You are an expert at summarizing long articles. Proceed to summarize the following text: 
under large perpendicular magnetic fields @xmath0 the motion of charged carriers in two - dimensional electron systems ( 2des ) is confined to small cyclotron orbitals . this confinement suppresses the kinetic energy of the electrons but on the other hand amplifies their coulomb interactions . in single layers these coulomb correlations can lead to the emergence of fractional quantum hall states . two individual but closely - spaced 2des may also exhibit a correlated state , however , the underlying physics is now also influenced by the coulomb interactions between the two systems . when the electron densities @xmath1 in both layers are identical and the individual filling factors @xmath2 are close to 1/2 ( i.e. , @xmath3 ) , the system may spontaneously develop interlayer phase coherence , provided the distance @xmath4 between the layers is sufficiently small . this led to the prediction of josephson - type phenomena in bilayer systems @xcite nearly 20 years ago . , l. v. keldysh and a. n. kozlov [ zh . 54 , 978 ( 1968 ) ] , yu . e lozovik and v.i . yudson [ jetf lett . 22 , 11 ( 1975 ) ] and s. i. shevchenko [ fiz . temp . 2 , 505 ( 1976 ) ; sov . j. low temp . phys . 2 , 251 ( 1977 ) ] . ] the ratio of the center - to - center layer separation @xmath4 and the magnetic length @xmath5 is commonly used to parameterize the strength of this emerging state at the bilayer s total filling factor of one . tunneling spectroscopy experiments @xcite demonstrated the phase coherence between the two layers by showing a dramatic enhancement of the tunneling conductance at @xmath3 . more recently , a critical behavior was observed in dc tunneling experiments @xcite , which had also been predicted @xcite but failed to appear in all prior experiments . the purpose of this paper is to elucidate on the requirements to observe such a critical behavior . our studies demonstrate that the coherent tunneling not only intensifies with the size of the sample but more importantly that the critical current grows linearly with the @xmath3 area . in order to deliver a thorough picture of the critical tunneling behavior we first briefly address those experimental conditions which can easily be manipulated , such as effective layer separation @xmath6 , temperature and filling factor , before discussing the more relevant size dependence . our data are obtained from samples of two different wafers grown in two different molecular beam epitaxy ( mbe ) machines ( hereby referred to as wafer @xmath7 and @xmath8 ) , both with a net barrier thickness of 9.6  nm , consisting of alternating alas ( 1.70  nm ) and gaas ( 0.28  nm ) layers . wafer @xmath7 is the same as used in @xcite . the intrinsic densities of approximately 4.0  @xmath9  @xmath10 ( wafer @xmath7 and @xmath8 ) of the two quantum wells originate from standard modulation doping . the low - temperature mobilities exceed 450000  @xmath11v@xmath12s@xmath12 ( wafer @xmath7 ) and 500000  @xmath11v@xmath12s@xmath12 ( wafer @xmath8 ) . the single - particle tunnel splitting @xmath13 in our double quantum wells was estimated to be approximately 150  @xmath14k . independent electrical contact to the two layers is achieved by growing the double quantum wells onto prestructured back gates @xcite and by using additional top gates in order to exploit a selective depletion technique @xcite . as the distance between back gate and 2des is only around 1  @xmath14 m , this overgrown back gate technique requires voltages of less than 1  v to locally deplete the contact arms and obtain independent electrical contacts to the two layers . the samples were either patterned into hall bars of different sizes or a quasi - corbino ring @xcite . the specific sample dimensions will be given later in the text . characteristics are measured at several magnetic fields around @xmath3 . the eight most inner curves are marked with symbols . ( b ) maximal ( critical ) currents as a function of the total filling factor ( data from labeled curves in subfigure ( a ) are used ) . at exactly @xmath3 the effective layer separation is 1.42 . hall bar sample of 0.88  @xmath15  0.08  mm@xmath16 ( wafer @xmath7 ) and @xmath17mk.