Electron-phonon interaction. Can dispersionless phonons provide relaxation?
|
|
- Merry Small
- 5 years ago
- Views:
Transcription
1 Electron-phonon interaction. Can dispersionless phonons provide relaxation? P. Gartner, J. Seebeck, F. Jahnke Institute for Theoretical Physics University of Bremen Kiel, 21
2 Introduction Self-assembled quantum dots S. Anders et al., Phys. Rev. B 66, (22) Kiel, 21 2
3 Introduction Self-assembled quantum dots Energy spectrum electrons bound (QD) extended (WL) holes S. Anders et al., Phys. Rev. B 66, (22) Kiel, 21 2
4 Introduction Discrete spectrum important for optoelectronics Energy spectrum electrons controlled by quantum dot geometry Carrier kinetics bound (QD) extended (WL) holes Kiel, 21 2
5 Introduction Discrete spectrum important for optoelectronics controlled by quantum dot geometry Capture and relaxation electrons p shell photon s shell Carrier kinetics holes Kiel, 21 2
6 Introduction Low carrier densities carrier-carrier scattering negligible carrier-lo-phonon interaction dominant Perturbation theory: capture and relaxation prevented phonon bottleneck Kiel, 21 3
7 Introduction Low carrier densities carrier-carrier scattering negligible carrier-lo-phonon interaction dominant Perturbation theory: capture and relaxation prevented WL QD ω LO ω LO phonon bottleneck U.Bockelmann, G. Bastard, PRB 42, 8947 (199) H. Benisty et al., PRB 44, 1945 (1991) Kiel, 21 3
8 Introduction Experiment: fast (ps) capture and relaxation Kiel, 21 4
9 Introduction Experiment: fast (ps) capture and relaxation Example: S. Trumm et al. APL 87, (25) rapid relaxation inside wetting layer rapid transfer to bound states characteristic times (ps) independent of excitation power Kiel, 21 4
10 Outline Boltzmann kinetics relaxation properties, in general and with dispersionless LO-phonons Carrier-phonon system in equilibrium carrier renormalization = the polaron Quantum kinetics 2-time quantum kinetics 1-time approximation Results (QWs and QDs) Numerical difficulties Kiel, 21 5
11 Boltzmann kinetics Carrier-phonon Hamiltonian: H = X i ǫ i a i a i + X q ω qb qb q + X i,j,q M i,j (q)a i a j(b q + b q ) ǫ j ω q ω q = ω LO, M i,j (q) = g q ϕ i e iqr ϕ j gq 2 α 1 Fröhlich coupling q 2 ǫ i Kiel, 21 6
12 Boltzmann kinetics Carrier-phonon Hamiltonian: H = X i ǫ i a i a i + X q ω qb qb q + X i,j,q M i,j (q)a i a j(b q + b q ) ǫ j ω q ω q = ω LO, M i,j (q) = g q ϕ i e iqr ϕ j gq 2 α 1 Fröhlich coupling q 2 ǫ i Time evolution of population f i = a i a i : f i t = X j {W i,j (1 f i )f j W j,i (1 f j )f i } Kiel, 21 6
13 Boltzmann kinetics Carrier-phonon Hamiltonian: H = X i ǫ i a i a i + X q ω qb qb q + X i,j,q M i,j (q)a i a j(b q + b q ) ǫ j ω q ω q = ω LO, M i,j (q) = g q ϕ i e iqr ϕ j gq 2 α 1 Fröhlich coupling q 2 ǫ i Time evolution of population f i = a i a i : f i t = X j {W i,j (1 f i )f j W j,i (1 f j )f i } W i,j = Golden Rule transition rate j i : W i,j = 2π X M i,j (q) 2 {N qδ(ǫ i ǫ j ω q) + (N q + 1)δ(ǫ i ǫ j + ω q)} q Kiel, 21 6
14 Boltzmann kinetics Relaxation properties (analytic): conserves positivity: f i () = f i (t) stationary solution: f i (t) = 1/[e β(ǫ i µ) + 1] = F(ǫ i ) for any f i () f i (t) F(ǫ i ) as t provided all states can be connected using paths with nonzero transition rates. Kiel, 21 7
15 Boltzmann kinetics Relaxation properties (analytic): conserves positivity: f i () = f i (t) stationary solution: LO-phonons + continuous spectrum (QW).5.4 f i (t) = 1/[e β(ǫ i µ) + 1] = F(ǫ i ) f e.3.2 for any f i ().1 f i (t) F(ǫ i ) as t provided all states can be connected using paths with nonzero transition rates. 4 t(fs) E(meV) 25 phonon cascade Kiel, 21 7
16 Boltzmann kinetics Relaxation properties (analytic): conserves positivity: f i () = f i (t) stationary solution: LO-phonons in quantum dots WL ω LO f i (t) = 1/[e β(ǫ i µ) + 1] = F(ǫ i ) for any f i () f i (t) F(ǫ i ) as t provided all states can be connected using paths with nonzero transition rates. QD ω LO phonon bottleneck Kiel, 21 7
17 Boltzmann kinetics Relaxation properties (analytic): conserves positivity: f i () = f i (t) stationary solution: LO-phonons in quantum dots WL ω LO f i (t) = 1/[e β(ǫ i µ) + 1] = F(ǫ i ) for any f i () QD ω LO f i (t) F(ǫ i ) as t provided all states can be connected using paths with nonzero transition rates. Proposed solutions: LO+LA: T.Inoshita, H.Sakaki, PRB.46, 726 (1992) LO+LO: A. Knorr group (Berlin) in press phonon bottleneck Kiel, 21 7
18 Boltzmann vs. quantum kinetics Experiment: fast capture and relaxation (ps) Boltzmann kinetics: weak coupling slow evolution long time no memory (Markovian) Kiel, 21 8
19 Boltzmann vs. quantum kinetics Experiment: fast capture and relaxation (ps) Boltzmann kinetics: weak coupling slow evolution long time no memory (Markovian) Quantum kinetics: strong coupling fast evolution both early and later times memory effects included Kiel, 21 8
20 Boltzmann vs. quantum kinetics Experiment: fast capture and relaxation (ps) Boltzmann kinetics: weak coupling slow evolution long time no memory (Markovian) Quantum kinetics: strong coupling fast evolution both early and later times memory effects included Relaxation properties (numeric) is a steady state reached? steady state = thermal equilibrium? Kiel, 21 8
21 Polarons electron polarizes crystal Kiel, 21 9
22 Polarons free carrier retarded GF G R α(t) = θ(t) i e i ǫαt G R α(ω) = 1 ω ǫ α + iδ + + electron polarizes crystal spectral function bg α(ω) = 2Im G R α(ω) = 2π δ( ω ǫ α) Kiel, 21 9
