Vol. 72, No. 1, 799.2
IN COUPLED QUANTUM
J.P. Eisenstein AT&T Bell Laboratories, Murray Hill, NJ 07974 (Received 4 August 1992)
Recent studies of bilayer two-dimensional electron systems in GaAs/AlGaAs double auantum wells are reviewed. After describing a techniaue for making seuarate connections to the individual 2D layers, three cl&ses of experiments will bi ouilined: “drag” studies of interlaver electron-electron interactions, 2D-2D resonant tunneling exp&iments, and lastly,-a new method for determining the compressibility of thk interacting 2D electron gas. As a final example of the new physics afforded by bilayer 2D systems, the recent discovery of a new fractional quantum Hall state, not found in single layer systems, will be discussed.
1. Introduction The successful development of high quality bilayer two-dimensional electron systems in double quantum wells has opened up a fruitful new area of research in low-dimensional electronic systems. This advance in crystal growth technology, coupled with the demonstration of a reliable means for producing low resistance ohmic contacts to the individual 2D layers, has made possible several new classes of experiments. Interestingly, not only are studies intrinsic to the bilayer nature of the electronic system newly accessible, but we have also found the separately contacted double layer structure an ideal vehicle for examining certain properties of a singlelayer 2D system. Examples from both areas will be described. The present paper only briefly reviews our efforts in this field; references are given for those interested in a detailed description. After a discussion of the double quantum well (DQW) structures themselves, the method we have developed for making the separate ohmic contacts to the individual layers will be outlined. This will be followed by the description of three experimental efforts for which the separate contacts are essential: direct measurements of interlayer electron-electron “drag” scattering rates, various 2D-2D resonant tunneling studies and, finally, a novel technique for determining the compressibility of the interacting 2D electron gas. We conclude with an outline of our observations of a new electronic quantum liquid state, found only in bilayer 2D systems, that exhibits the fractional quantum Hall effect. 2. Experimental Issues The present studies rely upon the availability of DQW structures in which each well contains a 2D electron gas of high mobility. Also required is good control over the electron densities in the individual wells. Both of these requirements can now be met using MBE-grown DQW’s in the Ga&/AlGaAs system. A typical sample consists of
+ 08 SOS.OO/O
two 2OOA-wide auantum wells senarated bv an undooed AlGaAs barrier bf similar thickness. Si’ delta-doiing layers are deposited both above and below the DOW. The p&&e location of these doping layers is determined by the desired electron densities, account being taken of the known upward diffusion of Si during,~wtl$l]. A typical sample contains a density of 1.5x 10 cm- m each well. While the electron mobility depends sensitively upon the well quantum thicknesses, values exceeding 3x 106cm2/Vs (in the dark) have been achieved. It is notable that these high mobilities are obtained in spite of the presence of a “reverse” interface (GaAs on AlGaAs) in each well. The technique we have developed for making separate ohmic contacts to the individual layers in the DQW has been discussed in detail elsewherel21. The basic idea is quite simple. Each contact consists-of a standard diffused In dot (which contacts both 2DEGs) and a pair of Schottky gates “surrounding” it, one on the sample top surface and one on its back side. (The samole is first thinned to -5Opm by etching the substrate with a bromine-methanol solution.) These gates are positioned so that any current flowing in or out of the In dot must pass the gates. By applying an appropriate bias to one of the two gates we can fully deplete the closer 2DEG without seriously affecting the remote ZDEG. In this way a given In contact “sees” the rest of the samnle through either one or the other of the 2DEGs, but noi both. These contacts are low resistance (tvpicallv lOOR), are well isolated from the .-_ undesired 2DEG [by more than 50MR), and can be switched between layers during an experiment. Figure 1 depicts a typical 4-terminal configuration, the measurement region being the center of the cross. 3. Interlayer Electron-Electron Scattering Because electron-electron (e-e) scattering conserves the total electronic momentum, the Drude resistivity of a simple metal gives no information on such scattering. A
0 1992 Academic Press Limited
