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ScienceWeek
CONDENSED MATTER: EXCITONS IN BOSE CONDENSATES
The following points are made by J.P. Eisenstein (Science 2004 305:950):
1) Only a few years after Bardeen, Cooper, and Schrieffer introduced their successful theory of superconductivity in metals (1,2), the idea that something similar might happen in semiconductors was advanced (3). Electrons in a superconductor, even though they repel one another, join to form pairs. Known as "Cooper pairs". These composite objects are members of a class of quantum particles called "bosons". Unlike individual electrons and the other members of the particles called "fermions", bosons are not bound by the Pauli exclusion principle: Any number of bosons can condense into the same quantum state. Bose (boson) condensation is at the root of the bizarre properties of superfluid helium and is nowadays being intensely studied in ultracold atomic vapors. The condensation of Cooper pairs in a metal leads not only to the well-known property of lossless conduction of electricity, but also to a variety of other manifestations of quantum mechanics on a macroscopic scale.
2) In a semiconductor, there are both electrons and holes. Holes are unfilled electron states in the valence band of the material. Remarkably, holes behave in much the same way as electrons, with one crucial difference: Their electrical charge is positive rather than negative. Electrons and holes naturally attract one another, and thus pairing seems very likely. Like Cooper pairs, these "excitons", as they are known, are bosons. If a suitably dense collection of excitons could be cooled to a sufficiently low temperature, Bose condensation ought to occur and a new state of matter should emerge. Or so went the thinking in the early 1960s.
3) However, there is a problem: Excitons are unstable. They typically survive only approximately a nanosecond before the electron simply falls into the hole, filling the empty valence band state and giving birth to a flash of light in the process. A nanosecond is not very long, and this left the prospects for creating a condensate of excitons in a bulk semiconductor very poor. Over the last decade the situation has improved considerably through the use of artificial semiconductor structures in which the electrons and holes are confined to thin slabs of material separated by a thin barrier layer. This physical separation slows the recombination substantially, and some very interesting and provocative results have been obtained (4,5). Excitonic Bose condensation has, however, remained elusive.
4) In March 2004, experimental results reported at the meeting of the American Physical Society in Montreal by independent groups revealed clear signs of excitonic Bose condensation. But the findings were made with samples consisting of two layers of electrons or two layers of holes. How can one have exciton condensation without electrons and holes in the same sample? The trick is to use a large magnetic field to level the playing field between electron-hole, electron-electron, and hole-hole double-layer systems.
References (abridged):
1. J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev. 106, 162 (1957)
2. J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)
3. L. V. Keldysh, Y. V. Kopaev, Fiz. Tverd. Tela. (Leningrad) 6, 2791 (1964) [Sov. Phys. 6, 2219 (1965)].
4. D. B. Snoke, Science 298, 1368 (2002)
5. L. V. Butov, Solid State Commun. 127, 89 (2003)
Science http://www.sciencemag.org
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CONDENSED MATTER: ON DEGENERATE EXCITON SYSTEMS
The following points are made by C.W. Lai et al (Science 2004 303:503):
1) During the past few years, the demonstration of Bose-Einstein condensation (BEC) in several atomic species confined in optical or magnetic traps has triggered intense interest (1,2). A variety of quasi-particles with bosonic character are also found in condensed matter. In particular, semiconductors can sustain bound electron-hole (e-h) pairs, called "excitons". Excitons have small effective mass (on the order of the free electron mass) and behave as bosons in the dilute limit. Theoretical work (3-5) suggests that Xs can undergo BEC at a critical temperature Tc ~ 1 K, a factor of 10^(6) that for atoms. However, BEC of excitons has not been established experimentally. The realization of excitonic BEC in semiconductors will open new opportunities in the manipulation of macroscopic quantum coherence because of the greater flexibilities and well-developed technology of semiconductor materials.
2) From a fundamental viewpoint, excitons are spatially extended (Bohr radius 10 to 50 nm) composite particles made of loosely bound fermions that evolve not in the real vacuum but in an extremely dense (10^(23) particles/cm^(3)) solid matrix. The exciton density can be widely varied with the photoexcitation, and when it approaches the level where the interparticle spacing becomes comparable to the Bohr radius, a crossover from Bose to Fermi statistics occurs. At sufficiently high densities, screening of the e-h coulomb attraction prevents the binding of e-h pairs, and the insulating exciton gas undergoes a Mott transition to a conducting e-h plasma. In some semiconductors, a gas-liquid phase transition can also occur where the exciton gas condenses into an e-h liquid (3-5).
