1 / 36

Transport and spin transport of excitons Leonid V. Butov, UCSD

Transport and spin transport of excitons Leonid V. Butov, UCSD. • Indirect excitons in coupled quantum wells • Exciton pattern formation and exciton transport • Exciton transport in potential landscapes • Lattices • Traps • Circuit devices

gyala
Download Presentation

Transport and spin transport of excitons Leonid V. Butov, UCSD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Transport and spin transport of excitonsLeonid V. Butov, UCSD • Indirect excitons in coupled quantum wells • Exciton pattern formation and exciton transport • Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials • Spin transport of excitons • Conveyers • Vortices In collaboration with: Michael Fogler, Joe Graves, Martin Griswold, Aaron Hammack, Alex High, Jason Leonard, Andrew Meyertholen, Katya Novitskaya, Mikas Remeika, Averi Thomas, Alex Winbow, Sen Yang, Yuliya Kuznetsova (UCSD) Tomas Ostatnick´y, Alexey Kavokin (Southampton), Yura Rubo (Cuernavaca) Leonid Levitov (MIT), Ben Simons (Cambridge) Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff) Micah Hanson, Arthur Gossard (UCSB)

  2. What temperature is “cold” for exciton gas? transition from classical to quantum gas takes place when thermal de Broglie wavelength is comparable to interparticle separation 3D: 2D: mexciton ~ 10 -6matom Kelvin for excitons is like microKelvin for atoms 3D gas of Rb atoms: n = 1015 cm-3, matom = 105 me → TdB ~ 5×10-6 K 2D gas of excitons in GaAs QW n = 1010 cm-2, mexciton= 0.2 me → TdB ~ 3 K n < nMott~ 1/aB2~ 2×1011 cm-2

  3. Tlattice << 1 K in He refrigerators finite lifetime of excitons could result to high exciton temperature: Texciton > Tlattice find excitons with lifetime >> cooling timeTexciton ~ Tlattice How to realize cold exciton gases ? Indirect excitons in coupled quantum wells Electron-electron bilayers in magnetic fields at n =1 Electron-hole bilayers with gate-induced carriers Electron-hole bilayers with photoexcited carriers e e solving these challenges has led to studies of various experimental systems and various types of exciton condensate

  4. 103-106 times longer exciton lifetime due to separation between electron and hole layers 103 times shorter exciton cooling time than that in bulk semiconductors Why indirect excitons in CQW ? realization of cold exciton gas in separated layers was proposed by Yu.E. Lozovik & V.I. Yudson (1975); S. I. Shevchenko (1976); T. Fukuzawa, S.S. Kano, T.K. Gustafson, T. Ogawa (1990) TX~ 100 mK has been realized experimentally 30 times below TdB TX ~ 10 ns to cool to 300 mK ~ 100 ns to cool to 100 mK A.L. Ivanov et al in PRL 86, 5608 (2001) Time (ns) high quality CQW samples with small in-plane disorder are required to overcome exciton localization

  5. Repulsive dipole-dipole interaction ● stabilizes exciton state against formation of metallic EHL ● results in effective screening of in-plane disorder Repulsive interaction between indirect excitons D. Yoshioka, A.H. MacDonald, J. Phys. Soc. Jpn. 59, 4211 (1990) X. Zhu, P.B. Littlewood, M. Hybertsen, T. Rice, PRL 74, 1633 (1995) the ground state is excitonic A.L. Ivanov, EPL 59, 586 (2002) R. Zimmermann d also high quality CQW samples with small initial disorder are required to overcome exciton localization indirect excitons are oriented dipoles Repulsive interaction in experiment exciton energy increases with density L.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993) energy shift: dE ~ n/C estimate for exciton density approximation for short-range 1/r3 interaction C = e/4pe2d C. Schindler, R. Zimmermann, PRB 78, 045313 (2008) C and n in experiments are higher

  6. e h the ability to control electron fluxes by an applied gate voltage potential energy of indirect excitons can be controlled by voltage electronic circuit devices mesoscopics the field which concerns electron transport in a potential landscapes in-plane potential landscapes can be created for excitons by voltage pattern e.g. traps, lattices, circuit devices the ability to control exciton fluxes by an applied gate voltage mesoscopics of bosons in semiconductors excitonic circuit devices