23 Polarons electron polarizes crystal + + free carrier retarded GF G R α(t) = θ(t) i e i ǫαt G R α(ω) = spectral function 1 ω ǫ α + iδ bg α(ω) = 2Im G R α(ω) = 2π δ( ω ǫ α) polaron retarded GF G R α(ω) = 1 ω ǫ α + Σ R α(ω) Σ R α(ω) self-energy for carrier-phonon interaction bg α(ω) =? Kiel, 21 9
24 Quantum well polaron Self-consistent Random Phase Approximation j i ff τ ǫ k Gk R (τ) = = Z τ dτ Σ R k (τ )G R k (τ τ ) G R Σ = 1 2 E k 2 (mev) τ(fs) arbitrary order in α multi-phonon processes GaAs at T= 3K α =.6, ω LO = 36 mev Kiel, 21 1
25 Quantum well polaron 1 ^G Spectral function ^ G k= (ω) InGaAs/GaAs T=3K Energy (h _ ω-e G ) / h _ ω LO Kiel, 21 11
26 Quantum well polaron 1 ^G Spectral function ^ G k= (ω) InGaAs/GaAs T=3K polaron shift energy broadening phonon satellites Energy (h _ ω-e G ) / h _ ω LO J. Seebeck, T.R. Nielsen, P. Gartner, F. Jahnke, Phys. Rev. B 71, (25) Kiel, 21 11
27 Quantum well polaron 1.E 1 Spectral function 1 1.E 2 1.E 4 1.E 6 1.E 8 1.E 1 1.E E 2 1.E 3 1.E 4 1.E 5 1.E 6 1.E 7 1.E E E 1 1 k ω E G / ω LO 4 1.E 11 ^G Spectral function ^ G k= (ω) InGaAs/GaAs T=3K Energy (h _ ω-e G) / h _ ω LO Kiel, 21 12
28 Quantum well polaron 8 1.E E 2 1.E E E 5 k 4 1.E E 7 1.E E hw/hwlo 1.E 1 1.E 11 ^G Spectral function ^ G k= (ω) InGaAs/GaAs T=3K Energy (h _ ω-e G) / h _ ω LO Kiel, 21 12
29 Quantum dot polaron LO-phonons + quantum dot states only Self-consistent Random Phase Approximation T.Inoshita, H.Sakaki, PRB 56, 261 (1998) K.Král, Z.Khás, PRB 57, 4355 (1998) finite number of phonons = diagonalization O.Verzelen, R.Fereira, G.Bastard, PRB 62, 489 (2) T.Stauber, R.Zimmermann, H. Castella, PRB 62, 7336 (2) BUT wetting layer states important for both kinetics and spectrum Kiel, 21 13
30 Quantum dot polaron LO-phonons + quantum dot + wetting layer states Kiel, 21 14
31 Quantum dot polaron LO-phonons + quantum dot + wetting layer states 1-2 QD p-shell 1-4 Spectral function QD s-shell InGaAs/GaAs T = 3K Energy (h _ ω - E G ) / h _ ω LO E = 1.1 ω LO Kiel, 21 14
32 Quantum dot polaron LO-phonons + quantum dot + wetting layer states p 1-2 QD p-shell ω LO 1-4 s Spectral function QD s-shell 1-4 Hybridization InGaAs/GaAs T = 3K Energy (h _ ω - E G ) / h _ ω LO E = 1.1 ω LO Kiel, 21 14
33 Quantum kinetics Quantity of interest: ρ α(t) f e α(t) ψ α(t) ψ α(t) 1 f h α(t) 1 A = i G < α (t, t) electrons p shell 2x2 matrix in the band index, α = k, s, p photon s shell Methods: Equation of Motion hierarchy problem Nonequilibrium Green s Functions polaronic effects 2-time quantities holes Kiel, 21 15
34 Quantum kinetics Quantity of interest: 1 fα(t) e ψ α(t) ρ α(t) A = i G < ψα(t) 1 fα(t) h α (t, t) 2x2 matrix in the band index, α = k, s, p Methods: Equation of Motion hierarchy problem Nonequilibrium Green s Functions polaronic effects 2-time quantities Nonequilibrium Green s Functions Closed Equations for G(t 1, t 2 ) = 1 D h ie T ψ(t 1 )ψ (t 2 ) i Procedure: solve for G α(t 1, t 2 ) recover physical data from the time-diagonal t 1 = t 2 Kiel, 21 15
35 Quantum kinetics 2-time Kadanoff-Baym equations: j i ff H (1) G α(t 1, t 2 ) = t 1 t 2 = {Σ G} α (t 1, t 2 ) t 1 Kiel, 21 16
36 Quantum kinetics 2-time Kadanoff-Baym equations: j i ff H (1) G α(t 1, t 2 ) = t 1 t 2 = {Σ G} α (t 1, t 2 ) j i ff + H (2) G α(t 1, t 2 ) = t 2 t 1 = {G Σ} α (t 1, t 2 ) Kiel, 21 16
37 Quantum kinetics 2-time Reparametrize: (t 1, t 2 ) = (t, t τ) t 2 t t - main time τ - relative time j i ff t H (1) + H (2) G α(t, t τ) = t 1 = {Σ G} α (t, t τ) {G Σ} α (t, t τ) τ Kiel, 21 16
38 Quantum kinetics 2-time Polaronic Green s Function: G R α(t, t τ) = G R α(τ) t 2 t initial condition natural memory cutoff equil. (t, t τ) t 1 τ Kiel, 21 16
39 Quantum kinetics 2-time i t GR,< k (t, t τ) = Σ δ k(t)g R,< k (t, t τ) G R,< k (t, t τ)σ δ k(t τ) + + i t GR,< k (t, t τ) ; τ coll Instantaneous self-energy: Σ δ k(t) = ǫ c k d vc E(t) d cv E(t) ǫ v k «The optical excitation connects the two bands. Kiel, 21 17
40 Quantum kinetics 2-time i t GR,< k (t, t τ) = Σ δ k(t)g R,< k (t, t τ) G R,< k (t, t τ)σ δ k(t τ) + + i t GR,< k (t, t τ) ; τ coll RPA self-energies: Σ R k (t, t ) = i X q g 2 q h i D > (t t )Gk q(t, R t ) + D R (t t )G k q(t, < t ) Σ < k (t, t ) = i X q g 2 q D < (t t )G < k q(t, t ) i D > (τ) = (N LO + 1) e i ω LO τ + N LO e i ω LO τ = i D < ( τ) Kiel, 21 17
41 Quantum kinetics 2-time Collision terms for G R : i t GR k (t, t τ) Z t = coll t τ h i dt Σ R k (t, t )Gk R (t, t τ) Gk R (t, t )Σ R k (t, t τ) t 2 t t Σ t τ G t 1 Kiel, 21 18
42 Quantum kinetics 2-time Collision terms for G R : i t GR k (t, t τ) Z t = coll t τ h i dt Σ R k (t, t )Gk R (t, t τ) Gk R (t, t )Σ R k (t, t τ) t 2 t t Σ t τ G t 1 Kiel, 21 18
43 Quantum kinetics 2-time Collision terms for G < : t 2 G t τ t Z t i t G< k (t, t τ) coll = dt h Σ R k (t, t )G < k (t, t τ) +Σ < G A G R Σ < G < (t, t )Σ Ai t memory depth G t 1 Σ Kiel, 21 19
44 Quantum kinetics 2-time Collision terms for G < : t 2 G t τ t Z t i t G< k (t, t τ) coll = dt h Σ R k (t, t )G < k (t, t τ) +Σ < G A G R Σ < G < (t, t )Σ Ai t memory depth G Σ G < (t 1, t 2 ) = ˆG < (t 2, t 1 ) h i G A (t 2, t 1 ) = G R (t 1, t 2 ) t 1 Kiel, 21 19
45 Quantum kinetics 2-time Initial conditions - the polaron Before the pulse = equilibrium «G R g R (t, t τ) = c (τ) gv R (τ) G < (t, t τ) = g R v (τ) «m e m o r y d e p t h t g < c (τ) = g > v (τ) = g R v (τ) = g > v (τ) g < v (τ) τ Kiel, 21 2
