Exciton Condensation

Far-Infrared Magneto-Optics in Spatially-Separated Electron-Hole Systems
- Search for excitonic ground states -

Project Summary

Over the past four decades, there has been considerable interest in correlation effects in systems with a large number of coexisting electrons and holes. Various possible collective ground states, including a Bose-Einstein condensate and an excitonic insulator, have been predicted for semimetals and highly-excited semiconductors. However, in spite of extensive experimental studies of bulk materials at low temperatures and at high magnetic fields/pressures, direct evidence of these ground states have not been given to date.

Recent attention has been paid to spatially-separated two-dimensional electron-hole (e-h) (SSEH) systems, in which the e-h separation as well as the e-h density are controllable. It is now possible to fabricate such devices owing to the advancement of semiconductor nanotechnology.

In this project we are designing new types of SSEH systems while at the same time carrying out a systematic far-infrared (FIR) magneto-optical study in search of exciton condensation or other collective effects. We expect to see evidence for many-body interactions in intraband FIR spectra. Although Kohn's theorem states that cyclotron resonance (CR) is not influenced by carrier-carrier interactions in a single-component plasma with perfect translational invariance, the coexistence of the electrons and holes intrinsically breaks this condition, allowing us to expect direct signatures of collective effects in the electron and hole CR spectra (even in disorder-free high-quality samples). Both optically-created e-h systems and "stable" e-h systems are being investigated. The experiments are performed with a Time-Domain Terahertz spectrometer and with the Stanford FEL.

This research will provide new insight into the unusual nature of interacting many-particle systems, but equally important, the realization of an e-h ground state in semiconductors would lead to the development of novel semiconductor devices. In particular, new observations in the FIR (or THz) spectral range would lead to breakthrough devices that operate in this technologically little-explored frequency range (0.1-10 THz).

Background

Bose-Einstein Condensation of Excitons
Bose-Einstein condensation (BEC) is one of the most striking quantum phenomena, in which a macroscopic number of particles all go into the same quantum state. It is well known that this phenomenon gives rise to superfluidity in liquid helium. The search for condensation in other systems such as excitons in semiconductors is an exciting field of research. The possibility of BEC of excitons in semiconductors has fascinated a number of authors for many years [e.g., Moskalenko 1962; Blatt et al. 1962; Casella 1963; Keldysh and Kozlov 1967, 1968; Kohn and Sherrington 1970; Hanamura and Haug 1974; Lerner and Lozovik 1978, 1981; Dzyubenko and Lozovik 1983, 1984, 1991; Paquet et al. 1985]. However, no direct experimental evidence has been given to date (a different type of condensation into a metallic liquid state or a "droplet" has been observed in highly-excited silicon and germanium [Rice 1977; Hensel 1977]).

Semiconductor-Semimatal Transition
According to the elementary one-electron band theory, crystalline solids with an even number of electrons per unit cell are classified into either semiconductors (insulators) or semimetals. In semiconductors an integral number of energy bands are fully occupied by electrons while the rest are completely empty, whereas in semimetals partially-filled conduction-band and valence-band with equal carrier densities with opposite carrier signs coexist at different points in k space as a consequence of band overlap. The important parameter here to distinguish between the two is obviously the fundamental energy gap, E_g; i.e., E_g > 0 for semiconductors and E_g < 0 for semimetals. Thus, according to the one-electron model, if one reduces E_g continuously from positive to negative values by varying externally applied pressure, a semiconductor-semimetal (S-S) transition should occur at E_g = 0 without any discontinuous change in the physical properties of the system.