  7. indirect excitons d have long lifetimes have built-in dipole moment ed can cool down to 0.1 K well below TdB ~ 3K can travel over large distances energy can be controlled by gate voltage condensation pattern formation transport spin transport potential profiles can be created and in situ controlled cold Bose gases in solid-state materials excitonic devices optical methods → local probe of excitons

  8. Exciton pattern formation and exciton transport

  9. 2D-fire Pattern Formation: Exciton Rings and Macroscopically Ordered Exciton State inner ring external ring same spatial order on macroscopic lengths PL intensity ring fragmentation localized bright spots position on the ring (mm) 410 mm T=1.8 K T=4.7 K appears abruptly at low T L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002)

  10. Inner ring flow of excitons out of excitation spot due to exciton drift, diffusion, phonon wind, etc. PL pattern spatial distribution of optically active low energy excitons Discussion exciton transport over tens of microns PL Intensity E E repulsive interaction → drift Energy (eV) r (mm) k k excitons can travel in a dark state after having been excited until slowed down to a velocity below photon emission threshold, where they can decay radiatively excitation spot high TX exciton drift lower occupation of radiative zone inner ring lower TX excitons relax to radiative zone higher occupation of radiative zone inner ring forms due to exciton transport and cooling L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002) A.L. Ivanov, L. Smallwood, A. Hammack, Sen Yang, L.V. Butov, A.C. Gossard, EPL 73, 920 (2006)

  11. Localization-delocalization transition for exciton transport in random potential exp. theory exp. theory low densities: emission profile follows excitation spot excitons are localized in random potential high densities: emission extends well beyond excitation spot excitons screen random potential, travel away from excitation spot and form inner ring

  12. Kinetics of inner ring exp. theory formation time of inner ring ~ 30 ns kinetics of inner ring estimate of exciton transport characteristics DX reaches ~ 20 cm2/s PL jump vs r → excitons outside laser spot including inner ring region are cooled to Tlattice even during laser excitation A.T. Hammack, L.V. Butov, J. Wilkes, L. Mouchliadis, E.A. Muljarov, A.L. Ivanov, A.C. Gossard, PRB 80, 155331 (2009)

  13. electrons holes excitons External ring above barrier laser excitation creates additional number of holes in CQW external ring heavier holes have higher collection efficiency to CQW E excess holes are photogenerated in the laser excitation spot electron source is spread out over the entire plane due to current through the CQW from n-doped GaAs layers z external ring forms at interface between electron-rich and hole-rich regions y holes created at the excitation spot diffuse out this depletes electrons in the vicinity of the laser spot creating electron-free and hole rich region x same for e ↔ h L.V. Butov, L.S. Levitov, B.D. Simons, A.V. Mintsev, A.C. Gossard, D.S. Chemla, PRL 92, 117404 (2004) R. Rapaport, G. Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K.West, Y.Liu, S.Denev, PRL 92, 117405 (2004)

  14. h e Kinetics of external ring and LBS rings time expansion of external ringcollapse of external ring a b c d e f g h external ring e h LBS ring 100mm 1.5 ms 2.5 ms 4 ms 3 ms - 9.5 ms - 8.8 ms - 6.5 ms 0.2 ms i j 5ms -10ms laser pulse 0 expansion of LBS rings collapse of external ring 250 50 kinetics of external and LBS rings estimation of e and h transport characteristics De ~ 80 cm2/s, Dh ~ 20 cm2/s De = 200 cm2/s 80 cm2/s Dh = 16 cm2/s 0 Radius (mm) Radius (mm) 30 cm2/s 40 cm2/s c 26 cm2/s 0 0 Sen Yang, L.V. Butov, L.S. Levitov, B.D. Simons, A.C. Gossard, PRB 81, 115320 (2010)

  15. indirect exciton PL direct exciton PL – pattern of hot spots localized bright spots have hot cores no hot spots in external ring and LBS rings macroscopically ordered exciton state (MOES) rings are far from hot spots due to long lifetimes of indirect excitons TX≈ Tlattice rings form is region where cold and dense exciton gas is created

  16. Spontaneous coherence the increase of the coherence lengthx is correlatedwith the macroscopic spatial ordering of excitons x ~ 2 mm >> the classical value ~ ldB ~ 0.1 mm PL Contrast along the Ring spontaneous coherence = = condensation in k-space Coherence Length (mm) MOES is a state with: ● macroscopic spatial ordering and ● large coherence length → a condensate in k-space Temperature (K) model: L.S. Levitov, B.D. Simons, L.V. Butov, PRL 94, 176404 (2005) experimental method: Mach-Zehnder interferometry with spatial and spectral resolution probing coherence far from laser both in space and energy: coherence is spontaneous Sen Yang, A. Hammack, M.M. Fogler, L.V. Butov, A.C. Gossard, PRL 97, 187402 (2006) right arm left arm