46 Quantum kinetics 2-time No t-evolution before excitation: i t GR,< k (t, t τ) = Σ δ k(t)g R,< k (t, t τ) G R,< k (t, t τ)σ δ k(t τ) + + i t GR,< k (t, t τ) ; τ coll Σ δ ǫ c k(t) = k ǫ v k «Σ δ k G R,< k (t, t τ) G R,< k (t, t τ)σ δ k = Kiel, 21 21
47 Quantum kinetics 2-time No t-evolution before excitation: t 2 G t τ t Z t i t G< k (t, t τ) coll = dt h Σ R k (t, t )G < k (t, t τ) +Σ < G A G R Σ < G < (t, t )Σ Ai t memory depth G t 1 Σ Kiel, 21 22
48 Quantum kinetics 2-time No t-evolution before excitation: t 2 G t τ t Z t i t G< k (t, t τ) coll = dt h Σ R k (t, t )G < k (t, t τ) +Σ < G A G R Σ < G < (t, t )Σ Ai t memory depth G Σ G R (t, t τ) = G < (t, t τ) = g R c (τ) g R v (τ) g R v (τ) ««t 1 Kiel, 21 22
49 Quantum kinetics 1-time Generalized Kadanoff-Baym ansatz (GKBA) G α (t, t ) i G R α(t t ) G α (t, t ) t > t Z d t fα(t) = 2Re dt X dt M α,β (q) 2 Gβ(t R t ) ˆG α(t R t ) β q n f α(t ) ˆ1 f β (t ) D > q (t t ) +ˆ1 f α(t ) f β (t )D < q (t t ) o D q (t) = N LO e iω LO t + (1 + N LO ) e ±iω LO t renormalized quasiparticles (polarons) beyond Markov approximation (memory effects) Kiel, 21 23
50 Quantum kinetics 1-time Generalized Kadanoff-Baym ansatz (GKBA) G α (t, t ) i G R α(t t ) G α (t, t ) t > t Z d t fα(t) = 2Re dt X dt M α,β (q) 2 e iǫ β(t t ) ˆe iǫα(t t ) β q n f ˆ1 α(t) f β (t) D q > (t t ) +ˆ1 f α(t) f β (t)d < q (t t ) o D q (t) = N LO e iω LO t + (1 + N LO ) e ±iω LO t bare particles Markov approximation (no memory effects) Kiel, 21 23
51 Quantum well results: polarization CdTe α =.31 T = 3K p p E(meV) t(fs) E(meV) t(fs) 2-time 1-time Strong dephasing Kiel, 21 24
52 Quantum well results: electron population CdTe α =.31 T = 3K f e f e E(meV) t(fs) E(meV) t(fs) 4 2-time 1-time Steady state reached Not the same! Kiel, 21 25
53 Kubo-Martin-Schwinger condition Exact relation in thermal equilibrium KMS condition Z f α = d( ω) 2π F(ω) b G α(ω) Kiel, 21 26
54 Kubo-Martin-Schwinger condition Exact relation in thermal equilibrium KMS condition Z f α = d( ω) 2π F(ω) b G α(ω) Non-interacting system b G α(ω) = 2π δ( ω ǫ α) f α = F(ǫ α) Kiel, 21 26
55 Kubo-Martin-Schwinger condition Exact relation in thermal equilibrium KMS condition Z f α = d( ω) 2π F(ω) b G α(ω) Non-interacting system G b α(ω) = 2π δ( ω ǫ α) f α = F(ǫ α) Interacting system Generalization of Fermi-Dirac distribution Kiel, 21 26
56 Kubo-Martin-Schwinger test in quantum wells CdTe, α =.31 GaAs, α =.6 f e time 1 time KMS.6.4 f e e 6 1e time 1 time KMS E ~k 2 (mev) E ~k 2 (mev) P. Gartner, J. Seebeck, F. Jahnke, Phys. Rev. B 73, (26) Kiel, 21 27
57 Kubo-Martin-Schwinger test in quantum dots CdTe α =.31 E = 2.4 ω LO p-level excitation electrons 2-time calculation photon p shell s shell f e.2.1 QD s state QD p state WL k= relaxation s shell p shell holes t (fs) Kiel, 21 28
58 Kubo-Martin-Schwinger test in quantum dots CdTe α =.31 E = 2.4 ω LO p-level excitation 1-time calculation 2-time calculation f e.2.1 QD s state QD p state WL k= f e.2.1 QD s state QD p state WL k= t (fs) t (fs) Kiel, 21 28
59 Numerics: instabilities.5.4 fefh+ct8 every :::79::79 u 2:3 fefh+ct8 every :::89::89 u 2: detuning = 12 mev t = 55fs t = 65fs abrupt cut of the collision integrals at memory depth = 5 fs Kiel, 21 29
60 Numerics: instabilities Collision integral t t 2 G t τ t memory depth G Σ Kiel, 21 3
61 Numerics: instabilities Collision integral t t 2 G t τ integral abruptly cut at memory depth t G Σ memory depth Kiel, 21 3
62 Numerics: instabilities Collision integral t t 2 G t τ integral abruptly cut at memory depth t G Σ beyond the memory depth extend with equilibrium Σ, G memory depth Kiel, 21 3
63 Numerics: instabilities Collision integral t t 2 G t τ integral abruptly cut at memory depth t G Σ beyond the memory depth extend with equilibrium Σ, G memory depth smooth interpolation to equilibrium Σ, G Kiel, 21 3
64 Numerics: instabilities Collision integrals extended with equilibrium GFs.35.3 fefh+c14 every :::79::79 u 2:3 fefh+c14 every :::89::89 u 2:3.8.6 fefh+c14 every :::79::79 u 2:3 fefh+c14 every :::99::99 u 2: t = 55fs t = 65fs t = 55fs t = 75fs Kiel, 21 31
65 Numerics: instabilities Collision integrals extended with equilibrium GFs smooth change using an interpolating (Fermi-like) function.4.35 fefh+c25 every :::79::79 u 2:3 fefh+c25 every :::99::99 u 2: t = 55fs t = 75fs Kiel, 21 32
66 Low temperatures The polaron G R α(t) WL p-shell s-shell energy ǫ e α in hω LO time in ps Polaronic GF: GaAs at T=1K Kiel, 21 33
67 Low temperatures The polaron spectral function Ĝα(ω) WL, k= s-shell p-shell 1e energy in hω LO Spectral function: GaAs at T=1K Kiel, 21 33
68 Low temperatures Quantum kinetics 1-time Z d t fα(t) = 2Re dt X dt M α,β (q) 2 Gβ(t R t ) ˆG α(t R t ) β q n f α(t ) ˆ1 f β (t ) D q > (t t ) +ˆ1 f α(t ) f β (t )D < q (t t ) o Kiel, 21 34
69 Low temperatures Quantum kinetics 1-time Z d t fα(t) = 2Re dt X dt M α,β (q) 2 Gβ(t R t ) ˆG α(t R t ) β q n f α(t ) ˆ1 f β (t ) D q > (t t ) +ˆ1 f α(t ) f β (t )D < q (t t ) o 2 Gα(t) R = 1 i Θ(t) 4 X j 3 e i (ǫα α,j)t + Gα(t) R 5 G R α(t) for t Kiel, 21 34
70 Low temperatures WL electron population population 1 2 energy in hω LO 2-time time in ps population 1 2 energy in hω LO 3 1-time time in ps Kiel, 21 35
71 Low temperatures Electron population (long time) population energy in hω LO time in ps population s-shell p-shell time in ps Kiel, 21 36