**,scaledwidth=49.0% ]    the dc @xmath18 tunneling measurements presented in this paper are performed as sketched in figure [ fig1 ] ( b ) , by applying a tuneable dc bias voltage ( herein after referred to as 2-terminal voltage v@xmath19 ) between the two layers and detecting the current flow @xmath20 toward ground as a voltage drop over a known resistance @xcite . as the interlayer phase coherence at @xmath3 allows to easily transfer charges between the layers , the tunnel conductance becomes enormously enhanced which is tantamount to a very small tunnel resistance . consequently , even if there is a finite bias @xmath21 applied , the interlayer voltage probes a and b ( located close to source and drain ) may read a value for @xmath22 of close to zero ( figure [ fig1 ] ( a ) ) . however , this coherent tunneling can be destroyed if the current ( figure [ fig1 ] ( c ) ) exceeds a critical value @xmath23 . for the representative measurement presented in figure [ fig1 ] the critical value is roughly @xmath241.5  na . figure [ fig1 ] ( d ) is a depiction of the measured current @xmath20 over the measured voltage @xmath22 . this representation will be used throughout this paper , and the critical currents @xmath25 now translate into the maximal positive and negative currents at v@xmath26=0 as indicated by the dashed lines . the data here are presented in a scatter plot which show a discontinuity in the measured current and voltage characteristics when the system moves from the coherent strong tunneling regime into the weak tunneling regime . the origin of this negative differential conductance is the sudden change in the total impedance @xmath27 , when a tunneling resistance @xmath28 of almost zero is replaced by a resistance much larger than the series resistance @xmath29 of the ( uncorrelated ) quantum hall systems , i.e. , @xmath30 . historically , the study of coherent tunneling at @xmath3 exploits the tunneling - spectroscopy technique where the differential tunneling conductance @xmath31 is obtained in an ac measurement . these tunneling - spectroscopy measurements ( tsm ) reveal a resonantly enhanced zero bias tunneling peak at a total filling factor of one @xcite . a critical behavior as discussed in this paper , however , is hidden in the dc part of the tsm which is usually not shown . if the critical current is intrinsically small , it may also be difficult to detect or conceal through the influence of the ac modulation . it does not come as a surprise that the critical tunneling behavior ( or the signatures of the @xmath3 state in general ) , is strongest when the total filling factor of the system is exactly 1 , or when the individual filling factors are exactly 1/2 , respectively.=@xmath32 . however , imbalancing the electron densities can be used as a tool to induce and intensify the @xmath3 state . see spielman _ et al . _ , phys . rev . b 70 , 081303 ( 2004 ) and @xcite for details . ] deviating to larger fields ( smaller total filling factors ) or smaller fields ( larger total filling factors ) will strongly suppress the coherent tunneling . in the uncorrelated regimes , carriers are exchanged between two individual two - dimensional electron systems , a process which now requires a finite amount of energy to overcome the coulomb repulsion between the electrons . figure [ fig4 ] ( a ) provides a qualitative picture of this behavior . it shows a set of several 4-terminal @xmath18 curves measured on a hall bar sample of 0.88  @xmath15  0.08  mm@xmath16 ( wafer @xmath7 ) at @xmath3 ( @xmath33 ) and for small offsets in steps of about @xmath34 thereof . while drifting to either side of @xmath3 , the critical tunneling behavior is getting progressively suppressed around zero bias . our data suggest that moving toward higher fields suppresses the tunneling slightly more rapidly than in the opposite low field direction as the coulomb exchange increases with @xmath35 . figure [ fig4 ] ( b ) gives a quantitative analysis of the maximum ( critical ) current as a function of the total filling factor . note that only the eight plots in the center of figure [ fig4 ] ( a ) allowed the determination of a maximal current . as the total filling factor one state resides within a large parameter space , the size dependence as we are about to discuss can not be studied fully independent of other important parameters . the purpose of sec . iv is thus to outline the effects