  17. Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials

  18. e h Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials potential energy of indirect excitons can be controlled by voltage in-plane potential landscapes for excitons can be created by voltage pattern can be controlled in-situ by voltages on timescale much shorter than exciton lifetime obstacle: in-plane electric field can lead to exciton dissociation proposed design in which in-plane electric field is suppressed allows creating virtually arbitrary in-plane potential landscape for excitons by voltage pattern A.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, JAP 99, 066104 (2006)

  19. photonic source photonic drain optical input gate optical output gate Gate i QWs n 5 mm OFF ON energy bump controlled by the Gate drain gate source Exciton energy exciton flow is off exciton flow is on x Exciton Optoelectronic Transistor (EXOT) 1 0 ON photon input photon output electronic control Intensity OFF Distance (mm) Time (ns) prototype EXOT performs switching at speeds > 1 GHz prototype excitonic IC performs directional switching and merging similar in geometry and operation to electronic FET A.A. High, A.T. Hammack, L.V. Butov, M. Hanson, A.C. Gossard, Opt. Lett.32, 2466 (2007) A.A. High, E.E. Novitskaya, L.V. Butov, M. Hanson, A.C. Gossard, Science 321, 229 (2008) demonstrated operation up to ~ 100 K G. Grosso, J. Graves, A.T. Hammack, A.A. High, L.V. Butov, M. Hanson, A.C. Gossard, Nat. Photonics 3, 577 (2009) delay between signal processing andopticalcommunication is effectively eliminated in excitonic devices→ advantage in applications where interconnection speed is important

  20. A.A. High, A.K. Thomas, G. Grosso, M. Remeika, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 103, 087403 (2009)

  21. Collection of exciton cloud to trap center with increasing density Width 5 mm 5 mm 5 meV width of exciton cloud in trap ▲ exp ▬ theory 5 mm density → repulsive interaction screening of disorder collection to trap bottom cold exciton gas in trap excitation power (mW) can be controlled in situ like traps for cold atoms

  22. Atoms in lattices M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, I. Bloch, Nature 415, 39, (2002) J.K. Chin, D.E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, W. Ketterle, Nature 443, 961 (2006) atoms in lattices – system with controllable parameters use atoms in lattices to emulate solid state materials Excitons in lattices Elattice = 3.7 meV Elattice = 0 controllable: exciton density, interaction, mass lattice amplitude, structure, constant a tool with a number of control knobs for studying the physics of excitons M. Remeika, J. Graves, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 102, 186803 (2009)

  23. Localization - delocalization transition (LDT) loc: emission profile follows excitation spot deloc: emission extends well beyond excitation spot model attributes LDT to interaction-induced percolation of exciton gas through external potential Etotal = Elattice + Erand Elattice >> Erand interaction energy at LDT ≈ amplitude of unscreened lattice Elattice << Erand interaction energy at LDT ≈ amplitude of unscreened random potential estimate for the strength of disorder: Erand ~ 0.8 meV

  24. Conveyers

  25. Transport of electrons, holes, excitons, and polaritons via SAW C. Rocke, S. Zimmermann, A. Wixforth, J.P. Kotthaus, G. Böhm, G. Weimann, PRL 78, 4099 (1997) P.V. Santos, M. Ramsteiner, R. Hey, PSS B 215, 253 (1999) J. Rudolph, R. Hey, P.V. Santos, PRL 99, 047602 (2007) this conference Electrostatic conveyers for excitons conveyers are created by applying AC voltages to lattice electrodes → traveling lattice wavelength  electrodes amplitude  voltage speed  frequency conveyer off conveyer on study dynamic LDT with varying conveyer amplitude conveyer speed exciton density A.G. Winbow, J.R. Leonard, M. Remeika, A.A. High, E. Green, A.T. Hammack L.V. Butov, M. Hanson, A.C. Gossard, unpublished phonon wind in the conveyer frame crossing phonon velocity

  26. Spin transport of excitons

  27. Spin transport of excitons exciton spin transport over substantial distances requires • exciton transport over substantial distances • long spin relaxation time long tr high D

