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Phenomena in Cold Exciton Gases: Condensation, Macroscopic Ordering and Beyond L.V

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Phenomena in cold exciton gases: Condensation, macroscopic ordering and beyond L.V. Butov University of California San Diego Excitons and Electron-Hole Plasma electron _ exciton – bound pair of electron and hole hole + mexciton = melectron + mhole << matom exciton – light bosonic particle in semiconductor _ _ at high densities + + excitons dissociate plasma of free electrons and holes exciton condensation d dilute exciton gas (na <<1) d B dense electron-hole system (na >>1) B excitons are weakly interacting Bose particles excitons are formed at Fermi level like Cooper pairs exciton condensation is analogous to exciton condensate called excitonic insulator is analogous to BCS superconductor state Bose-Einstein condensation Tc matched electron and hole Fermi surfaces mismatched d n L.V. Keldysh, Yu.E. Kopaev (1964) naB ~1 L.V. Keldysh, A.N. Kozlov (1968) why it's interesting? Kelvin for excitons exciton condensate is a new form of matter high T for exciton BEC due to light exciton mass: T exciton ~ 1 K c c microKelvin for atoms possibility to study crossover from BEC to BCS-like state possibility of manipulating condensate in microscopic semiconductor devices how to get cold exciton gas? T << 1 K in He refrigerators lattice finite lifetime of excitons could result to high exciton temperature: T > T X lattice find excitons with lifetime >> cooling time T ~T X lattice find materials with low e-h recombination rate Condensation in 3D and 2D systems BEC Macroscopic occupation of ground state quasi-condensate - macroscopic occupation of low energy states difference between quasicondensate and BEC is not essential for most experiments 2/ 3 2πh2 n 3D systems: BEC is possible a t finite T T =0.527 c M g2/ 3 2D systems: BEC is possible at T=0 only 2 4πh n 1 / n s 1 Bogoliubov temperature T ~ B 2 n 2Mg ln[ln(g/na )] y t i Onset of nonzero order parameter = onset of local superfluidity 2 2 - d dens π h n (T=T ) s KT ui f Kosterlitz-Thouless temperature TKT= 2Mg uper s T =0 T T pairing of vortexes = onset of macroscopic BEC KT B superfluidity which is not destoyed by vortexes 4πh2n 1 Finite 2D systems: BEC is possible at finite T T = c 2Mg ln(nS/g) include 2D systems with in-plane (random) potential in this case S - area of local potential minimum V.N. Popov, Theor. Math. Phys. 11, 565 (1972) D.S. Fisher, P.C. Hohenberg, PRB 37, 4936 (1988) W. Ketterle, N.J. van Drutten, PRA 54, 656 (1996) Materials with low e-h recombination rate classical semiconductors obstacles for with low e-h highlights experimental realization recombination rate of cold exciton gases Ge, Si discovery of electron-hole ground state – metallic liquid electron-hole liquid alternative to excitonic ground state Cu2O a number of high rate of Auger interesting effects in recombination exciton gases Novel systems indirect excitons in coupled quantum wells polaritons in microcavities excitons in quantum-Hall bilayers Why indirect excitons in CQWs? Al Ga As x 1-x GaAs e long exciton lifetime due to separation GaAs/AlGaAs between electron and hole layers 103 times shorter exciton cooling time h CQW than that in bulk semiconductors Γ coldest exciton gas: T << 1K < T X e X c AlAs/GaAs CQW E h potential candidate for realization of exciton condensation z exciton energy relaxation by LA-phonon emission 3D: coupling of E=0 state to single state E=E0 2D: coupling of E=0 state to continuum of energy states E > E 0 E =2M v 2 exciton 0 x s dispersion ~ 0.05 meV effective cooling of 2D excitons by bulk phonons E K How to get cold exciton gas? excitons are generated hot and cool TX drops down down to Tlattice via phonon emission to 400 mK in 5 ns < Tc << lifetime ways to overcome the obstacle of hot generation and study cold gases of indirect excitons with TX ~Tlattice separation in time separation in space study indirect excitons study indirect excitons a few ns after the end of excitons beyond photoexcitation pulse photoexcitation spot Repulsive interaction between indirect excitons e Dipole-dipole repulsive interaction stabilizes exciton state against formation of metallic electron-hole droplets h 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 of the + system is excitonic indirect excitons results in effective screening of in-plane disorder are oriented dipoles A.L. Ivanov, EPL (2002) R. Zimmermann 2 Wex=4 W/cm W =0.5 W/cm2 ex Repulsive interaction in experiment: y sit Exciton energy increases with density ten L.