The Excitonic Insulator
It was N.F. Mott (1961) who first pointed out that the above one-electron model is not correct in the neighborhood of the S-S transition. When E_g begins to be negative, a very small number of electrons and holes start to populate the conduction and valence bands, respectively. They attract each other via their mutual Coulomb interaction, which is only insignificantly screened because of the small number of carriers present, and hence bind to form an insulator: i.e., the normal semimetallic ground state would be unstable against the formation of excitons. When one reduces E_g further, the carrier densities increase, and so the excitonic state should die out due to screening. Thus there must be a point E_g = E₀, where the normal semimetallic state is recovered. Subsequent to this idea, R.S. Knox (1963) made a similar observation for the semiconducting side of the S-S transition. If the exciton binding energy, E_B, exceeds the energy gap, E_g, then the excitation (i.e., creation) energy of the exciton (defined by E_g - E_B) becomes negative, indicating an instability of the normal semiconducting ground state against the spontaneous formation of excitons. Hence, combining the above two pictures, in the range,

E₀ < E_g < E_B (E₀ < 0, E_B > 0),

the normal semiconducting and semimetallic ground states appear to be unstable.

Excitonic Instabilities and Excitonic Phases
Following these two intuitive arguments, various authors investigated such an excitonic instability in more detail in the 1960s [e.g., Keldysh and Kopaev 1965; des Cloizeaux 1965; Kozlov and Maksimov 1965, 1966; Baklanov and Chaplik 1965; Jérome et al. 1967; Zittartz 1967a, 1967b, 1968a, 1968b; Kohn 1967, 1968; Halperin and Rice 1968a, 1968b]. It was shown by des Cloizeaux (1965) that in the excitonic insulator the crystal symmetry is broken, similar to the charge/spin density wave states. A BCS-like theory was developed by Jérome et al. (1967), who pointed out the similarity between the excitonic insulator state and the superconducting state. According to the theory of Kozlov and Maksimov (1965), the excitonic insulator phase should exist in the vicinity of the S-S transition below some critical temperature, T_c, which becomes maximum around E_g = 0. Kohn (1967, 1968) proposed more complicated but fascinating phase diagrams, predicting an infinite number of phase transitions into successively lower excitonic phases. However, such instabilities have not been experimentally observed in real systems.

Collective Ground States in Spatially-Separated Electron-Hole Systems
Recently, much attention has been paid to spatially separated 2D electrons and holes (SSEH) in layered structures since the pioneering work of Russian workers [Lozovik and Yudson 1975, 1976; Lozovik and Nishanov 1976; Shevchenko 1976; Kulik and Shevchenko 1977], who considered the pairing of electrons and holes across the interface of two media and the superfluidity of such pairs. A very interesting but complicated many-particle situation arises in such systems, especially in the presence of strong perpendicular magnetic fields B. In such a situation, 2D SSEHs, both Landau quantized, are present and there is the Coulomb attraction between them as well as e-e and h-h correlations. At very low T and high B, the ground state of such a system could be a dipole-density-wave state (a crystalline state of dipoles) [Yoshioka and Fukuyama 1978], a 2D excitonic insulator [Kuramoto and Horie 1978], independent Laughlin (fractional quantum Hall) states, coupled Wigner solid states [Yoshioka and MacDonald 1990], excitonic charge-density-wave state [Chen and Quinn 1991], or anyonic ions [Chen and Quinn 1993], depending on the layer separation, temperature, and magnetic field. Owing to the advancement of semiconductor nanotechnology, it has now become possible to fabricate a variety of quantum-confined e-h systems in a well-controlled manner. Recent interesting experimental observations in SSEH systems [Fukuzawa 1990; Kash 1991; Sivan 1992; Butov 1994; Kono 1994; Cheng 1995; Kono 1997; Butov and Filin 1998; Negoita 1999] have rekindled interest in this old problem, and many theoretical papers have been published in recent years [Tso 1993; Shevchenko 1994, 1997, 1998; Korolev and Liberman 1994; Swierkowski 1995; Wang 1995; Zhu 1995; Östreich 1996; Vignale and MacDonald 1996; Yudson 1996; Naveh and Laikhtman 1996; Sham 1996; Chu and Chu 1997; Lozovik and Berman 1997; Lozovik and Ruvinskii 1997; Reyes and del Castillo-Mussot 1998; Conti 1998; Jan and Lee 1998; Laikhtman 1998]. All these theoretical investigations strongly suggest the existence of excitonic condensates, urging experimentalists to discover more interesting effects.

