Intersubband Response:

Transcription

1 Intersubband Response: Lineshape,, Coulomb Renormalization, and Microcavity Effects F. T. Vasko Inst. of Semiconductor Physics Kiev, Ukraine

2 In collaboration with: A.V. Korovin and O.E. Raichev (Inst. Semicond. Phys., Ukraine) A. Hernandez-Cabrera and P. Aceituno (Univ. La Laguna, Spain) Motivation: Mid-IR THz spectral region (solid state devices for generation, detection, and modulation). Two (multi)-level physics (coherence, e.g. macro-qbit formed ~ 10 6 electrons).

3 QW: levels, disorder, e-e interaction, spin-flip, and microcavity E-E renormalization: depolarization and exchange Lineshape: homogeneous and inhomogeneous broadening Spin-flip transitions Short-range scattering: beyond the Born approximation Microcavity effect

4 QW levels Disorder IR Pumping d d ε 2 AlGaAs or InGaAs ε 1 GaAs or InAs Dispersion law: ε n+p 2 /2m in-plane motion E d l c δd Inhomogeneous Broadening: δε n =ε n (2δd/d) δd

5 EE-interaction Microcavity effect MQWs Metals ε 2 d MQWs Momentum transfer: ( q, ~d -1 ) ε 1 ε 2 Dielectric waveguide (ε 1 > ε 2 )

6 Spin splitting E σ=+1 σ=-1 p V s appears due to: Transverse field Heterojunction potential Bulk asymmetry

7 Unscreened inhomogeneities Different random potentials + the single Poisson equation Screened potentials: Non-screened potential

8 Excange Current density: Wigner eq. for polarization: Energy splitting Perturbatrion Induced density Basic Equations

9 Coulomb matrix element: The 2D-limit: qd<<1 a B is the Borh radius

10 Kin. eq. for polarization (integral eqs.): The local approximation ( l c, algebr. eqs.): The hydrodynamics chain for: 2 δn ss ( x ) = (2 / L ) δ f ss ' δ ' p i ss ' f p ss 2 ( x ) = (2 / L ) v δ ' ( p, x ), ( p, x ),

11 1-2 Transitions: ± δ n = δ n 12 ± δ n 21 The relative absorption: The lineshape transformation: Lorentzian -- Gaussian ~ γ s ε 21 δ d / d JETP 93, 1270 (2001) Phys.Rev. B 66, (2002)

12 ω min ε F ε Spin-flip transitions ξ ω ω max p ω min ω max ω Single particle absorption at T=0

13 Hamiltonian: Perturbation: In-plane current density: Linearized kinetic Eq.: (integral equntion) V Q is the Coulomb matrix element Distribution function:

14 2 x 2 matrix eq.: 2D approximation:

15 n φ = (cos φ,sin φ ) Momentum relaxation rate

16 The relative absorption: Effect of exchange: spread of line, weak shift JETP 96, 102 (2003) J. Phys. D 36, 1166 (2003) Lineshape of absorption at T=0, InGaAs structure: Level splitting Energy of transitions

17 Intrsubband Transitions in Biased SL Intrsubband transitions Current In the Born approximation Identical QWs, Equipopulated levels absorption =0? But there is absorption/gain for unbiased SL,? with cos-dispersion law?

18 Gain α Distribution functions f in, f f Spectral functions A in, A f Absorption Stimulated emission ε Beyond the Born approximation: Absorption α ε A in x A f x f

19 Absorption: Perturbation: Linearized Kinetic Eq.: High-frequency current & Complex conductivity An exact spectral density function:

20 α ω Reσ ω, Averaging over random potentials in r-th QWs: The averaged spectral density function: Results: Phys.Rev. B 69, (2004)

21 Excitonic microcavity Haygens, 1665 (a) Schematics of band diagram of structure and field distribution; (b) Schematics of structure; (c) A coupled oscillators; (d) Energy of peaks as a function of detuning between excitons and cavity

22 Mid-IR microcavity (intersubband polariton) Reflectance of the sample as obtained at different incidence angles. In the inset: a comparison between the experimental and calculated spectrum at the resonance angle of ? (a) Transmittance of a 3.9 µm thick layer of AlAs embedded in GaAs at an angle of incidence of 60 ; the arrow indicates the energy of the chosen intersubband transition (143 mev). (b) Schematic view of the prism-shaped microresonato;; thickness values are given in nm. (D. Dini, et al. Phys. Rev. Lett. 90, , 2003).

23 Response (Lorentz oscillators):?? Virtual transitions to another levels?? to continuum?? continuum 2 1 ε i Reflectance of the microcavity sample for different angles of incidence in TM polarization. dashed lines are just a guide to the eye. In the left inset: the exp. points corresponding to the energy position of the dips are reported and the solid lines are fitted with a standard dipole oscillator dispersion. The right inset: a spectrum recorded under TE polarization.

24 Kubo formula + single particle approximation: f-mass fule (, ) ω 0 ε = const ε ω = 0 ε i nm nm nm

25 Conclusions: I. Unscreened inhomogeneities in multi-level system due to the single Poisson equation. II. EE-renormalization: depolarization (self-consistent field) + non-local exchange III. Interplay between EE-renormalization and inhomogeneous broadening (for non-local response) IV. Exchange effect on spin-flip transitions V. Gain without global inversion in a biased SL VI. Microcavity polariton splitting of intersubband transitions Q.: Is intersubband exciton possible?

26 Doubling of intersubband absorption due to non-local excange DQWs Absorption: BSL DQWs: Phys. Rev. B 60, 7776 (1999) BSL: Phys. Rev. B 66, (2002) New intersubband excitation (??) ω

27 Intreband exciton ε F Intersubband exciton??