72 Low temperatures KMS test of the steady state population e-5 KMS kinetics 1e energy in hω LO no thermalization (asymptotic bottleneck) Kiel, 21 37
73 Summary and conclusions Carrier-LO-phonon interaction role - twofold: equilibrium: polaron kinetics: polaron-phonon scattering Relaxation properties (room temp.): Steady state reached both in 2-time and in 1-time kinetics Thermalization: 2-time kinetics: Yes! 1-time kinetics, only low α Problems with low temperatures: 2-time - only the early kinetics 1-time - no thermalization (asymptotic bottleneck?) Kiel, 21 38
Microscopic Modelling of the Optical Properties of Quantum-Well Semiconductor Lasers
Microscopic Modelling of the Optical Properties of Quantum-Well Semiconductor Lasers Stephan W. Koch Department of Physics Philipps University, Marburg/Germany OVERVIEW - Outline of Theory - Gain/Absorption
More informationEquilibration in ϕ 4 theory in 3+1 dimensions
Equilibration in ϕ 4 theory in 3+1 dimensions Alejandro Arrizabalaga Work in collaboration with Anders Tranberg (Sussex) and Jan Smit (Amsterdam) Physical Review D 72 020514 (2005) NIKHEF (Amsterdam) Summer
More informationSummary lecture VI. with the reduced mass and the dielectric background constant
Summary lecture VI Excitonic binding energy reads with the reduced mass and the dielectric background constant Δ Statistical operator (density matrix) characterizes quantum systems in a mixed state and
More informationCooperative Phenomena
Cooperative Phenomena Frankfurt am Main Kaiserslautern Mainz B1, B2, B4, B6, B13N A7, A9, A12 A10, B5, B8 Materials Design - Synthesis & Modelling A3, A8, B1, B2, B4, B6, B9, B11, B13N A5, A7, A9, A12,
More informationEnergy Band Calculations for Dynamic Gain Models in Semiconductor Quantum Well Lasers
Energy Band Calculations for Dynamic Gain Models in School of Electrical and Electronic Engineering University of Nottingham; Nottingham NG7 2RD; UK Email: eexpjb1@nottingham.ac.uk Presentation Outline
More informationSemiclassical Electron Transport
Semiclassical Electron Transport Branislav K. Niolić Department of Physics and Astronomy, University of Delaware, U.S.A. PHYS 64: Introduction to Solid State Physics http://www.physics.udel.edu/~bniolic/teaching/phys64/phys64.html
More informationCarrier-Phonon Interaction in Semiconductor Quantum Dots
ITP Institut für Theoretische Physik Carrier-Phonon Interaction in Semiconductor Quantum Dots Dissertation zur Erlangung des akademischen Grades Doktor der Naturwissenschaften (Dr. rer. nat) am Fachbereich
More informationSummary lecture VII. Boltzmann scattering equation reads in second-order Born-Markov approximation
Summary lecture VII Boltzmann scattering equation reads in second-order Born-Markov approximation and describes time- and momentum-resolved electron scattering dynamics in non-equilibrium Markov approximation
More informationESE 372 / Spring 2013 / Lecture 5 Metal Oxide Semiconductor Field Effect Transistor
Metal Oxide Semiconductor Field Effect Transistor V G V G 1 Metal Oxide Semiconductor Field Effect Transistor We will need to understand how this current flows through Si What is electric current? 2 Back
More informationElectrically Driven Polariton Devices
Electrically Driven Polariton Devices Pavlos Savvidis Dept of Materials Sci. & Tech University of Crete / FORTH Polariton LED Rome, March 18, 211 Outline Polariton LED device operating up to room temperature
More informationElectron-phonon scattering (Finish Lundstrom Chapter 2)
Electron-phonon scattering (Finish Lundstrom Chapter ) Deformation potentials The mechanism of electron-phonon coupling is treated as a perturbation of the band energies due to the lattice vibration. Equilibrium
More informationTheory for strongly coupled quantum dot cavity quantum electrodynamics
Folie: 1 Theory for strongly coupled quantum dot cavity quantum electrodynamics Alexander Carmele OUTLINE Folie: 2 I: Introduction and Motivation 1.) Atom quantum optics and advantages of semiconductor
More informationNon-equilibrium Green s functions: Rough interfaces in THz quantum cascade lasers
Non-equilibrium Green s functions: Rough interfaces in THz quantum cascade lasers Tillmann Kubis, Gerhard Klimeck Department of Electrical and Computer Engineering Purdue University, West Lafayette, Indiana
More informationAll optical quantum computation by engineering semiconductor. macroatoms. Irene D Amico. Dept. of Physics, University of York
All optical quantum computation by engineering semiconductor macroatoms Irene D Amico Dept. of Physics, University of York (Institute for Scientific Interchange, Torino) GaAs/AlAs, GaN/AlN Eliana Biolatti
More informationTime Dependent Perturbation Theory. Andreas Wacker Mathematical Physics Lund University
Time Dependent Perturbation Theory Andreas Wacker Mathematical Physics Lund University General starting point (t )Ψ (t ) Schrödinger equation i Ψ (t ) = t ^ (t ) has typically no analytic solution for
More informationWhite Rose Research Online URL for this paper:
This is a repository copy of Self-consistent solutions to the intersubband rate equations in quantum cascade lasers: Analysis of a GaAs/AlxGa1-xAs device. White Rose Research Online URL for this paper:
More informationLandau s Fermi Liquid Theory
Thors Hans Hansson Stockholm University Outline 1 Fermi Liquids Why, What, and How? Why Fermi liquids? What is a Fermi liquids? Fermi Liquids How? 2 Landau s Phenomenological Approach The free Fermi gas