Project Description

Systems Studied

In addition to designing and creating new types of spatially-separated e-h (SSEH) devices, we are currently investigating three systems: (a) excitons in undoped GaAs/AlGaAs coupled double quantum wells, (b) indirect excitons in undoped GaAs/AlAs type-II quantum wells, and (c) spatially-separated degenerate e-h systems in AlSb-InAs-AlSb-GaSb-AlSb structures. Schematic band diagrams for these structures are shown in Fig. 3.

Direct excitons in undoped GaAs/AlGaAs quantum wells are very important since they provide a simple model system for theoretical analysis [see, e.g., Zhu 1995; Östreich 1996]. However, the short lifetime (~1 ns) of these excitons makes it difficult to achieve a large population of cold excitons. As suggested and demonstrated by Fukuzawa et al. (1990) and Kash et al. (1991), in a coupled double quantum well in a DC perpendicular electric field, lifetimes as long as ~100 ns can be achieved due to the smaller e-h wavefunction overlap. This bias electric voltage is applied to spatially separate the electrons and holes after optical pumping [see Fig. 3(a)]. Even longer exciton lifetimes (as long as 10 us) have been reported for GaAs/AlAs coupled quantum well structures [Fig. 3(b)], in which electrons in the AlAs layer are at the X point and holes in the GaAs layer are at the gamma point, so that the excitons in this structure are indirect both in real space and k space. Recent observations of PL anomalies in this system have been interpreted as the onset of exciton superfluidity and fluctuation near a possible phase transition [Butov 1994]. The third system, an InAs-AlSb-GaSb heterostructure, is a unique system where spatially-separated degenerate 2D electrons and holes coexist without optical excitation. In this specially-designed structure [Fig. 3(c)], as suggested by Datta et al. (1985) and Zhu et al. (1990), the electrons in the InAs layer and the holes in the GaSb layer are separated by the large AlSb center barrier, which prevents unnecessary band-structure mixing between the InAs conduction-band and the GaSb valence-band, making the e-h coupling purely Coulombic [Kono 1994, 1997a].

Approaches

We use two different approaches. In the first approach, we monitor the linewidth of the 1s-2p+ transitions of the excitons in these structures while varying other experimental parameters. It has been shown theoretically that the in-plane dispersion relations of the excited 2D magneto-exciton states are non-monotonic [Lerner and Lozovik 1979; Dzyubenko and Yablonskii 1996a,b; Lozovik and Ruvinskii 1997]. The dispersions for the 1s and 2p+ states for 2D magneto-excitons are schematically shown in Fig. 4. At finite temperatures, in addition to the immobile (K = 0) 1s magneto-excitons, thermally-excited magneto-excitons having finite K are present. In principle, all the K-conserving (or vertical) intraexcitonic transitions are possible. Thus, resulting from the combination of the thermal distribution of the 1s excitons with different K's and the negative (positive) effective mass of the 2p+ (1s) state, the 1s-2p+ transition is broadened to lower energies at a finite temperature. Therefore, if a macroscopic number of excitons all go into the K = 0 state due to condensation, a dramatic line narrowing is expected to occur.

Fig. 4 Schematic in-plane dispersion relations for the 1s and 2p+ states of 2D magneto-excitons.