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0 0 Figure 1: Typical geometry for DQW experiments with independent contacts to the layers. Hatched regions are In contacts, shaded areas are gates. double layer ZDEG, however, offers an interesting way to circumvent this problem. If current is driven through one layer while the voltage across the other layer is measured, the resulting rruns-resistivity is a direct measure of the rate of momentum transfer, via e-e scattering, between the two layers. Such “drag” measurements[3-61 provide a new, direct, and highly sensitive probe of e-e scattering. The DQW samples now available, coupled with our technique for making separate electrical contact to the individual layers have allowed for a detailed study[4,5], here briefly summarized, of interlayer e-e interactions. Figure 2 shows the drag scattering rate, TD’, versys temuerature for a DOW samule consisting of two2OOAwidk GaAs quantum wells ‘separated by a 175A-wide AIn 9 Gan ‘IAs barrier. The rate in’ is defined via the ratio of the measured open-circuit drag voltage in one 2D layer to the current flowing in the adiacent 2D laver. The sian of the drag voltage-is oppo&e that de&loped in tYhe current-carrying well, as expected for an interlayer momentum transfer process. As the figure suggests, the observed drag scattering rate is roughly quadratic in temoerature. This is consistent with simole Coulomb scaiering between two 2DEG’s; the T* arising from the kaT smearing of both the initial and final state Fermi s&aces. In” fact, detailed numerical calculations of screened interlaver Coulomb scatteringl4.71 predict not only the T* behavior, but also agree in t&gnitide with the exoerimentallv determined rates. The dotted line in Fig. 2 is a the result of our calculations. It should-be emphasized that uncertainties in the calculations remain, especially in the vertex corrections to RPA screening, and that the excellent agreement between theory and experiment shown in Fig. 2 may be somewhat fortuitous. Y..,
2 4 Temperature
Figure 2: Measured drag scattering rate vs. temperature. Dashed line is the calculated rate for Coulomb scattering. Inset depicts experimental arrangement.
electron densities in the two wells, strongly points an acoustic phonon channel for momentum transfer. A straightforward calculation however, including both screened deformation potential and piezoelectric interactions, reveals that sequential emission and absorption of real phonons is too weak a process (by a factor of 25-100) to account for our observations. By contrast, a model including virtual phonons, can reproduce both the temperature dependence and the magnitude of this unexpectedly strong second coupling process.
To further examine the nature of the interlayer e-e scattering a series of samples was grown, all identical in structure except for the thickness of the barrier layer between the quantum wells. This has lead to an important while Coulomb scattering conclusion: additional dominates the momentum relaxation at small layer separation, for larger spacings a second, much longer range, process takes over. Careful examination of the temperature dependence of this second process, coupled with studies of the dependence of the drag on the relative
4. Resonant Tunneling Tunneling is perhaps the most obvious area to investigate using DQW’s with independent ohmic contacts. While extensive work has been done on double barrier structuresl91. for which the tunneling is basicallv a 3D-2D-3D process, relatively little has be& reported’on eenuinelv 2D-2D resonant tunnelinpll01. It is worth emphasizing that the simultaneous c&se&ation of both energy and in-plane momentum places much more stringent cons&nts upon 2D-2D _ tunneling than is familiar from conventional double barrier studies. These constraints are directly apparent in the very narrow tunneling resonances observed in the I-V characteristics and gate transconductances[ 111. Figure 3 shows the low temnerature tunneling condu%ance dI/dV, vs. interlayer bia&voltage V, for ‘; DQW sample consisting gf two 200A GaAs quantum wells separated by a 175A Alo.~Gao,~As barrier. Data from both zero magnetic field and with B = 0.2T applied perpendicular to &e 2D layers (parallel to the &nnel current) are shown. The tunneling region is a 25Ox250pm square mesa from which four 20l.trn arms extend, similar to that shown in Fig. 1. Each arm is terminated by a In ohmic contact and is fitted with the top and bottom gates needed to make separate contact to the layers. The data in Fig. 3 are from two-terminal measurements, the tunneling resistance overwhelming any series lead resistance effects.
Gated Tunneling Structures
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: : : :
‘: :. : : 1.’
Figure 3: Tunneling conductance dI/dV vs. interlayer bias voltage V at T=0.3K. Solid curve obtained at zero magnetic field, dotted curve at B=0.2T.