3) The crucial issue from a practical viewpoint is the realization of cold statistically degenerate exciton systems. Because excitons are quasiparticles of excited semiconductors with a finite lifetime, this requires excitons to cool down by emitting phonons and to reach quasiequilibrium in a time much shorter than their lifetimes. In semiconductor coupled quantum wells (CQWs) under a static electric field perpendicular to the QW plane (Z direction), the ground state is spatially an indirect exciton with the electron confined in one QW and the hole in the other. This separation reduces the electron and hole wave function overlap, which results in an increased radiative lifetime that in the GaAs/AlGaAs CQWs samples used by the authors is about two orders of magnitude that of the direct exciton (e-h pairs in the same QW).
4) In summary: The authors have produced degenerate exciton systems in quasi-two-dimensional confined areas in semiconductor coupled quantum well structures. The authors observed contractions of clouds containing tens of thousands of excitons within areas as small as 100 square microns near 10 kelvin. The spatial and energy distributions of optically active excitons were determined by measuring photoluminescence as a function of temperature and laser excitation and were used as thermodynamic quantities to construct the phase diagram of the exciton system, which demonstrates the existence of distinct phases. The authors suggest that understanding the formation mechanisms of these degenerate exciton systems can open new opportunities for the realization of Bose-Einstein condensation in the solid state.
References (abridged):
1. E. A. Cornell, C. E. Wieman, Rev. Mod. Phys. 74, 875 (2002)
2. W. Ketterle, Rev. Mod. Phys. 74, 1131 (2002)
3. L. V. Keldysh, Y. V. Kopaev, Soviet Phys. Solid State 6, 2219 (1965)
4. L. V. Keldysh, A. N. Kozlov, Soviet Phys. JETP 27, 521 (1968)
5. L. V. Keldysh, in Bose-Einstein Condensation, A. Griffin, D. W. Snoke, S. Stringari, Eds. (Cambridge Univ. Press, Cambridge, 1995), pp. 246-280
Science http://www.sciencemag.org
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CONDENSED-MATTER PHYSICS: EXCITON DEVELOPMENTS
The following points are made by Ilias E. Perakis (Nature 2002 417:33):
1) The first Bose Einstein condensate using atomic gases was created in 1995. This achievement, initially with rubidium, was made possible by the design of appropriate magnetic traps to hold the atoms, and the development of sophisticated cooling techniques(1). Work on producing a new kind of condensate -- this time, using "excitons" -- has so far produced controversial results.
2) Excitons are quasiparticles: in semiconductors, electrons can be excited from the valence band to the conduction band using optical fields; this conduction electron is attracted, through the Coulomb interaction, to the positively charged hole left behind in the valence band. As a result, the electron and hole form a bound state called an exciton. Like a rubidium atom, this neutral bound complex can behave as a boson -- a particle with integer spin which obeys Bose Einstein statistics. When the temperature of a boson gas drops below a certain value, a large number of bosons "condense" into a single quantum state -- this is a Bose Einstein condensate (BEC). All of these bosons then behave in exactly the same way, and quantum-mechanical effects become visible at a macroscopic level. Such collective boson behavior gives rise to phenomena such as frictionless flow, or superfluidity, and quantum interference.
3) Several semiconductor systems have been investigated(3) for evidence of an exciton BEC, with mixed results. Excitons have much lower mass than the atoms typically used to make BECs. This means that an exciton BEC can form at higher temperatures (although still only around the 1 K mark). The problem is that excitons exist only for a short time, just a few nanoseconds, before the electron and hole recombine. So it is difficult to create a "gas" -- a Bose gas -- of excitons that is cold and dense enough to condense within this short time(4,5).
References (abridged):
1. Pethick, C. J. & Smith, H. Bose-Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2002)
2. Butov, L. V., Lai, C. W., Ivanov, A. L., Gossard, A. C. & Chemla, D. S. Nature 417, 47-52 (2002)
3. Griffin, A., Snoke, D. W. & Stringari, S. Bose-Einstein Condensation of Excitons and Biexcitons (Cambridge Univ. Press, 1995)
4. Butov, L. V. et al. Phys. Rev. Lett. 86, 5608-5611 (2001)
5. Trauernicht, D. P., Wolfe, J. P. & Mysyrowicz, A. Phys. Rev. B 34, 2561-2575 (1986)
Nature http://www.nature.com/nature
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