In the second approach, we monitor the THz optical sidebands [Kono 1997b] while varying experimental parameters. A recent theoretical study by Östreich et al. (1996) and Sham (1996) predicts the emergence of second-order nonlinear response, i.e., finite chi(2), associated with exciton condensation. A second order response, which does not exist in the normal state because of inversion symmetry, can exist in the exciton condensate because of its dipole nature. These authors argue that the second-order response in the exciton condensate arises from replacing one electric field in the third-order response, which exists in the normal state, by an order parameter. We can expect, if this theory is correct, that odd-photon sidebands w = w_NIR +/- (2n + 1)w_THz (n = 1, 2, ...), which have not been observed in the earlier experiments [Kono 1996, 1997b] due to the existence of inversion symmetry in the normal state, appear resulting from exciton condensation. If this effect is observed, it could become the first unambiguous evidence of exciton condensation.

References Cited

Baklanov, E.V. and A.V. Chaplik, "Dielectric constant in a two-band model of a semimetal" Fiz. Tverd. Tela (Leningrad) 7, 2768 (1965) [Sov. Phys. Solid State 7, 2240 (1966)].
Bauer, G.E.W. and T. Ando, "Exciton mixing in quantum wells" Phys. Rev. B 38, 6015 (1988).
Blatt, J.M, K.W. Boer, and W. Brandt, "Bose-Einstein condensation of excitons" Phys. Rev. 126, 1691 (1962).
Butov, L.V., A. Zrenner, G. Abstreiter, G. Bohm, and G. Weimann, "Condensation of indirect excitons in coupled AlAs/GaAs quantum wells" Phys. Rev. Lett. 73, 304 (1994).
Butov, L.V. and A.I. Filin, "Anomalous transport and luminescence of indirect excitons in AlAs/GaAs coupled quantum wells as evidence for exciton condensation" Phys. Rev. B 58, 1980 (1998).
Casella, R.C., J. Appl. Phys. 34, 1703 (1963).
Cerne, J., J. Kono, M.S. Sherwin, M. Sundaram, A.C. Gossard, and G.E.W. Bauer, "Terahertz dynamics of excitons in GaAs/AlGaAs quantum wells" Phys. Rev. Lett. 77, 1131 (1996).
Chen, X.M. and J.J. Quinn, "Excitonic charge-density-wave instability of spatially separated electron-hole layers in strong magnetic fields" Phys. Rev. Lett. 67, 895 (1991).
Chen, X.M. and J.J. Quinn, "Numerical study of fractional quantum Hall electron-hole systems: evidence of stable anyonic ions" Phys. Rev. Lett. 70, 2130 (1993).
Cheng, J.-P., J. Kono, B.D. McCombe, I. Lo, W.C. Mitchel, and C.E. Stutz, "Evidence for a stable excitonic ground state in a spatially separated electron-hole system" Phys. Rev. Lett. 74, 450 (1995).
Chu, C.S. and K.D. Chu, "Low-lying exciton states in a type-II broken-gap quantum-well structure: A variation-basis-set approach" Chinese J. Phys. 35, 164 (1997).
Conti, S., G. Vignale, and A.H. MacDonald, "Engineering superfluidity in electron-hole double layers" Phys. Rev. B 57, R6846 (1998).
Datta, S., M.R. Melloch, and R.L. Gunshor, "Possibility of an excitonic ground state in quantum wells" Phys. Rev. B 32, 2607 (1985).
des Cloizeaux, J., "Excitonic instability and crystallographic anomalies in semiconductors" J. Phys. Chem. Solids 26, 259 (1965).