Narrow Resonances Most obvious from Fig. 3 is the narrowness of the features. For the B=O case, the full width at half maximum of the underlying tunnel resonance is only r-O.3 meV. This contrasts with a Fermi energy of about EF-~ meV for each of the 2DEG’s (mean 2D density around 1.6x1011cm-2). Unlike the case for 3D-2D resonant tunneling diodes, the conservation of in-plane momentum allows for tunneling only when the subband edges of the two layers are closely aligned. This is because for 2D, where the electronic states are quantized in the tunneling direction, momentum conservation is eauivalent to kinetic enerev conservation. Since the “natural” tunneling linewidtrfor the present samples (set bv the svmmetric-antisvmmetric solittina of the DOW) is in’the l&V range, the observed width is, in fact, a-direct measure of the degree of momentum conservation. For the present example, since r-E~/20, the maximum change in in-plane momentum upon tunneling is only 23% of the Fermi momentum. Such small angle scattering events are consistent with the modulation-doped structure of these samples and not surprising given the very high electronic mobility l.t-3x 106cm2/Vs. As the figure shows, applying a small magnetic field creates several side-bands to the main tunnel resonance. These arise via inter-Landau level tunneling processes. The observed splitting closely matches the cyclotron at B=O.2T, Ace, =0.34meV. If in-plane energy momentum were perfectly conserved upon tunneling then such inter-Landau level transitions would be forbidden[ lo]. Their observation, however, is consistent with the finite tunneling linewidth observed at B=O. We remark however, that a small component of magnetic field parallel to the 2D plane, due to a slight tilt of the sample, will also couple Landau levels.
Resonant tunneling between two 2D electron gases reauires that the difference in subband edge energies. AEn. be’small. An applied interlayer bias v&age 9 sets the difference in the Fermi levels Au. not AEn. That the resonances shown in Fig. 3 are centered at V=O therefore implies that the 2D densities in the two wells are closely matched, for only then will AEc = Ap. Slight tuning of the densities, via an overall backside gate, was in fact required to obtain the data in Fig. 3. These considerations reveal a novel way to externally, and locally, control the tunneling in a DQW. Figure 4 shows the equilibrium tunneling conductance. i.e. measured with onlv a small ac excitation voltage, as a.function of the voltage-applied to an external top-side “tunnel” gate. This gate, not to be confused with those employed for creating the separate ohmic contacts, occunies a small fraction (-6%) of the total DOW area. Data’tiom two samnles are‘shown: in the first “&metric” sample, the individual wells contain roughly ‘the same electron density, -1 5~lO”crn-~, while in the second sampiethe wells were intentional12 “asymmetric” unbalanced, with densities of 1 and 2xlO”cm, respectively[lJ,l2]. For both samples the Ga& quantum wells are 140A wide while the barrier is a 70A nure AlAs layer.
In both cases the peak in the tunnel conductance occurs when the tunnel gate produces local balance in the quantum well electron densities. For the symmetric case this adds only a small, narrow resonance to the total observed conductance. This is expected since there is substantial tunneling occurring throughout the mesa area as the densities are nearly balanced to begin with. In the asymmetric case however, the gate-induced tunnel peak dominates the background conductance. The background conductance is small since the quantum well subband edges are globally misaligned by the density difference. Considering the small fraction of the mesa area covered by the tunnel gate, the true peak-to-background ratio for the asymmetric sample is about 15O:l. The “built-in” subband misalignment in asymmetric DQW’s can, of course, be simulated in the symmetric DQW’s by employing a large area back-side gate to globally change the lower quantum well density[l 11. In our view the real novelty of gated tunneling structures lies in the freedom to locally define the tunneling area. Multi-point tunneling “circuits” are thus possible. As an illustration, consider Fig. 5 in which two interferometer configurations are displayed[ 121. In the upper diagram we have a DQW for which we assume separate connections to the individual quantum wells are provided, either with our technique or some other. The figure represents a longitudinal cross-section through a thin bar-shaped mesa. Two tunnel gates are deposited on the front surface. We make the distance d, between the gates short compared to the dephasing length lo in the 2DEG’s. The gate lengths themselves must be small compared to ds. We further assume that although the DQW barrier is thin enough to permit tunneling, the sample is an unbalanced asymmetric DQW and so very little tunneling occurs in the absence of gating. By adjusting the gate biases we can turn on tunneling under each. A loop with two tunnel junctions is thus created. The area of the loop is the product of the gate separation d and the quantum well center-to-center spacing d,. T!i1s “double-slit” device should exhibit Bohm-Aharonov
: (b) ASYMMETRIC
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TUNNEL GATE BIAS (Volts)
Figure 4: Equilibrium tunneling conductance vs. tunnel gate bias for two DQW samples. Data taken at T=l.2K.
