Walking hand in hand Two-body quantum dynamics in excitronics Guido Goldoni Federico Grasselli SISSA Andrea Bertoni CNR-NANO
Long live the exciton! Chemla, 1985 - - ns - s A.A. High, et al., Nature 483, 584 (2012))
Driving excitons External gates Electron layer Hole layer d F z ( x, y) Permanent electric dipole ed Coupling to external fields F Z (x,y) U ( x, y) = ed F ( x, y) High mobility Sub-nanosecond time resolved spectroscopy z
(all optical) Excitonicdevices Transistor Split gate Andreakou App. Phys Lett 104, 091101 (2014) Traps Dorov et at. arxiv:1801.01553 SAW G. J. Schinner et al., Phys. Rev. B 83, 165308 (2011); Phys Rev. Lett. 110, 127403 (2013) A. Violante et al., New J Phys 16, 033035 (2014)
Composite particle dynamics Is the scattering of a two-body object a trivial textbook problem? - CM internal motion correlation No Born-Oppenheimer approximation Gate potentials comparable to internal modes Electrostatic forces have opposite sign for the two charges No perturbative / mean-field approach Full (two-body) quantum dynamics needed in principle
Two-body particle tunnel R - - r - reflection H = T T V ( ) V (, ; t) R r int r ext R r CM relative motion external Coupled CM & relative motions? transmission,; ; ;
Two-particle scattering HOW? tunnel - - reflection? transmission
Yes, we can! Two-body TD Schrödinger eq.! Ψ,; Ψ,; Total Hamiltonian,; Initial state c.m. Internal Ψ ( R, r; t = 0) = Gaussian Ground State
Up and downs the hills - EXP - - straight transmission straight reflection - - - EXP Grasselli, Bertoni, GG J Chem Phys 142, 034701 (2015)
Two-particle scattering HOW MUCH? # =T R= #
Transmission resonances Exact propagation r h,% r e L = 60 nm E c.m. = 0.2 mev
Mean-fieldmethods Wave function factorisation Ψ,; ; (; Rigid-Mean Field ( ; ( % & %% #' ( %, Rigid exciton
Transmission resonances Exact propagation r h,% r e L = 60 nm E c.m. = 0.2 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
Transmission resonances Exact propagation Rigid-MF r h,% r e L = 60 nm E c.m. = 0.2 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
Transmission resonances An energy dependent renormalization? Exact propagation Rigid-MF r h,% r e L = 60 nm E c.m. = 0.2 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
a self-energy approach
Total Hamiltonian H = T T V ( ) V (, ; t) R r int r ext R r CM relative motion external General Wave Function Coupled Channel Equations Ψ,; = 2 ; ( CM envelopes H %% & % & % & % H & & % & H % 1 % H = 3 25 6 & () & 7 = #' ( 7, ( ()
Total Hamiltonian H = T T V ( ) V (, ; t) R r int r ext R r CM relative motion external General Wave Function Ψ,; 2 ; ( Coupled Channel Equations MF H %% & % & % & % H & & % & H % =1 % H = 3 25 6 & () & 7 = #' ( 7, (
Total Hamiltonian H = T T V ( ) V (, ; t) R r int r ext R r CM relative motion external General Wave Function Ψ,; = 2 ; ( Coupled Channel Equations 8 99 & % & % & % H & & % & H % 1 % H 3 25 6 & & 7 #' ( 7, ( ()
Mean Field 9 approach CM (only!) propagation of % ; under H= 3 25 6 %& %% 8 99 Σ % (;1 inclusion of internalvirtualtransitions via a localself-energyσ % Σ % ;1 ; 2 < 9= > 1?6?& @%... m = 2 m = 1 m = 0 - < 9B C > - - < 9> () > R
The effect of 9 Exact propagation Rigid-MF r h,% r e L = 60 nm E c.m. = 0.2 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
The effect of 9 Exact propagation Rigid-MF Rigid-MFD 9 r h,% r e Negative energy correction near potential edge L = 60 nm E c.m. = 0.2 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
Tunnel effect Tunnelling through a (overall) barrier =,%? E,% with,% F E,%, and E,%?0.6 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
Tunnel effect Tunnelling through a (overall) barrier =,%? E,% with,% F E,%, and E,%?0.6 mev Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
Tunnel effect Tunnelling through a (overall) barrier =,%? E,% with,% F E,%, and E,%?0.6 mev Negative energy correction near potential edge Grasselli, Bertoni, GG Phys. Rev. B 93, 195310 (2016)
TD-diffraction pattern c.m. marginal probability distribution I J.7. (;K Ψ,;t ' FG, A. Bertoni, and G. Goldoni. Phys. Rev. B 94, 125418 (2016)
TD-diffraction pattern diffraction pattern restored Standing states Serial code CPU time =30 min Parallel code CPU time >1000 h FG, A. Bertoni, and G. Goldoni. Phys. Rev. B 94, 125418 (2016)
single barrier single slit double slit
A new radiation sensitive to localized potentials SAW excitonic devices
When should we care? E M E = E,% 1 1exp? M E R Large R Small & 7 ( 7 (,T U Small Σ FG, A. Bertoni, and G. Goldoni. Superlattices and Microstructures (2017)
Conclusions Coherent transport in excitonic devices is a genuine twobody problem A proper local self-energy restores virtual transitions SE-corrected CM wavepacket propagation coincides with full calculations at no additional computational cost