Dzyubenko, A.B., "Intraexcitonic transitions in two-dimensional systems in a high magnetic field" Pis'ma Zh. Éksp. Teor. Fiz. 66, 588 (1997) [JETP Lett. 66, 617 (1997)].
Dzyubenko, A.B. and Yu.E. Lozovik, "Exact solutions and Bogolyubov transformations of quasi-zero-dimensional electron-hole systems" Fiz. Tverd. Tela (Leningrad) 25, 1519 (1983) [Sov. Phys. Solid State 25, 874 (1983)].
Dzyubenko, A.B. and Yu.E. Lozovik, "Quasi-two-dimensional electron-hole pair condensate in a strong magnetic field" Fiz. Tverd. Tela (Leningrad) 26, 1540 (1984) [Sov. Phys. Solid State 26, 938 (1984)].
Dzyubenko, A.B. and Yu.E. Lozovik, "Symmetry of Hamiltonians of quantum two-component systems: condensate of composite particles as an exact eigenstate" J. Phys. A: Math. Gen. 24, 415 (1991).
Dzyubenko, A.B. and A.L. Yablonskii, "Far-infrared s - p(+/-) interexciton transitions in InGaAs/GaAs coupled double quantum wells" JETP Lett. 64, 213 (1996a).
Dzyubenko, A.B. and A.L. Yablonskii, "Theory of intraband far-infrared magneto-optics of excitons in coupled double quantum wells" (preprint) submitted to Phys. Rev. B (1996b).
Fenton, E.W., "Excitonic insulator in a magnetic field" Phys. Rev. 170, 816 (1968).
Fukuzawa, T., E.E. Mendez, and J.M. Hong, "Phase transition of an exciton system in GaAs coupled quantum wells" Phys. Rev. Lett. 64, 3066 (1990).
Gershenzon, E.M., G.N. Gol'tsman, and N.G. Ptitsina, "Investigation of free excitons in Ge and their condensation at submillimeter wavelengths" Zh. Eksp. Teor. Fiz. 70, 224 (1976) [Sov. Phys. JETP 43, 116 (1976)].
Groeneveld, R.H.M. and D. Grischkowsky, "Picosecond time-resolved far-infrared experiments on carriers and excitons in GaAs-AlGaAs multiple quantum wells" J. Opt. Soc. Am. B 11, 2502 (1994).
Halperin, B.I. and T.M. Rice, "Possible anomalies at a semimetal-semiconductor transition" Rev. Mod. Phys. 40, 755 (1968a).
Halperin, B.I. and T.M. Rice, "The excitonic state at the semiconductor-semimetal transition" in Vol. 21 of Solid State Physics, eds. F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press, New York, 1968b), pp. 115-192.
Hanamura, E. and H. Haug, "Will a Bose-condensed exciton gas be superfluid?" Solid State Commun. 15, 1567 (1974).
Haug, H. and S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd Edition (World Scientific, Singapore, 1990).
Hensel, J.C., C.C. Phillips, and G.A. Thomas, "Electron-hole liquid in semiconductors -- Experimental aspects" in Vol. 32 of Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, 1977), p. 87.
Hodge, C.C., C.C. Phillips, M.S. Skolnick, G.W. Smith, C.R. Whitehouse, P. Dawson, and C.T. Foxon, "Induced absorption spectroscopic determination of exciton binding energies in type-II GaAs/AlAs superlattices" Phys. Rev. B 41, 12319 (1990).
Jan, J.F. and Y.C. Lee, "Bose-Einstein condensation of excitons in two dimensions" Phys. Rev. B 58, R1714 (1998).
Jérome, D., T.M. Rice, and W. Kohn, "Excitonic insulator" Phys. Rev. 158, 462 (1967).
Kane, B.E., J.P. Eisenstein, W. Wegscheider, L.N. Pfeiffer, and K.W. West, "Separately contacted electron-hole double layer in a GaAs/AlxGa1-xAs heterostructure" Appl. Phys. Lett. 65, 3266 (1994).
Kash, J.A., M. Zachau, E.E. Mendez, J.M. Hong, and T. Fukuzawa, "Fermi-Dirac distribution of excitons in coupled quantum wells" Phys. Rev. Lett. 66, 2247 (1991).