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993) In L.V. Butov, A. Zrenner, G. Abstreiter, G. Bohm, G. Weimann, PRL 73, 304 (1994)... V. Negoita, D.W. Snoke, K. Eberl, PRB 61, 2779 (2000) PL energy shift: δE~4πne2d/ε → estimate for exciton density 1.54 1.55 1.56 1.57 Energy (eV) Experiments on cold exciton gases in CQW nanostructures effects indicating exciton condensate 0.12 superradiance (macroscopic dipole), 0.020 ity 0.10 s 0.015 ) onset of exciton superfluidity, and 1 - ) 0.08 1 s - n s 0.010 ( n 1 ( - 0.06 r 1 fluctuations near phase transition M M - τ 12 12 PL inten a 0.005 a τ g g 0.04 n 8 n 8 e e t 0.000 t ic 6 ic 0.02 0481216 4 4 F 5 F 6 Butov et al. J. de Physique 3, 167 (1993) i ie 4 e 5 ) l ld 3 e (K d 4 ) B (T) ur 3 (K ( 0 2 rat ( 0 re T pe T 2 ratu ) em ) pe T Tem PRL 73, 304 (1994) PRB 58, 1980 (1998) bosonic stimulation of exciton shrinkage of spatially ity scattering - signature of localized exciton cloud s degenerate Bose-gas of excitons with reducing T → PL inten Butov et al. PRL 86, 5608 (2001) degenerate exciton gas 50 100 150 PRL 87, 216804 (2001) Butov et al. Nature 417, 47 (2002) Time (ns) exciton rings macroscopically ordered exciton state Butov et al. cond-mat/0204482 [Nature, 418, 751 (2002)] cond-mat/0308117 [PRL 92, 117404 (2004)] SSC 127, 89 (2003) http://physics.ucsd.edu/~lvbutov/ Bosonic stimulation of exciton scattering exciton E exciton PL kinetics rectangular photon phonon excitation pulse PL jump occupation kinetics 10 W/cm2 of optically active 0.15 W/cm2 0.1 meV exciton states monoexponential PL kinetics exciton mass 50 100 150 is controlled in situ 10 K T =50 mK 1.2 bath 0 4 exp 0.8 / m X ) end of excitation 1.6 M 0.4 -1 0.5 theory pulse normalized PL intensity 010 (ns B (T) 0.15 Butov et al. rise τ PRL 87, 26804 (2001) W/cm2 1/ 0 73 74 75 76 77 0100.1 1 10 0816 2 Time (ns) W (W/cm ) T (K) B (T) enhancement of exciton scattering rate to low energy states with increasing exciton concentration reveals bosonic stimulation of exciton scattering scattering rate of bosons signature of degenerate Bose-gas of excitons to a state p is ~(1+Np) L.V. Butov, A.L. Ivanov, A. Imamoglu, P.B. Littlewood, A.A. Shashkin, V.T. Dolgopolov, K.L. Campman, and A.C. Gossard, PRL 86, 5608 (2001) Experiment vs theory 10 10 experiment 1 4 (K) E=0 1 10 theory X N 0.1 T 0.01 0.1 3 10 50 100 150 50 100 150 Time (ns) PL intensity 2 T/0 T X 10 NE=0 = e -1 rectangular _ 2 excitation pulse T0 = πh n / 2gMXkB 50 100 150 temperature of quantum degeneracy Time (ns) ph ph dNE=0/dt = ΓphNE(1 + NE=0)(1 + nE ) – Γph (1 + NE)NE=0 nE –NE=0 / τ = ph ph = Γph (NE -nE )NE=0 + Γph (1 + nE ) NE –NE=0 / τ at low Tlattice and in presence Frolich inversion condition of generation of hot excitons counterpart of population ph inversion condition for lasers NE –nE >0 2D image of indirect exciton PL vs Pex L.V. Butov, A.C. Gossard, and D.S. Chemla, cond-mat/0204482 [Nature 418, 751 (2002)] Radial dependence of indirect exciton PL indirect internal bulk exciton D ring r=0 external ring D PL peak intensity 0 40 80 120 excitation r (µm) spot profile external ring center m µ I internal PL intensity ring center 3.7 D excitation spot center r=0 1.54 1.55 1.56 1.57 PL intensity x4 Energy (eV) 1.54 1.56 1.58 Energy (eV) Ring structure of indirect exciton PL internal ring P (µW) ex 220 external ring can be remote from 95 excitation spot by 290 hundreds of microns 390 33 530 PL peak intensity 770 6 0 40 80 120 160 200 r (µm) at low densities: spatial profile of indirect exciton PL intensity follows laser excitation intensity at high densities: spatial profile of indirect exciton PL intensity is characterized by ring structure Temperature dependence of ring-shaped PL structure T=2.4 K T (K) 2.4 4.4 7 10 L intensity P 14 1.54 1.55 1.56 1.57 PL peak intensity T=14 K 04080120 r (µm) ring structure of indirect exciton PL is observed at low T PL intensity with increasing T rings wash out and spatial profile approaches monotonic bell-like shape 1.54 1.55 1.56 1.57 Energy (eV) peak m ity µ s pass n 440 te in L P 1.54 1.55 Energy (eV) m) Pex µ 800 ( g 400 the rin n o PL intensity tion 0 0 si 0 100 200 300 400 500 o 02040 position on the ring (µm) P Peak number external ring is fragmented into circular structures that form a periodic array over macroscopic lengths, up to ~1 mm exciton state with spatial order on macroscopic lengths – macroscopically ordered exciton state Temperature dependence of ring fragmentation into spatially ordered array of beads m T=1.8 K e h t ansfor ude of Tr t r i e i Ampl Four 0 0246 T (K) T (K) 1.8 T=4.7 K 4.7 PL intensity 7.7 0 100 200 300 400 500 Position on the ring (µm) ring fragmentation into spatially ordered array of beads appears abruptly at low T Ordered state ring onset 6 ) K 4 T ( 2 low-temperature ordered phase state 0 0 400 800 1200 excitation power (µW) Features in exciton PL pattern PL Intensity 04080120 inner rings r (µm) external rings localized bright spots macroscopically ordered exciton phase PL pattern spatial distribution of optically active low energy excitons origin of inner ring flow of excitons out of excitation spot due E to exciton drift, diffusion, phonon wind, etc.
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