of manipulating temperature and effective layer separation @xmath6 which largely influence the magnitude of the critical current as well . the latter is achieved experimentally by increasing the electron densities in both layers simultaneously and adjusting the magnetic field , i.e. , @xmath36 . figure [ fig3 ] ( a ) shows the positive and negative critical currents as a function of @xmath6 for a hall bar sample of 0.88  @xmath15  0.08  mm@xmath16 ( wafer @xmath8 ) at below 20  mk . for @xmath37 the current appears to saturate at 2  na , even to decrease . this however is related to the effect of the sample s very low electron density , which begins to suppress the transport current altogether ( the single layer density is roughly 1.65  @xmath15  10@xmath38  m@xmath39 ) . for intermediate @xmath6 on the other hand the trend is clearly linear . for @xmath40 the system undergoes a phase transition and the critical tunneling behavior ( and the @xmath3 qh state ) disappears . this value is in very good agreement with those found in magneto - transport @xcite or tunneling - spectroscopy experiments @xcite . generally , if the onset of the @xmath3 state is observed at @xmath41 , its origin is a pure many - body effect , and in weakly tunneling samples ( i.e. , @xmath42 ) the phase - coherence would develop spontaneously @xcite . the smooth phase transition we observed supports a `` puddle model '' as suggested by a. stern and b. i. halperin @xcite where the @xmath3 phase breaks up into domains near the phase boundary . in this model , the type of phase transition would have to be of first order as two phases co - exist in the sample . figure [ fig3 ] ( c ) shows three 4-terminal @xmath18 curves corresponding to a @xmath6 of 1.40 , 1.61 and 1.79 . the expected phase transition for correlated bilayers occurring at finite temperatures is not a regular second order phase transition such as for normal superconductors at zero field or ferromagnets but a kosterlitz - thouless type of phase transition . however , standard transport experiments are not able to judge type and form of the occurring phase transition . nevertheless , what we see experimentally in transport ( i.e. , tunneling ) at finite temperatures is summarized in figure [ fig3 ] ( b ) . there we plot the critical current as a function of the inverse temperature for a fixed @xmath33 measured on a hall bar sample of 0.88  @xmath15  0.08  mm@xmath16 ( wafer @xmath7 ) . figure [ fig3 ] ( d ) shows several corresponding 4-terminal @xmath18 curves . at a temperature exceeding approximately 80  mk , the critical current begins to decrease rapidly . extrapolation of the data in this region indicates the suppression of the critical behavior for temperatures above 250  mk . the @xmath3 qh state as observed in magneto - transport is very weak at 250  mk and disappears entirely at temperatures exceeding approximately 350  mk @xcite . the exact type of this phase transition is unknown to us . spielman @xcite found similar overall trends on the temperature and @xmath6 in tunneling spectroscopy measurements using samples which display very small critical currents . the following study of the size dependence was motivated by magneto - transport and tunneling measurements performed on a corbino ring @xcite . these experiments had shown a vanishing conductance across the annulus , suggesting that the bulk of the @xmath3 phase is incompressible . as any interedge charge transfer is suppressed , tunneling would then ( generally ) only occur in the vicinity of the edges of the coherent @xmath3 system and its magnitude would have to scale with the circumference of the sample . tunneling spectroscopy measurements on hall bar samples on the other hand indicated that the zero bias tunneling conductance may be related to the area of the sample instead @xcite . to obtain a better understanding and trying to solve this contradiction we compared the critical currents , rather the properties of the tsm tunneling peak , in terms of the circumference and area . comparing different samples of course may introduce a systematic error , yet we still found that the effect of different sample sizes had much more dramatic consequences as we will see next . ( right - hand side ) and the @xmath3 sample area @xmath43 ( left - hand side ) for @xmath441.6 for samples from wafer @xmath7 and @xmath8 . fitting yields a linear dependence on the area . see text for further discussions . ( b ) corresponding 4-terminal @xmath18 curves . the sample dimensions are ( from largest to smallest ) : corbino ring : @xmath45=860  @xmath14 m , @xmath46=270  @xmath14 m ; hall bar type 1 : 0.88  @xmath15  0.08  mm@xmath16 ; hall bar type 2 : 0.15  @xmath15  0.05  mm@xmath16.