Keldysh, L.V., "Macroscopic coherent states of excitons in semiconductors" in Bose-Einstein Condensation, edited by A. Griffin, D.W. Snoke, and S. Stringari (Cambridge University Press, Cambridge, 1995), pp. 246-280.
Keldysh, L.V. and Yu.V. Kopaev, "Possible instability of the semimetallic state toward Coulomb interaction" Fizika Tverdogo Tela 6, 2791 (1964) [Sov. Phys.-Solid State 6, 2219 (1965)].
Keldysh, L.V. and A.N. Kozlov, "Collective properties of large-radius excitons" JETP Pis'ma 5, 238 (1967) [JETP Lett. 5, 190 (1967)].
Keldysh, L.V. and A.N. Kozlov, "Collective properties of excitons in semiconductors" Zh. Eksp. Teor. Fiz. 54, 978 (1968) [Sov. Phys. JETP 27, 521 (1968)].
Knox, R.S., Theory of Excitons, Suppl. 5 of Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press, New York, 1963), p.100.
Kohn, W., "Excitonic phases" Phys. Rev. Lett. 19, 439 (1967).
Kohn, W., "Metals and insulators" in Many Body Physics, eds. C. de Witt and R. Balian (Gordon and Breach, New York, 1968), pp. 351-411.
Kohn, W. and D. Sherrington, "Two kinds of bosons and Bose condensates" Rev. Mod. Phys. 42, 1 (1970).
Kono, J., B.D. McCombe, J.-P. Cheng, I. Lo, W.C. Mitchel, and C.E. Stutz, "Cyclotron resonance oscillations in a two-dimensional electron-hole system" Phys. Rev. B 50, 12242 (1994).
Kono, J., S.T. Lee, M.S. Salib, G.S. Herold, A. Petrou, and B.D. McCombe, "Optically detected far-infrared resonances in doped GaAs quantum wells" Phys. Rev. B 52, R8654 (1995).
Kono, J., J. Cerne, T. Inoshita, M.S. Sherwin, M. Sundaram, and A.C. Gossard, "Mixing of near-infrared radiation with intense far-infrared radiation in GaAs/AlGaAs quantum wells" in The Physics of Semiconductors, edited by M. Scheffler and R. Zimmermann (World Scientific, Singapore, 1996), pp. 1911-1914.
Kono, J., B.D. McCombe, J.-P. Cheng, I. Lo, W.C. Mitchel, and C.E. Stutz, "Far-infrared magneto-optical study of two-dimensional electrons and holes in InAs/AlxGa1-xSb quantum wells" Phys. Rev. B 55, 1617 (1997a).
Kono, J., M.Y. Su, T. Inoshita, T. Noda, M.S. Sherwin, S.J. Allen, Jr., and H. Sakaki, "Resonant terahertz optical sideband generation from confined magnetoexcitons" Phys. Rev. Lett. 79, 1758 (1997b).
Kono, J. and B.D. McCombe, "Comment on 'Conduction-valence Landau-level mixing effect'" Phys. Rev. Lett. 80 2497, (1998).
Korolev, A.V. and M.A. Liberman, "Superfluidity of excitons in a high magnetic field" Phys. Rev. Lett. 72, 270 (1994).
Kozlov, A.N. and L.A. Maksimov, "The metal-dielectric divalent crystal phase transition" J. Expt. Theoret. Phys. (U.S.S.R.) 48, 1184 (1965) [Sov. Phys. JETP 21, 790 (1965)].
Kozlov, A.N. and L.A. Maksimov, "Collective excitations in semimetals" J. Expt. Theoret. Phys. (U.S.S.R.) 49, 1284 (1966) [Sov. Phys. JETP 22, 889 (1966)].
Kuramoto, Y. and C. Horie, "Two-dimensional excitonic phase in strong magnetic fields" Solid State Commun. 25, 713 (1978).
Labrie, D., M.L.W. Thewalt, I.J. Booth, and G. Kirczenow, "Detailed ground- and excited-state spectroscopy of indirect free excitons" Phys. Rev. Lett. 61, 1882 (1988).
Laikhtman, B., "Coherence of the exciton condensate luminescence" Europhys. Lett. 43, 53 (1998).