More informationUltrafast Dynamics in Complex Materials
Ultrafast Dynamics in Complex Materials Toni Taylor MPA CINT, Center for Integrated Nanotechnologies Materials Physics and Applications Division Los Alamos National Laboratory Workshop on Scientific Potential
More informationResonantly Excited Time-Resolved Photoluminescence Study of Self-Organized InGaAs/GaAs Quantum Dots
R. Heitz et al.: PL Study of Self-Organized InGaAs/GaAs Quantum Dots 65 phys. stat. sol. b) 221, 65 2000) Subject classification: 73.61.Ey; 78.47.+p; 78.55.Cr; 78.66.Fd; S7.12 Resonantly Excited Time-Resolved
More informationLuminescence Process
Luminescence Process The absorption and the emission are related to each other and they are described by two terms which are complex conjugate of each other in the interaction Hamiltonian (H er ). In an
More informationOpen Quantum Systems and Markov Processes II
Open Quantum Systems and Markov Processes II Theory of Quantum Optics (QIC 895) Sascha Agne sascha.agne@uwaterloo.ca July 20, 2015 Outline 1 1. Introduction to open quantum systems and master equations
More informationElectronic Squeezing by Optically Pumped Phonons: Transient Superconductivity in K 3 C 60. With: Eli Wilner Dante Kennes Andrew Millis
Electronic Squeezing by Optically Pumped Phonons: Transient Superconductivity in K 3 C 60 With: Eli Wilner Dante Kennes Andrew Millis Background: Mean-Field Theory of Simple Superconductivity If the effective
More informationQuantum Light-Matter Interactions
Quantum Light-Matter Interactions QIC 895: Theory of Quantum Optics David Layden June 8, 2015 Outline Background Review Jaynes-Cummings Model Vacuum Rabi Oscillations, Collapse & Revival Spontaneous Emission
More informationSummary lecture IX. The electron-light Hamilton operator reads in second quantization
Summary lecture IX The electron-light Hamilton operator reads in second quantization Absorption coefficient α(ω) is given by the optical susceptibility Χ(ω) that is determined by microscopic polarization
More informationUnified theory for collisional dephasing in strong radiation fields. A generalisation of the Karplus-Schwinger formula
J. Phys. B: Atom. Molec. Phys. 13 (1980) L331-L335. Printed in Great Britain LETI'ER TO THE EDITOR Unified theory for collisional dephasing in strong radiation fields. A generalisation of the Karplus-Schwinger
More informationLecture Models for heavy-ion collisions (Part III): transport models. SS2016: Dynamical models for relativistic heavy-ion collisions
Lecture Models for heavy-ion collisions (Part III: transport models SS06: Dynamical models for relativistic heavy-ion collisions Quantum mechanical description of the many-body system Dynamics of heavy-ion
More informationField-Driven Quantum Systems, From Transient to Steady State
Field-Driven Quantum Systems, From Transient to Steady State Herbert F. Fotso The Ames Laboratory Collaborators: Lex Kemper Karlis Mikelsons Jim Freericks Device Miniaturization Ultracold Atoms Optical
More informationPart III: Impurities in Luttinger liquids
Functional RG for interacting fermions... Part III: Impurities in Luttinger liquids 1. Luttinger liquids 2. Impurity effects 3. Microscopic model 4. Flow equations 5. Results S. Andergassen, T. Enss (Stuttgart)
More informationTwo-Color three-pulse Photon Echoes
Two-Color three-pulse Photon Echoes Intensity (normalized) 1 0.8 0.6 0.4 0.2 IR144 in Methanol 0 600 650 700 750 800 850 900 Wavelength (nm) 1 Intensity (normalized) 0.8 0.6 0.4 0.2 DTTCI in Methanol 0
More informationRenormalization of microscopic Hamiltonians. Renormalization Group without Field Theory
Renormalization of microscopic Hamiltonians Renormalization Group without Field Theory Alberto Parola Università dell Insubria (Como - Italy) Renormalization Group Universality Only dimensionality and
More informationInfluence of hyperfine interaction on optical orientation in self-assembled InAs/GaAs quantum dots
Influence of hyperfine interaction on optical orientation in self-assembled InAs/GaAs quantum dots O. Krebs, B. Eble (PhD), S. Laurent (PhD), K. Kowalik (PhD) A. Kudelski, A. Lemaître, and P. Voisin Laboratoire
More informationAb initio phonon calculations in mixed systems
Ab initio phonon calculations in mixed systems Andrei Postnikov apostnik@uos.de Outline: Experiment vs. ab initio theory Ways of theory: linear response and frozen phonon approaches Applications: Be x
More informationChiral kinetic theory and magnetic effect. Yoshimasa Hidaka (RIKEN)
Chiral kinetic theory and magnetic effect Yoshimasa Hidaka (RIKEN) What is chiral kinetic theory? Relativistic Boltzmann equation (v µ @ µ + v µ F µ @ p )f = C[f] widely used in plasma physics Transport
More informationQuantum Dot Lasers. Andrea Fiore. Ecole Polytechnique Fédérale de Lausanne
Quantum Dot Lasers Ecole Polytechnique Fédérale de Lausanne Outline: Quantum-confined active regions Self-assembled quantum dots Laser applications Electronic states in semiconductors Schrödinger eq.:
More informationTHREE-dimensional electronic confinement in semiconductor
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 3, MARCH 2007 287 Differential Gain and Gain Compression in Quantum-Dot Lasers Andrea Fiore and Alexander Markus Abstract The dynamics of optical gain
More informationSUPPLEMENTARY INFORMATION
