Transport and spin transport of excitons Leonid V

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 • 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)

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 3 D: mexciton ~ 10 -6 matom Kelvin for excitons is like micro. Kelvin for atoms 3 D gas of Rb atoms: n = 1015 cm-3, matom = 105 me → Td. B ~ 5× 10 -6 K 2 D: 2 D gas of excitons in Ga. As QW n = 1010 cm-2, mexciton= 0. 2 me → Td. B ~ 3 K n < n. Mott ~ 1/a. B 2 ~ 2× 1011 cm-2

How to realize cold exciton gases ? Tlattice << 1 K in He refrigerators finite lifetime of excitons could result to high exciton temperature: Texciton > Tlattice find excitons with lifetime >> cooling time Challenges for realization of exciton condensates Indirect excitons in Texciton ~ Tlattice To solve: Find or design semiconductor structures where coupled quantum wells short lifetime bilayers excitons have long lifetimes >> cooling Electron-electron Electron-hole bilayers times in magnetic fields at n =1 with gate-induced carriers with photoexcited carriers competing ground states, e. g. EHL excitons form the lowest energy state exciton destruction, e. g. due to Mott transition excitons have large binding energy disordere disorder is weak e solving these challenges has led to studies of various experimental systems and various types of exciton condensate

Why indirect excitons in CQW ? 103 -106 times longer exciton lifetime due to separation between electron and hole layers 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) 103 times shorter exciton cooling time than that in bulk semiconductors TX ~ 100 m. K has been realized experimentally 30 times below Td. B TX ~ 10 ns to cool to 300 m. K ~ 100 ns to cool to 100 m. K A. L. Ivanov et al in PRL 86, 5608 (2001) Time (ns)

Repulsive interaction between indirect excitons Repulsive dipole-dipole interaction ● stabilizes exciton state against formation of metallic EHL D. Yoshioka, A. H. Mac. Donald, 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 ● results in effective screening of in-plane disorder d indirect excitons are oriented dipoles A. L. Ivanov, EPL 59, 586 (2002) R. Zimmermann also high quality CQW samples with small initial disorder are required to overcome exciton localization 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: d. E ~ n/C estimate for exciton density approximation for short-range 1/r 3 interaction C = e/4 pe 2 d C. Schindler, R. Zimmermann, PRB 78, 045313 (2008) C and n in experiments are higher

the ability to control electron fluxes by an applied gate voltage electronic circuit devices mesoscopics the field which concerns electron transport in a potential landscapes potential energy of indirect excitons can be controlled by voltage e h 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 excitonic circuit devices mesoscopics of bosons in semiconductors

indirect excitons d have long lifetimes can cool down to 0. 1 K well below Td. B ~ 3 K condensation pattern formation have built-in dipole moment ed can travel over large distances transport spin transport cold Bose gases in solid-state materials energy can be controlled by gate voltage potential profiles can be created and in situ controlled excitonic devices optical methods → local probe of excitons

Exciton pattern formation and exciton transport

Pattern Formation: Exciton Rings and Macroscopically Ordered Exciton State external ring inner ring same ring fragmentation spatial order on macroscopic lengths localized bright spots 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)

Inner ring PL pattern spatial distribution of optically active low energy excitons flow of excitons out of excitation spot due to exciton drift, diffusion, phonon wind, etc. PL Intensity exciton transport over tens of microns E Energy (e. V) E repulsive interaction → drift r (mm) excitons can travel in a dark state after having been excited until slowed down inner ring forms due to to a velocity below photon emission threshold, where they canand decay radiatively exciton transport cooling k excitation spot high TX exciton drift lower occupation of radiative zone k inner ring lower TX excitons relax to radiative zone higher occupation of radiative zone 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)

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

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 cm 2/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)