Lerner, I.V. and Yu.E. Lozovik, "Phase diagram of quasi-zero-dimensional electron-hole system" Pis'ma Zh. Eksp. Teor. Fiz. 27, 497 (1978) [JETP Lett. 27, 467 (1978)].
Lerner, I.V. and Yu.E. Lozovik, "Mott exciton in a quasi-two-dimensional semiconductor in a strong magnetic field" Zh. Eksp. Teor. Fiz. 78, 1167 (1979) [Sov. Phys. JETP 51, 588 (1980)].
Lerner, I.V. and Yu.E. Lozovik, "Two-dimensional electron-hole system in a string magnetic field as an almost ideal exciton gas" Zh. Eksp. Teor. Fiz. 80, 1488 (1981) [Sov. Phys. JETP 53, 763 (1981)].
Lozovik, Yu. E. and O.L. Berman, "Phase transitions in a system of spatially separated electrons and holes" Zh. Eksp. Teor. Fiz. 111, 1879 (1997) [JETP 84, 1027 (1997)].
Lozovik, Yu.E. and V. N. Nishanov, "Wannier-Mott excitons in layer structures and near an interface of two media" Fiz. Tverd. Tela (Leningrad) 18, 3267 (1976) [Sov. Phys. Solid State 18, 1905 (1976)].
Lozovik, Yu. E. and A.M. Ruvinskii, "Magnetoexciton absorption in coupled quantum wells" Zh. Eksp. Teor. Fiz. 112, 1791 (1997) [JETP 85, 979 (1997)].
Lozovik, Yu.E. and V. I. Yudson, "Feasibility of superfluidity of paired spatially separated electrons and holes; a new superconductivity mechanism" Pis'ma Zh. Eksp. Teor. Fiz. 22, 556 (1975) [JETP Lett. 22, 274 (1975)].
Lozovik, Yu.E. and V. I. Yudson, "Superconductivity at dielectric pairing of spatially separated quasiparticles" Solid State Commun. 19, 391 (1976).
Moskalenko, S.A., "Reversible optico-hydrodynamic phenomena in a nonideal exciton gas" Fiz. Tverd. Tela (Leningrad) 4, 276 (1962) [Sov. Phys. Solid State 4, 199 (1962)].
Mott, N.F., "The transition to the metallic state" Phil. Mag. 6, 287 (1961).
Naveh, Y. and B. Laikhtman, "Excitonic instability and electric-field-induced phase transition towards a two-dimensional exciton condensate" Phys. Rev. Lett. 77, 900 (1996).
Negoita, V., D.W. Snoke, and K. Eberl, "Harmonic-potential traps for indirect excitons in coupled quantum wells" Phys. Rev. B 60, 2661 (1999).
Nozieres, P., "Phase transitions in electron-hole liquids" Physica 117B&118B, 16 (1983).
Nurmikko, A.V., "Transient spectroscopy by ultrafast laser pulse techniques" in The Spectroscopy of Semiconductors, Vol. 36 of Semiconductors and Semimetals, edited by D.G. Seiler and C.L. Littler (Academic Press, San Diego, 1992), pp. 85-136.
Östreich, Th., T. Portengen, and L.J. Sham, "Second-order optical response from a Bose-Einstein condensate of excitons" Solid State Commun. 100, 325 (1996).
Paquet, D., T.M. Rice, and K. Ueda, "Two-dimensional electron-hole fluid in a strong perpendicular magnetic field: Exciton Bose condensate or maximum density two-dimensional droplet" Phys. Rev. B 32, 5208 (1985).
Reyes, J.A. and M. del Castillo-Mussot, "Wannier-Mott exciton formed by electron and hole separated in parallel quantum wires" Phys. Rev. B 57, 1690 (1998).
Rice, T.M., "Electron-hole liquid in semiconductors -- Theoretical aspects" in Vol. 32 of Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, 1977), pp. 1-86.
Salib, M.S., H.A. Nickel, G.S. Herold, A. Petrou, B.D. McCombe, R. Chen, K.K. Bajaj, and W. Schaff, "Observation of internal transitions of confined excitons in GaAs/AlGaAs quantum wells" Phys. Rev. Lett. 77, 1135 (1996).