doi:10.1038/nature12036 We provide in the following additional experimental data and details on our demonstration of an electrically pumped exciton-polariton laser by supplementing optical and electrical
More informationStopping dynamics of ions passing through correlated honeycomb clusters
Stopping dynamics of ions passing through correlated honeycomb clusters Karsten Balzer, 1, Niclas Schlünzen, 2 and Michael Bonitz 2 1 Rechenzentrum, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Strasse
More informationMean field theories of quantum spin glasses
Mean field theories of quantum spin glasses Antoine Georges Olivier Parcollet Nick Read Subir Sachdev Jinwu Ye Talk online: Sachdev Classical Sherrington-Kirkpatrick model H = JS S i j ij i j J ij : a
More informationGeSi Quantum Dot Superlattices
GeSi Quantum Dot Superlattices ECE440 Nanoelectronics Zheng Yang Department of Electrical & Computer Engineering University of Illinois at Chicago Nanostructures & Dimensionality Bulk Quantum Walls Quantum
More informationLaser Induced Control of Condensed Phase Electron Transfer
Laser Induced Control of Condensed Phase Electron Transfer Rob D. Coalson, Dept. of Chemistry, Univ. of Pittsburgh Yuri Dakhnovskii, Dept. of Physics, Univ. of Wyoming Deborah G. Evans, Dept. of Chemistry,
More informationScattering theory of current-induced forces. Reinhold Egger Institut für Theoretische Physik, Univ. Düsseldorf
Scattering theory of current-induced forces Reinhold Egger Institut für Theoretische Physik, Univ. Düsseldorf Overview Current-induced forces in mesoscopic systems: In molecule/dot with slow mechanical
More informationRelativistic magnetotransport in graphene
Relativistic magnetotransport in graphene Markus Müller in collaboration with Lars Fritz (Harvard) Subir Sachdev (Harvard) Jörg Schmalian (Iowa) Landau Memorial Conference June 6, 008 Outline Relativistic
More informationIntraband emission of GaN quantum dots at λ =1.5 μm via resonant Raman scattering
Intraband emission of GaN quantum dots at λ =1.5 μm via resonant Raman scattering L. Nevou, F. H. Julien, M. Tchernycheva, J. Mangeney Institut d Electronique Fondamentale, UMR CNRS 8622, University Paris-Sud
More informationNonadiabatic dynamics and coherent control of nonequilibrium superconductors
Nonadiabatic dynamics and coherent control of nonequilibrium superconductors Andreas Schnyder Workshop on strongly correlated electron systems Schloss Ringberg, November 13 k F 1 t (ps 3 4 in collaboration
More information7. FREE ELECTRON THEORY.
7. FREE ELECTRON THEORY. Aim: To introduce the free electron model for the physical properties of metals. It is the simplest theory for these materials, but still gives a very good description of many
More informationThe interaction of light and matter
Outline The interaction of light and matter Denise Krol (Atom Optics) Photon physics 014 Lecture February 14, 014 1 / 3 Elementary processes Elementary processes 1 Elementary processes Einstein relations
More information22.51 Quantum Theory of Radiation Interactions
.5 Quantum Theory of Radiation Interactions Mid-Term Exam October 3, Name:.................. In this mid-term we will study the dynamics of an atomic clock, which is one of the applications of David Wineland
More informationIntensity / a.u. 2 theta / deg. MAPbI 3. 1:1 MaPbI 3-x. Cl x 3:1. Supplementary figures
Intensity / a.u. Supplementary figures 110 MAPbI 3 1:1 MaPbI 3-x Cl x 3:1 220 330 0 10 15 20 25 30 35 40 45 2 theta / deg Supplementary Fig. 1 X-ray Diffraction (XRD) patterns of MAPbI3 and MAPbI 3-x Cl
More informationFemtosecond Spectral Hole Burning Spectroscopy as a Probe of Exciton Dynamics in Quantum Dots
Vol. 113 (2008) ACTA PHYSICA POLONICA A No. 3 Proceedings of the 13th International Symposium UFPS, Vilnius, Lithuania 2007 Femtosecond Spectral Hole Burning Spectroscopy as a Probe of Exciton Dynamics
More informationOpen quantum systems
Open quantum systems Wikipedia: An open quantum system is a quantum system which is found to be in interaction with an external quantum system, the environment. The open quantum system can be viewed as
More informationPlasma Spectroscopy Inferences from Line Emission
Plasma Spectroscopy Inferences from Line Emission Ø From line λ, can determine element, ionization state, and energy levels involved Ø From line shape, can determine bulk and thermal velocity and often
More informationɛ(k) = h2 k 2 2m, k F = (3π 2 n) 1/3
4D-XY Quantum Criticality in Underdoped High-T c cuprates M. Franz University of British Columbia franz@physics.ubc.ca February 22, 2005 In collaboration with: A.P. Iyengar (theory) D.P. Broun, D.A. Bonn
More informationTheory of quantum dot cavity-qed
03.01.2011 Slide: 1 Theory of quantum dot cavity-qed -- LO-phonon induced cavity feeding and antibunching of thermal radiation -- Alexander Carmele, Julia Kabuss, Marten Richter, Andreas Knorr, and Weng
More informationSupplementary Information for Experimental signature of programmable quantum annealing
Supplementary Information for Experimental signature of programmable quantum annealing Supplementary Figures 8 7 6 Ti/exp(step T =.5 Ti/step Temperature 5 4 3 2 1 0 0 100 200 300 400 500 Annealing step
More informationA path integral approach to the Langevin equation
A path integral approach to the Langevin equation - Ashok Das Reference: A path integral approach to the Langevin equation, A. Das, S. Panda and J. R. L. Santos, arxiv:1411.0256 (to be published in Int.