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

Kinetics of external ring and LBS rings time expansion of external ring a b collapse of external ring c d e f g h external ring e h 100 mm - 9. 5 ms i -10 ms - 8. 8 ms - 6. 5 ms laser pulse 50 0 40 cm 2/s 0 c 26 cm 2/s 3 ms 4 ms j expansion of LBS rings collapse of external ring Dh = 16 cm 2/s 2. 5 ms 5 ms 0 De = 200 Radius (mm) 250 1. 5 ms 0. 2 ms LBS ring h e cm 2/s kinetics of external and LBS rings 80 cm 2/s 30 cm 2/s estimation of e and h transport characteristics De ~ 80 cm 2/s, Dh ~ 20 cm 2/s 0 Sen Yang, L. V. Butov, L. S. Levitov, B. D. Simons, A. C. Gossard, PRB 81, 115320 (2010)

indirect exciton PL – pattern of hot spots localized bright spots have hot cores no hot spots in external ring and LBS 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 macroscopically ordered exciton state (MOES)

Coherence Length (mm) PL Contrast along the Ring Spontaneous coherence Temperature (K) the increase of the coherence length x is correlated with the macroscopic spatial ordering of excitons x ~ 2 mm >> the classical value ~ ld. B ~ 0. 1 mm spontaneous coherence = = condensation in k-space MOES is a state with: ● macroscopic spatial ordering and ● large coherence length → a condensate in k-space 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) left arm right arm

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

Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials potential energy of indirect excitons can be controlled by voltage e h 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)

Exciton Optoelectronic Transistor (EXOT) optical input gate 5 mm photonic drain Gate QWs optical output gate 1 ON drain gate source 0 i n Exciton energy OFF energy bump controlled by the Gate photon input photon output electronic control Intensity photonic source exciton flow is off exciton flow is on x similar in geometry and operation to electronic FET ON OFF Distance (mm) Time (ns) prototype EXOT performs switching at speeds > 1 GHz prototype excitonic IC performs directional switching and merging 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 and optical communication is effectively eliminated in excitonic devices → advantage in applications where interconnection speed is important

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)

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

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 me. V 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)

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 random potential Elattice >> Erand interaction energy at LDT ≈ amplitude of unscreened lattice estimate for the strength of disorder: Erand ~ 0. 8 me. V

Conveyers

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 amplitude speed electrodes voltage 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

Spin transport of excitons

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

Spin-Flip Pathways polarization relaxation time tr tr tex optically active states tex is determined by exchange te dark states te th interaction between e and h control tp by changing e-h overlap Ga. As SQW direct exciton Ga. As CQW indirect exciton with small e-h overlap M. Z. Maialle, E. A. de Andrada e Silva, L. J. Sham, PRB 47, 15776 (1993). fast depolarization within tens of ps orders of magnitude enhancement of exciton spin relaxation time exciton spin transport over substantial distances is problematic makes possible exciton spin transport over substantial distances J. R. Leonard, Y. Y. Kuznetsova, Sen Yang, L. V. Butov, T. Ostatnick´y, A. Kavokin, A. C. Gossard, Nano Lett. 9, 4204 (2009)

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

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

Decrease of P and t. P with increasing density complies with D’yakonov-Perel’ spin relaxation mechanism spin splitting constant experiment: theoretical estimate:

Vortices

Vortices quantized vortex is characterized by point (or line) around which phase of wave function varies by 2 pn 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

Fork-like topological defects in interference pattern of indirect excitons indicating the presence of quantized vortices Pex for different polarizations hor vert s 1 s 2 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

Number of forks in various regions of exciton pattern formation number of forks in 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

Acknowledgements 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 supported by ARO, NSF, DOE 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) Collaborators in studies of indirect excitons: Gerhard Abstreiter, WSI Daniel Chemla, UCB&LBNL Valerii Dolgopolov, ISSP RAS Alexander Dzyubenko, CSB Michael Fogler, UCSD Nikolai Gippius, Blaise Pascal Arthur Gossard, UCSB Atac Imamoglu, UCSB Alexei Ivanov, Cardiff Alexey Kavokin, Southampton Leonid Levitov, MIT Peter Littlewood, Cambridge Yuri Lozovik, IS RAS Yuri Rubo, Cuernavaca Ben Simons, Cambridge Arthur Zrenner, WSI