Shah, J., "Ultrafast luminescence spectroscopy using sum frequency generation" IEEE J. Quantum Electron. QE-24, 276 (1988).
Shah, J., Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer-Verlag, Berlin, 1996).
Sham, L.J., "Coherence and correlation of excitons in conventional and highly correlated semiconductors" in The Physics of Semiconductors, edited by M. Scheffler and R. Zimmermann (World Scientific, Singapore, 1996), pp. 641-648.
Schmitt-Rink, S., D.S. Chemla, and D.A.B. Miller, "Linear and nonlinear optical properties of semiconductor quantum wells" Adv. Phys. 38, 89 (1989).
Shevchenko, S.I., Fiz. Nizk. Temp. 2, 505 (1976) [Sov. J. Low Temp. Phys. 2, 251 (1976)].
Shevchenko, S.I., "Phase-diagram of systems with pairing of spatially separated electrons and holes" Phys. Rev. Lett. 72, 3242 (1994).
Shevchenko, S.I., "Vortices and vortical structures in systems with pairing of spatially separated electrons and holes" Phys. Rev. B 56, 10355 (1997).
Shevchenko, S.I., "Superfluidity and quantum vortices in systems with pairing of spatially separated electrons and holes in crossed magnetic and electric fields" Phys. Rev. B 57, 14809 (1998).
Sivan, U., P.M. Solomon, and H. Shtrikman, "Coupled electron-hole transport" Phys. Rev. B 68, 1196 (1992).
Swierkowski, L., J. Szymanski, and Z.W. Gortel, "Coupled electron-hole transport: Beyond the mean field approximation" Phys. Rev. Lett. 74, 3245 (1995).
Tso, H.C., P. Vasilopoulos, and F.M. Peeters, "Coulomb coupling between spatially separated electron and hole layers: generalized random-phase approximation" Phys. Rev. Lett. 70, 2146 (1993).
Vignale, G. and A.H. MacDonald, "Drag in paired electron-hole layers" Phys. Rev. Lett. 76, 2786 (1996).
Wang, E.G., Y.C. Zhou, C.S. Ting, J.B. Zhang, T. Pang, and C.F. Chen, "Excitons in spatially separated electron-hole systems: A quantum Monte-Carlo study" J. Appl. Phys. 78, 7099 (1995).
Yoshioka, D. and H. Fukuyama, "Existence of dipole-density-wave state in electron-hole junction systems" J. Phys. Soc. Japan 50, 725 (1978).
Yoshioka, D. and A.H. MacDonald, "Double quantum well electron-hole systems in strong magnetic fields" J. Phys. Soc. Jpn. 59, 4211 (1990).
Yudson, V.I., "Charged 'few-electron(single spatially separated hole" complexes in a double quantum well near a metal plate" Phys. Rev. Lett. 77, 1564 (1996).
Zhu, X., J.J. Quinn, and G. Gumbs, "Excitonic insulator transition in a GaSb-AlSb-InAs quantum-well structure" Solid State Commun. 75, 595 (1990).
Zhu, X., P.B. Littlewood, M.S. Hybertsen, and T.M. Rice, "Exciton condensate in semiconductor quantum well structures" Phys. Rev. Lett. 74, 1633 (1995).
Zittartz, J., "Anisotropy effects in the excitonic insulator" Phys. Rev. 162, 752 (1967a).
Zittartz, J., "Theory of the excitonic insulator in the presence of normal impurities" Phys. Rev. 164, 575 (1967b).
Zittartz, J., "Transport properties of the "excitonic insulator": electrical conductivity" Phys. Rev. 165, 605 (1968a).
Zittartz, J., "Transport properties of the "excitonic insulator": thermal conductivity" Phys. Rev. 165, 612 (1968b).

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