More informationOut-of-equilibrium electron dynamics in photoexcited topological insulators studied by TR-ARPES
Cliquez et modifiez le titre Out-of-equilibrium electron dynamics in photoexcited topological insulators studied by TR-ARPES Laboratoire de Physique des Solides Orsay, France June 15, 2016 Workshop Condensed
More informationDispersion interactions with long-time tails or beyond local equilibrium
Dispersion interactions with long-time tails or beyond local equilibrium Carsten Henkel PIERS session Casimir effect and heat transfer (Praha July 2015) merci à : G. Barton (Sussex, UK), B. Budaev (Berkeley,
More informationPolariton laser in micropillar cavities
Polariton laser in micropillar cavities D. Bajoni, E. Wertz, P. Senellart, I. Sagnes, S. Bouchoule, A. Miard, E. Semenova, A. Lemaître and J. Bloch Laboratoire de Photonique et de Nanostructures LPN/CNRS,
More informationSolid State Device Fundamentals
4. lectrons and Holes Solid State Device Fundamentals NS 45 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 4N101b 1 4. lectrons and Holes Free electrons and holes
More informationNon-equilibrium time evolution of bosons from the functional renormalization group
March 14, 2013, Condensed Matter Journal Club University of Florida at Gainesville Non-equilibrium time evolution of bosons from the functional renormalization group Peter Kopietz, Universität Frankfurt
More informationTalk online at
Talk online at http://sachdev.physics.harvard.edu Outline 1. CFT3s in condensed matter physics Superfluid-insulator and Neel-valence bond solid transitions 2. Quantum-critical transport Collisionless-t0-hydrodynamic
More informationPHYSICAL SCIENCES PART A
PHYSICAL SCIENCES PART A 1. The calculation of the probability of excitation of an atom originally in the ground state to an excited state, involves the contour integral iωt τ e dt ( t τ ) + Evaluate the
More informationS.K. Saikin May 22, Lecture 13
S.K. Saikin May, 007 13 Decoherence I Lecture 13 A physical qubit is never isolated from its environment completely. As a trivial example, as in the case of a solid state qubit implementation, the physical
More informationIntroduction to Relaxation Theory James Keeler
EUROMAR Zürich, 24 Introduction to Relaxation Theory James Keeler University of Cambridge Department of Chemistry What is relaxation? Why might it be interesting? relaxation is the process which drives
More informationTransient dynamics without time propagation
Transient dynamics without time propagation Department of Physics University of Jyväskylä Aug 30th, 2012 1 Introduction 2 3 4 5 We study quantum transport of non-interacting electrons. Why? Ideal conditions
More informationSupplementary Figure 1 Transient absorption (TA) spectrum pumped at 400 nm in the FAPbI3 sample with different excitation intensities and initial
Supplementary Figure 1 Transient absorption (TA) spectrum pumped at 400 nm in the FAPbI3 sample with different excitation intensities and initial carrier concentrations: (a) N0 = 4.84 10 18 cm -3 ; (c)
More information3. LATTICE VIBRATIONS. 3.1 Sound Waves
3. LATTIC VIBRATIONS Atoms in lattice are not stationary even at T 0K. They vibrate about particular equilibrium positions at T 0K ( zero-point energy). For T > 0K, vibration amplitude increases as atoms
More informationwhere β = 1, H = H µn (3.3) If the Hamiltonian has no explicit time dependence, the Greens functions are homogeneous in time:
3. Greens functions 3.1 Matsubara method In the solid state theory class, Greens functions were introduced as response functions; they can be used to determine the quasiparticle density of states. They
More informationPhotoemission Studies of Strongly Correlated Systems
Photoemission Studies of Strongly Correlated Systems Peter D. Johnson Physics Dept., Brookhaven National Laboratory JLab March 2005 MgB2 High T c Superconductor - Phase Diagram Fermi Liquid:-Excitations
More informationLecture 1: The Equilibrium Green Function Method
Lecture 1: The Equilibrium Green Function Method Mark Jarrell April 27, 2011 Contents 1 Why Green functions? 2 2 Different types of Green functions 4 2.1 Retarded, advanced, time ordered and Matsubara
More informationLandau-Fermi liquid theory
Landau-Fermi liquid theory Shreyas Patankar Chennai Mathematical Institute Abstract We study the basic properties of Landau s theory of a system of interacting fermions (a Fermi liquid). The main feature
More informationQuantum Condensed Matter Physics Lecture 9
Quantum Condensed Matter Physics Lecture 9 David Ritchie QCMP Lent/Easter 2018 http://www.sp.phy.cam.ac.uk/drp2/home 9.1 Quantum Condensed Matter Physics 1. Classical and Semi-classical models for electrons
More informationQuantum Kinetic Transport under High Electric Fields
VLSI DESIGN 1998, Vol. 6, Nos. (1-4), pp. 3-7 Reprints available directly from the publisher Photocopying permitted by license only 1998 OPA (Ov+rseas Publishers Association) N.V. Published by license
More information(002)(110) (004)(220) (222) (112) (211) (202) (200) * * 2θ (degree)
Supplementary Figures. (002)(110) Tetragonal I4/mcm Intensity (a.u) (004)(220) 10 (112) (211) (202) 20 Supplementary Figure 1. X-ray diffraction (XRD) pattern of the sample. The XRD characterization indicates
More informationSemiconductor device structures are traditionally divided into homojunction devices
0. Introduction: Semiconductor device structures are traditionally divided into homojunction devices (devices consisting of only one type of semiconductor material) and heterojunction devices (consisting
More informationCondensed Matter Physics 2016 Lecture 13/12: Charge and heat transport.
Condensed Matter Physics 2016 Lecture 13/12: Charge and heat transport. 1. Theoretical tool: Boltzmann equation (review). 2. Electrical and thermal conductivity in metals. 3. Ballistic transport and conductance
More informationBCS Pairing Dynamics. ShengQuan Zhou. Dec.10, 2006, Physics Department, University of Illinois
BCS Pairing Dynamics 1 ShengQuan Zhou Dec.10, 2006, Physics Department, University of Illinois Abstract. Experimental control over inter-atomic interactions by adjusting external parameters is discussed.