Figure 5: Two possible interferometer configurations.
oscillations if a magnetic field is applied in the 2D plane and perpendicular to the loop. A variation on this theme is depicted in the lower part of Fig. 5 wherein a third gate has been deposited between the other two. This middle gate is not used to induce tunneling, but rather to simply alter the Fermi wavevector in the top 2DEG inside the loop. Interference fringes, as a function of voltage applied to this central gate, should appear in the tunnel conductance of the device, without any magnetic field. Fermi Surface Mapping via Tunneling Application (perpendicular
of an to the
magnetic field B alters the current)
consequences of momentum conservation for 2D-2D resonant tunneling[l3] and, as we have described, provides a novel method for mapping the Fermi surface[l4]. For equilibrium tunneling, i.e. with only electrons at the Fermi surface contributing, conservation of momentum implies that tunneling can occur only where the Fermi surfaces intersect. If there is no magnetic field, this is equivalent to the equal density, aligned subband edge criterion already discussed, the “intersection” occurs all around the Fermi surface. Adding an in-plane magnetic field, however, fundamentally alters this. As described earlier, to lowest order the effect of the magnetic field is to produce a relative displacement of the initial and final Fermi surfaces in k-space[l4]. With the field along the y-axis the displacement is in the xdirection, having magnitude Ak, =eBd,/h (d, is the quantum well center-to-center spacing). With an in-plane field then, tunneling can occur even if the subband edges are not aligned, since unequal diameter Fermi surfaces can intersect if their origins are relatively displaced. In the upper panel of Fig. 6 the twneling conductan% of a symmetric DQW sample (140A GaAs wells, 70A pure AlAs barrier) is plotted VS.in-plane magnetic field, B. As the field is first applied the conductance drops rapidly. It then levels out for a wide field range. By B=6T it rises to a small peak just before falling to zero. This field dependence is simply explained with the arguments just given. At B=O there is substantial tunneling since the densities of the 2DEG’s are equal and so the Fermi surfaces are of equal diameter. As soon as the field is applied the circles separate and the momentum-conserving phase space is reduced to, two points; the conductance dropping substantially. Over a range of magnetic field the conductance varies slowly as the intersection points move around the circle. By 6T the circles are about to separate, the small bump reflecting the enhanced density of states
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5. Negative Compressibility of 2D Electrons In many DQW experiments electric fields are applied to the 2D electron gases via external Schottky gates. It is usually adequate to assume that such gate fields affect only the closer of the two 2D lavers, i.e. that the nearer 2DEG fully screens out the electric field. This is, of course, only an approximation, some of the electric field does penetrate and affects the remote 2D layer[l6]. It can be shown that for thin 2D systems the equilibrium ratio of the differential penetrating electric field 8Et, to the differential applied gate field SE,, is 6Ep/SE,
where d, is the layer spacing and dj (j=t,b) are distance parameters directly proportional to the inverse thermodynamic density of states of the top and bottom 2D gases: d. = ([email protected]
/e2) dl+/dNj.,This derivative of chemical potentta.i with respect to density is also closely related to the compressibility K and total energy E,, (per unit area) of the 2D system: [email protected]
Thus, a measurement of the differential penetration field urovides direct access to the thermodvnamic variables associated with the 2D electron system. The complicating influences characteristic of non-equilibrium probes like transport or optics do not arise. While estimates of dlt/dN for non-interacting electrons (di,b =25A) yield positive differential penetration fields of a few percent for tvuical DOW’s, the observed penetration is often @yxrive[ 17;18]. This seemingly unphysical result is due to the great importance of electron-electron interactions in real 2D systems[l9,20].
Figure 6: Upper panel: Measured tunneling conductance vs. in-plane magnetic field at T=lSK. Lower panel: tunneling with conductance along Calculated representative Fermi surface alignments.
expected when circles osculate. For higher magnetic fields the circles are separated by more than scattering can overcome and the tunneling is quenched. The lower panel of Fig. 6 displays a simple calculation, including only and a phenomenological phase space limitations broadening mechanism adiusted to match the B=O tunneling Tinewidth. The quench field BF = 2AkF/ed,, determined bv the measured 2D densities and well separation, is
Given separate contacts to the individual 2D layers in a DQW, measuring the differential penetration field is easy. The inset to Fig. 7 depicts the experimental In essence, the technique consists of arrangement. measuring the capacitance between top-side gate and the lower 2D electron layer, with the upper layer grounded. Any electric field which penetrates the upper layer causes currents to flow to the lower layer and these are detected. A dc bias is applied to the gate in addition to a small ac voltage, this allows measurements of the differential penetration as a function of the density of the upper layer. Since the penetration is usually weak, the lower layer is density remains near its nominal value, and 6 determined almost entirely by the top Epayer compressibility. In effect, the lower layer serves only to collect the penetrating electric field lines. Any lower conducting plane would work, provided the necessary independent contacts could be made. Figure 7 shows the observed[lir] differential at T=1.2K, normalized by the penetration field 6 applied gate field 6?3 as a function of the top layer density N,. The large increase in signal below V,<-1V represents the full depletion of the top layer. Beyond this point, obviously, the entire differential gate field penetrates and SE, = SE+ This allows for normalizing the signal and defines the sign gf the penetration. The sample us&consists of two 200A GaAs wells separated by a 175A AlGaAs bw Each layer has a nominal density of 1.5xlO”cm.