  28. tr tr tex te te th Spin-Flip Pathways polarization relaxation time Polarization of emission decays when both e and h flip their spins. This can occur in two-step process due to separate e and h spin flips and single step process due to exciton spin flip. optically active states tex is determined by exchange interaction between e and h control tp by changing e-h overlap dark states GaAs SQW direct exciton GaAs CQW indirect exciton with small e-h overlap M.Z. Maialle, E.A. de Andrada e Silva, L.J. Sham, PRB 47, 15776 (1993). orders of magnitude enhancement of exciton spin relaxation time fast depolarization within tens of ps makes possible exciton spin transport over substantial distances exciton spin transport over substantial distances is problematic J.R. Leonard, Y.Y. Kuznetsova, Sen Yang, L.V. Butov, T. Ostatnick´y, A. Kavokin, A.C. Gossard, Nano Lett. 9, 4204 (2009)

  29. Density dependence deloc loc tP of indirect excitons reaches several ns >> tP of direct excitons P and tP drop with increasing density decrease of tP is correlated with the increase D → tP drops when excitons become delocalized mo complies with DP spin relaxation mechanism

  30. Spin transport of excitons experiment theory experiment and theory extension of polarization profiles beyond excitation spot shows exciton spin transport spin transport of indirect excitons originates from long spin relaxation time and long lifetime

  31. Decrease of P and tP with increasing density complies with D’yakonov-Perel’ spin relaxation mechanism spin splitting constant experiment: theoretical estimate:

  32. Vortices

  33. Vortices quantized vortex is characterized by point (or line) around which phase of wave function varies by 2pn fork-like dislocation in phase pattern is signature of quantized vortex quantized atom vortices S. Inouye, S. Gupta, T. Rosenband, A.P. Chikkatur, A. Görlitz, T.L. Gustavson, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, PRL 87, 080402 (2001) F. Chevy, K.W. Madison, V. Bretin, J. Dalibard, PRA 64, 031601(R) (2001) Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006) quantized optical vortices J. Scheuer, M. Orenstein, Science 285, 230 (1999) and references therein quantized polariton vortices K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, Le Si Dang, B. Deveaud-Plédran, Nature Physics 4, 706 (2008) K.G. Lagoudakis, T. Ostatnický, A.V. Kavokin, Y.G. Rubo, R. André, B. Deveaud-Plédran, Science 326, 974 (2009) polariton half-vortices

  34. Fork-like topological defects in interference pattern of indirect excitons indicating the presence of quantized vortices Pex for different polarizations s2 s1 vert hor topological defects in multicomponent spin systems Y.G. Rubo, PRL 99, 106401 (2007) A.A. High, A.T. Hammack, J.R. Leonard, L.V. Butov, T. Ostatnicky´, A. Kavokin, Y.G. Rubo, A.C. Gossard, unpublished

  35. Number of forks in various regions of exciton pattern formation number of forks in LBS ring region LBS ring region external ring region excitation and inner ring region number of forks in external ring region no forks in excitation and inner ring region

  36. In collaboration with: Tomas Ostatnick´y, Alexey Kavokin (Southampton) Yuri Rubo (Cuernavaca) Andrew Meyertholen, Michael Fogler (UCSD) Leonid Levitov (MIT) Ben Simons (Cambridge) Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff) Micah Hanson, Arthur Gossard (UCSB) UCSD: Aaron Hammack Alex High Alex Winbow Anton Mintsev Averi Thomas James Lohner Jason Leonard Joe Graves Gabriele Grosso Katya Novitskaya Martin Griswold Mikas Remeika Sen Yang Yuliya Kuznetsova Acknowledgements Collaborators in studies of indirect excitons: Gerhard Abstreiter, WSI Daniel Chemla, UCB&LBNL ValeriiDolgopolov, ISSP RAS Alexander Dzyubenko, CSB Michael Fogler, UCSD Nikolai Gippius, Blaise Pascal Arthur Gossard, UCSB AtacImamoglu, UCSB Alexei Ivanov, Cardiff AlexeyKavokin, Southampton Leonid Levitov, MIT Peter Littlewood, Cambridge Yuri Lozovik, IS RAS Yuri Rubo, Cuernavaca Ben Simons, Cambridge Arthur Zrenner, WSI supported by ARO, NSF, DOE

More Related