More informationModeling of Transport and Gain in Quantum Cascade Lasers
Modeling of Transport and Gain in Quantum Cascade Lasers Andreas Wacker in collaboration with: M.P. Pereira Jr., NMRC, Cork p.1 Introduction p.2 The Challenge: Intersubband Lasing tunneling Kazarinov and
More information8 Quantized Interaction of Light and Matter
8 Quantized Interaction of Light and Matter 8.1 Dressed States Before we start with a fully quantized description of matter and light we would like to discuss the evolution of a two-level atom interacting
More information[ ( )] + ρ VIII. NONLINEAR OPTICS -- QUANTUM PICTURE: 45 THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE 88
THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE 88 VIII. NONLINEAR OPTICS -- QUANTUM PICTURE: 45 A QUANTUM MECHANICAL VIEW OF THE BASICS OF N ONLINEAR OPTICS 46 In what follows we draw on
More informationRadiation-Induced Magnetoresistance Oscillations in a 2D Electron Gas
Radiation-Induced Magnetoresistance Oscillations in a 2D Electron Gas Adam Durst Subir Sachdev Nicholas Read Steven Girvin cond-mat/0301569 Yale Condensed Matter Physics Seminar February 20, 2003 Outline
More informationTransport in the Outer Core of Neutron Stars
Stephan Stetina Institute for Theoretical Physics Vienna UT Transport in the Outer Core of Neutron Stars SEWM 018, Barcelona Ermal Rrapaj (University of Guelph), Sanjay Reddy (INT Seattle) [S. Stetina,
More informationChapter 12: Semiconductors
Chapter 12: Semiconductors Bardeen & Shottky January 30, 2017 Contents 1 Band Structure 4 2 Charge Carrier Density in Intrinsic Semiconductors. 6 3 Doping of Semiconductors 12 4 Carrier Densities in Doped
More informationPH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5
PH575 Spring 2014 Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 POP QUIZ Phonons are: A. Fermions B. Bosons C. Lattice vibrations D. Light/matter interactions PH575 POP QUIZ Phonon dispersion relation:
More informationF r (t) = 0, (4.2) F (t) = r= r a (t)
Chapter 4 Stochastic Equations 4.1 Langevin equation To explain the idea of introduction of the Langevin equation, let us consider the concrete example taken from surface physics: motion of an atom (adatom)
More informationCourse overview. Me: Dr Luke Wilson. The course: Physics and applications of semiconductors. Office: E17 open door policy
Course overview Me: Dr Luke Wilson Office: E17 open door policy email: luke.wilson@sheffield.ac.uk The course: Physics and applications of semiconductors 10 lectures aim is to allow time for at least one
More informationDensity-matrix theory of the optical dynamics and transport in quantum cascade structures: The role of coherence
Density-matrix theory of the optical dynamics and transport in quantum cascade structures: The role of coherence Weber, Carsten; Wacker, Andreas; Knorr, A. Published in: Physical Review B (Condensed Matter
More informationPerturbation Theory. Andreas Wacker Mathematical Physics Lund University
Perturbation Theory Andreas Wacker Mathematical Physics Lund University General starting point Hamiltonian ^H (t) has typically noanalytic solution of Ψ(t) Decompose Ĥ (t )=Ĥ 0 + V (t) known eigenstates
More informationApplications of Renormalization Group Methods in Nuclear Physics 2
Applications of Renormalization Group Methods in Nuclear Physics 2 Dick Furnstahl Department of Physics Ohio State University HUGS 2014 Outline: Lecture 2 Lecture 2: SRG in practice Recap from lecture
More informationA Zero Field Monte Carlo Algorithm Accounting for the Pauli Exclusion Principle
A Zero Field Monte Carlo Algorithm Accounting for the Pauli Exclusion Principle Sergey Smirnov, Hans Kosina, Mihail Nedjalkov, and Siegfried Selberherr Institute for Microelectronics, TU-Vienna, Gusshausstrasse
More informationOptical Investigation of the Localization Effect in the Quantum Well Structures
Department of Physics Shahrood University of Technology Optical Investigation of the Localization Effect in the Quantum Well Structures Hamid Haratizadeh hamid.haratizadeh@gmail.com IPM, SCHOOL OF PHYSICS,
More informationSupplementary Materials
Supplementary Materials Sample characterization The presence of Si-QDs is established by Transmission Electron Microscopy (TEM), by which the average QD diameter of d QD 2.2 ± 0.5 nm has been determined
More informationOptics and Quantum Optics with Semiconductor Nanostructures. Overview
Optics and Quantum Optics with Semiconductor Nanostructures Stephan W. Koch Department of Physics, Philipps University, Marburg/Germany and Optical Sciences Center, University of Arizona, Tucson/AZ Overview
More informationNonrenormalizability of nonequilibrium quantum field theory in the classical approximation
Nonrenormalizability of nonequilibrium quantum field theory in the classical approximation Bin Wu IPhT, CEA/Saclay RPP 2015, Institut Henri Poincare Jan 16, 2015 T. Epelbaum, F. Gelis and B. Wu, Phys.
More informationTransport Properties of Semiconductors
SVNY85-Sheng S. Li October 2, 25 15:4 7 Transport Properties of Semiconductors 7.1. Introduction In this chapter the carrier transport phenomena in a semiconductor under the influence of applied external
More informationTransient Intersubband Optical Absorption in Double Quantum Well Structure
Commun. Theor. Phys. (Beijing, China) 43 (2005) pp. 759 764 c International Academic Publishers Vol. 43, No. 4, April 15, 2005 Transient Intersubband Optical Absorption in Double Quantum Well Structure
More informationinterband transitions in semiconductors M. Fox, Optical Properties of Solids, Oxford Master Series in Condensed Matter Physics
interband transitions in semiconductors M. Fox, Optical Properties of Solids, Oxford Master Series in Condensed Matter Physics interband transitions in quantum wells Atomic wavefunction of carriers in
More informationIntroduction to DMFT
Introduction to DMFT Lecture 2 : DMFT formalism 1 Toulouse, May 25th 2007 O. Parcollet 1. Derivation of the DMFT equations 2. Impurity solvers. 1 Derivation of DMFT equations 2 Cavity method. Large dimension
More informationTransport coefficients in plasmas spanning weak to strong correlation
Transport coefficients in plasmas spanning weak to strong correlation Scott D. Baalrud 1,2 and Jerome Daligault 1 1 Theoretical Division, Los Alamos National Laboratory 2 Department of Physics and Astronomy,
More informationDynamically assisted Sauter-Schwinger effect
Dynamically assisted Sauter-Schwinger effect Ralf Schützhold Fachbereich Physik Universität Duisburg-ssen Dynamically assisted Sauter-Schwinger effect p.1/16 Dirac Sea Schrödinger equation (non-relativistic)
More information