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GATE BIAS Vg (Volts)
Figure 7: Normalized penetrating electric field 6E /SE0 vs. gate bias (and top layer density) at T=l.2K. Batted curve represents Monte Carlo results, dashed line is non-interacting result.
As the figure clearly shows, the differential penetration field, and thus K; ‘, is positive at large N, but crosses over and becomes negative as N, falls below about 1.1 x 10” cm-‘. The signal becomes increasingly until incipient depletion cuts off the negative “divergence”. This peculiar result is, in fact, entirely expected owing to interaction effects[ 19,201. For non-interacting 2D electrons (at zero magnetic field) ap/dN is a positive constant independent of density. For this situation E,, =%NEF-N2 with &F the Fermi energy. Interactions, however, add exchange and correlation terms to E,O,. These additional terms are negative and of order Eh,-- Ne’/Er with r the mean spacing between electrons. Thus Eh, scales as N3’2 and dominates E!.!.t at low density, leading to a divergent ap/dN=NThe critical density at which [email protected]
changes sign is around 0.8~10” cmm2, not far from our observation. The dotted curve in Fig. 7 represents the latest Monte-Carlo calculations of I$combined with Eq. 1 in which d, has been set to 375A, the quantum well center-to-center spacing. While the qualitative agreement is excellent, proper account has not yet been taken of the finite quantum well thicknesses. The data in Fig. 7 demonstrate that these measurements offer a highly sensitive new probe of interactions in 2D electron systems and that a new level of comparison to many-body theory is accessible. Perhaps even more interesting than these zero magnetic field results are the compressibility data obtained at high field, in the extreme quantum limit where the Fermi level lies in the lowest Landau level. In that regime the total energy is determined only by interactions, the kinetic energy being quenched by the field. As discussed elsewhere[ 17,221, this leads to a generally negative compressibility punctuated by structure associated with the fractional quantum Hall effect (FQHE). In Fig. 8
Figure 8: Compressibility vs. Landau level filling factor in the extreme quantum limit. Solid curve taken at B=l6T, dotted at 12T. Note weak v= 2/5 FQHE state. Vertical axis proportional to ap/dN, see text for details.
compressibility data is shown, for the same sample as in Fig. 7, at both B=l2 and 16T. The horizontal axis has been converted from gate voltage into Landau level filling fraction v while the vertical axis represents the distance parameter d,-aI.tJaN, divided by the magnetic length en. The primary feature, of course, is the strong upward peak associated with the v = l/3 FQHE. As the data shows, this peak narrows slightly and strengthens as the magnetic field is increased. Were the sample ideal, i.e. no disorder, no inhomogeneity, etc, the FQHE would create a dense family of upward Gfunctions in K-t owing to the formation of a hierarchy of incompressible quantum liquids. In reality, disorder smears out these spikes and leaves behind only the strongest; note the weak appearance of the daughter v=2/5 state in the 16T data. The data, however, reveal other interesting features as well. Note the minima adjacent to the main l/3 maximum. These imply negative curvature of the total energy vs. density curve on both sides of the slope discontinuity responsible for the energy gap at v= l/3. These features can be consistently explained[ 171 as due to interactions between the fractionally charged quasiparticles associated with the l/3 state. Approaching v= l/3 from either direction continuously dilutes the quasiparticle gas leading, in analogy to the low density behavior seen at zero magnetic field, to a negatively divergent [email protected]
The minima may thus be viewed. as a thermodynamic observation of the quasiparticle gases fundamental to the theory of the FQHE. There are a number of interesting problems that can now be studied. For example, the present technique offers a way to sensitively test the accuracy of the local-density approximation for treating exchange and correlation
