulses <1 fs (X-Ray) 2003 TDDFT 10 -18 as
Why so fast ? 5 fs ~ 10 13 slow down of time (1 Ang ~ 10 6 –10 7 space magnification) Shortest laser pulses <1 fs (X-Ray) 2003 MBPT 10 -18 as
Pump and Probe experiments Two photons photo-emission
Pump and Probe experiments Two photons photo-emission
Pump and Probe experiments Two photons photo-emission
Pump and Probe experiments Transient absorption (reflectivity)
Pump and Probe experiments 2012 Transient absorption (reflectivity)
Pump and Probe experiments 2012 Transient absorption (reflectivity) Recent measures perfomed at Politecnico in Milano
Strong technological interest Ultra-fast magnetization control Magnetic field Spin precession spin- orbit Exchange interaction Laser pulses femto-magnetism Phys. Rev. Lett. 76 , 4250 (1996) sub-ps circularly Nature 435 , 635 (2005) polarized pulses Rev. Mod. Phys. 82 , 2731 (2010)
Time resolved magnetization Ultra-fast magnetization control New generation Magnetic field magnetic recording devices Phys. Rev. Lett. 99 , 047601 (2007) Spin Phys. Rev. Lett. 103 , 117201 (2009) precession Selected for viewpoint in physics and editor's suggestion spin- orbit Exchange interaction Laser pulses Phys. Rev. Lett. 76 , 4250 (1996) Nature 435 , 635 (2005) Rev. Mod. Phys. 82 , 2731 (2010)
Time resolved magnetization Ultra-fast magnetization control New generation Magnetic field magnetic recording devices Phys. Rev. Lett. 99 , 047601 (2007) Spin Phys. Rev. Lett. 103 , 117201 (2009) precession Selected for viewpoint in physics and editor's suggestion spin- orbit Theory ? Exchange interaction Laser pulses Phys. Rev. Lett. 76 , 4250 (1996) Nature 435 , 635 (2005) Rev. Mod. Phys. 82 , 2731 (2010)
Strong need of theoretical modelling No easy interpretation of the data Strong request for theoretical modelling both to describe table top experiments
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
Description of pump & probe experiments Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements
Description of pump & probe experiments Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements Photo-carriers excitations: how are carriers created ? 1 - Coherent evolution
Description of pump & probe experiments Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements carriers relaxation: Photo-carriers excitations: how is the equilibrium how are carriers created ? restored? 1 - Coherent evolution 2 - Scattering term
Description of pump & probe experiments Compute the equilibrium properties of the material: band structure, phonons, electron-phonon matrix elements carriers relaxation: Photo-carriers excitations: Measurement process how is the equilibrium how are carriers created ? restored? 1 - Coherent evolution 2 - Scattering term 3 - Define the measured physical quantities
Ab-Initio Many-Body Perturbation Theory DFT [ + v s ( r ) ] ψ nk ( r )=ϵ nk ψ nk ( r ) 2 −∇ 2 v s ( r )= v ions ( r )+ v Hxc [ n ]( r ) DFT AiMBPT G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74 , 601 (2002)
Ab-Initio Many-Body Perturbation Theory DFT [ + v s ( r ) ] ψ nk ( r )=ϵ nk ψ nk ( r ) 2 −∇ 2 v s ( r )= v ions ( r )+ v Hxc [ n ]( r ) DFT MBPT + MBPT ∗ ( r ) ψ nk ( r ' ) ψ nk ( r ) ( r ,r ' , ω)= ∑ G KS AiMBPT KS + i η ω−ϵ nk nk KS +⟨Σ(ϵ QP =ϵ nk QP )− V Hxc ⟩ G. Onida, L. Reining, and A. Rubio, ϵ nk Rev. Mod. Phys. 74 , 601 (2002) Computationally very demanding Predictive, parameters free and accurate
The Kadanoff Baym equation - DFT band structure - DFPT phonons and - QP corrections el-ph matrix elements
The Kadanoff Baym equation - DFPT phonons and Many body effects el-ph matrix elements - DFT band structure - QP corrections Pump laser pulse < ( t ,t )−[ H eq +Δ V H +Δ Σ s + U ext ( t ) ,G < ( t ,t )] nmk = S nmk ( t ) i ∂ t G nmk Coherent evolution Scattering term < ( t )=⟨ψ nk | G < ( 0 )=δ nm f nk < ( rt ,r ' t ) eq | ψ mk ⟩ G nmk G nmk
The Kadanoff Baym equation - DFPT phonons and Many body effects el-ph matrix elements - DFT band structure - QP corrections Pump laser pulse < ( t ,t )−[ H eq +Δ V H +Δ Σ s + U ext ( t ) ,G < ( t ,t )] nmk = S nmk ( t ) i ∂ t G nmk Coherent evolution Scattering term < ( t )=⟨ψ nk | G < ( 0 )=δ nm f nk < ( rt ,r ' t ) eq | ψ mk ⟩ G nmk G nmk < ( t ) < ( t ) P ( t )=− e ∑ nmk r nmk Δ G nmk f nk ( t )=− iG nnk χ[ f nk ( t )](ω)
Pump and probe experiments Phys. Rev. B 84, 235230 (2011) Phys. Rev. Lett. 102, 087403 (2009) Photo-emission intensity -0.2 0 0.2 0.4 0.6 0.8 Time (ps)
Pump and probe experiments Phys. Rev. B 84, 235230 (2011) Phys. Rev. Lett. 102, 087403 (2009) Photo-emission intensity -0.2 0 0.2 0.4 0.6 0.8 Time (ps) L Γ X W K Γ L' D. Sangalli, and A. Marini, Europhysics Letters 110, 47004 (2015)
Recommend
More recommend