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effects at B=O. At high B, the compressibility anomalies associated with the FQHE can be integrated to yield the discontinuity in the chemical potential Ap. The ratio of this to the quasiparticle energy gap Es, determined via magneto-transport, should determine the charge of the quasiparticles. Compressibility studies in the regime of Wigner crystallization, may help to determine the nature of that phase transition. In passing, we note that stability negative compressibility poses interesting questions; it has even been noted that in a closely spaced DQW all electrons will jump into one of the wells if the density is low enough. 6. New FQHE States in Double Quantum Wells In this final example of the interesting physics of DQW’s we examine the new electronic ground states available when the layers are close enough together that Coulomb interactions between the layers are comparable to those within each layer. For these studies separate contacts to the layers are not employed. Figure 9 shows both the longitudinal magneto-resistance pxx and $e Hall resistance pxY for a DQW copsisting of two 180A GaAs wells separated by a 30A AlAs banier. The individual layers have 2D densities of only 5.2~lO’~cm. The total filling factor VT is defined to be the sum of that in the individual layers: VT=vt +v2. Since the layers are closely balanced, vi =v2. As the data show, both the integer and fractional quantum Hall effects are observed with this sample. Plateaus in pxY are observed at (h/e2)vT’ with VT= l/2, 2/3, 1, 2 and a host of larger values. Thus QI-IE’s are observed where v1 =v2 = l/4, l/3, l/2, 1 and higher. The cases VT=2/3 and 2 are expected: the 2/3 state arising when the Laughlin l/3 state in each layer is stable, while VT= 2 represents the ordinary v = 1 integer QHE in a single layer. The really new observation contained in the data of Fig. 9 is the QHE state at VT= l/2. For this case there is no known single layer counterpart: no observation of a l/4-FQHE state has yet been made. We have shown that the existence of the vr = l/2 QHE state depends sensitively upon the layer separation d and the magnetic field. Increasing the spacing to d= 1OOA wipes out this l/2-state. Examining a number of samples has shown is increased the l/2-state smoothly that as d/en destabilizes, disappearing beyond about d/en -3. This is a strong argument that the l/2-state is dependent upon a dzl ic ate balance between interlayer interactions (s aling as e /d) and intralayer interactions (which scale as e $ /en). There is a well-defined theoretical explanation for the occurrence of a l/2-state in double layer 2D systems. It is based upon a generalization, originated by Halperin, of Laughlin’s wavefunction to multi-component systems. The main point is that new electronic configurations are possible when two layers are present and it is just this competition between inter- and intralayer interactions that determines whether they are stable. In fact, the state we observe at VT= 1 is perhaps also a new quantum liquid of this type. Unfortunately, there is an alternative explanation for the vr = 1 state that relies on purely single electron effects (tunneling). While we argue the present VT= 1 is of collective origin, we cannot completely rule out the more mundane alternative. Finally, we note the recent obgervation of a v= l/2 FQHE in a single wide (-700A) quantum well. Being doped from both sides, the electronic charge distribution
Figure 9: Longitudinal resistivity and Hall resistance for a DQW exhibiting the v= l/2 fractional quantum Hall effect. Note pxx scale change at B=7T. in such a well is much like a double layer system. While it seems likely that the v= l/2 state seen in such systems is essentially the same as we find in DQW’s, the possibility of a new, and very different ground state remains. These initial observations of new collective states in DQW’s are. surely just the beginning. Beyond just finding more such states, the DQW geometry (plus separate contacts!) offers possibilities for studying these states in new ways. Drag experiments, analogous to those discussed in section 3 above, are one obvious candidate Tunneling studies are another with some work already underway. 7. Conclusion Several new experiments on double layer 2D electron systems have been briefly described. All depend upon the availability of high quality modulation-doped double quantum well structures with controllable electron densities in each well. Most of the experiments here discussed also depend critically on the ability to make low resistance ohmic contacts to the individual 2D layers. One technique that accomplishes this has also been outlined. Clearly, our emphasis has been on the basic physics of these bilayer 2D systems. Nevertheless, there may be technological implications for this avenue of research as well. In any case, it seems clear that much more remains to be extracted from this relatively new area of study. work AcknowledgementThis represents active collaborations with G.S. Boebinger, T.J. Gramila, Song He, A.H. MacDonald, L.N. Pfeiffer, and K.W. West; their contributions cannot be minimized. I also thank A.L. Efros, F. Capasso, B.I. Halperin, M.S. Hybertsen, and R.L. Willett for numerous fruitful discussions. References 1.
L.N. Pfeiffer, E.F. Schubert, K.W. West and C. Ma ee, Applied Physics Letters 58, 2258 (1911).
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18. 19. 20. 21. 22.
;:. 25: 26. 27. 28.
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