**,title="fig:",scaledwidth=49.0% ] +   ( right - hand side ) and the @xmath3 sample area @xmath43 ( left - hand side ) for @xmath441.6 for samples from wafer @xmath7 and @xmath8 . fitting yields a linear dependence on the area . see text for further discussions . ( b ) corresponding 4-terminal @xmath18 curves . the sample dimensions are ( from largest to smallest ) : corbino ring : @xmath45=860  @xmath14 m , @xmath46=270  @xmath14 m ; hall bar type 1 : 0.88  @xmath15  0.08  mm@xmath16 ; hall bar type 2 : 0.15  @xmath15  0.05  mm@xmath16.**,title="fig:",scaledwidth=47.0% ]    figure [ fig2 ] ( a ) plots the value of the critical current as a function of the sample circumference @xmath47 and as a function of the sample s @xmath3 area @xmath43 when the effective layer separation @xmath6 for all samples is @xmath48  1.6 . the data points are labeled with the wafer index @xmath7 or @xmath8 . our data clearly indicates that the critical current @xmath23 grows as the sample increases in size . when we apply a linear fit in the @xmath49 diagram , we find that the trend is best described by 1.04@xmath50 for the area and 2.11@xmath51 for the circumference . based on these data we propose that the parameter that determines coherent tunneling at @xmath3 is the sample area with a linear dependence and not the circumference . figure [ fig2 ] ( b ) shows the corresponding 4-terminal @xmath18 curves . please note that the sample with the largest area ( and circumference ) displayed a strong hysteresis between up- and downsweeping the applied voltage @xmath21 . subfigure ( b ) shows the upsweep , where the negative and positive critical currents differ , i.e. , @xmath52 . in a subsequent downsweep , the situation and the absolute values are reversed , i.e. , @xmath53 and @xmath54(upsweep)=@xmath55(downsweep ) . for that reason , the fits in figure [ fig2 ] ( a ) ignore the error bar of these data points .    for comparison we extracted a critical current of 17  pa at @xmath44  1.6 from @xcite . this value originates from the dc part of a tsm on a 250  @xmath15  250  @xmath14m@xmath16 sample . we believe that the disagreement between our data and this value is related to a different single particle tunneling splitting @xmath13 , which is determined by the height and width of the tunneling barrier , and to the large enhancement of the tunneling amplitude at @xmath3 @xcite . their double quantum well is differently designed , with 18 nm gaas quantum wells separated by a 9.9  nm barrier layer . the center - to - center separation @xmath4 , however , is nearly identical to ours .    our studies indicate that the initial notion of a length dependence on tunneling as mentioned at the beginning of this chapter is a misinterpretation due to the astonishing properties of the coherent phase . coherent inter - edge tunneling in a corbino topology is suppressed because injected electrons do not become part of the @xmath3 state . in the excitonic condensate picture this can be understood as it is impossible for the condensate to create an interlayer exciton by placing a hole at the site of the injected electron , when the drain lead where the hole has to originate from is far away on the other side of the bulk . true coherent tunneling on the other hand occurs when new interlayer excitons are created or existing ones are annihilated . these processes appear to be bulk phenomena after all . however , as the @xmath3 phase could break up into domains near the phase boundary @xcite , it is possible that certain physical conditions may arise which yield a different dependence on the area ( and circumference ) than the one presented here . generally , the observation of a critical behavior requires - vaguely speaking - `` sufficiently large samples '' . the tangible sample size depends on the underlying design of the double quantum well and the sample structure , but may also be influenced by other unknown factors . more specifically , our studies identify the area rather than the circumference as the determining parameter for coherent tunneling at @xmath3 . a tunneling experiment in the general sense of charge transfer between two electron reservoirs through a sufficiently thin barrier is an inappropriate interpretation for the peculiar case of the total filling factor one state . instead , as the two layers are considered to be indistinguishable , correlated interlayer tunneling is a direct signature of interlayer phase coherence . the model of indistinguishable layers also implies that the critical behavior and its dependence on the parameters we discussed in this paper have several implications for magneto - transport experiments performed in the regime of the total filling factor one state @xcite . it can be shown that the leakage or tunneling current in the counterflow configuration @xcite depends on whether the driving current in the system is larger or smaller than the critical current for a given condition @xcite , i.e. , @xmath6 , temperature and sample size . the observed gap in magneto - transport on the other hand is only slightly altered . it nevertheless implies that temperature - activation measurements at a total filling factor of one @xcite require a much more careful interpretation of the gap energy . what makes matters experimentally complicated is the strong dependence of the critical current @xmath23 on the size of the sample , meaning that for samples of certain dimensions the transport current may already be much larger than the critical current , even when the system is at base temperature . this fact could be able to account for several unsettled observations such as finite dissipation in counterflow experiments for example @xcite . future magneto - transport experiments in the regime of the coherent total filling factor one state need to take the relevance of the driving current into account . in summary , we discussed the relevant parameters necessary for the observation of a critical behavior in the coherent @xmath3 state . we find a linear dependence of the value of the critical tunneling current @xmath23 on the @xmath3 area of the sample . @xmath23 will decrease when the system is brought toward the phase boundary by increasing @xmath6 or the temperature . it is also rapidly destroyed by moving away from a total filling factor of one . we would like to thank both a. h. macdonald and m. gilbert for discussions and comments . our bilayer wafers were grown in collaboration with m. hauser ( max - planck institute , stuttgart ) and h .- tranitz ( university of regensburg ) . especially , we would like to acknowledge j. g. s. lok for his initial and intensive work on our electron double layer systems . this project was supported by the bmbf ( german ministry of education and research ) under grant no . 01bm456 . h. a. fertig , _ phys . b _ * 40 * 1087 ( 1989 ) z. f. ezawa and a. iwazaki , _ int b _ * 6 * 3205 ( 1992 ) x. g. wen and a. zee , _ phys . lett . _ * 69 * 1811 ( 1992 ) i. b. spielman , j. p. eisenstein , l. n. pfeiffer and k. w. west , _ phys . lett . _ * 84 * 5808 ( 2000 ) i. b. spielman , j. p. eisenstein , l. n. pfeiffer and k. w. west , _ phys . rev . lett . _ * 87 * 036803 ( 2001 ) z. f. ezawa and a. iwazaki , _ int b _ * 8 * 2111 ( 1994 ) l. tiemann , w. dietsche , m. hauser and k. v. klitzing , _ new j. phys . _ * 10 * 045018 ( 2008 ) h. rubel , a. fischer , w. dietsche , k. v. klitzing and k. eberl , _ phys . lett . _ * 78 * 1763 ( 1997 ) j. p. eisenstein , l. n. pfeiffer and k. w. west _ appl . * 57 * 2324 ( 1990 ) l. tiemann , w. dietsche , m. hauser and k. v. klitzing , _ phys . b _ * 77 * 033306 ( 2008 ) r. d. wiersma , j. g. s. lok , l. tiemann , w. dietsche , k. von klitzing , d. schuh and w. wegscheider , _ physica e _ * 35 ( 2 ) * 320 ( 2006 ) a. d. k. finck , a. r. champagne , j. p. eisenstein , l. n. pfeiffer and k. w. west , _ phys . rev . b _ * 78 * 075302 ( 2008 ) a. r. champagne , j. p. eisenstein , l. n. pfeiffer and k. w. west , _ phys lett . _ * 100 * 096801 ( 2008 ) s. q. murphy , j. p. eisenstein , g. s. boebinger , l. n. pfeiffer and k. w. west , _ phys . lett . _ * 72 * 728 ( 1994 ) i. b. spielman , ph.d . thesis , caltech ( 2004 ) e. rossi , a. s. nunez and a. h. macdonald , _ phys . lett . _ * 95 * 266804 ( 2005 ) a. stern and b. i. halperin , _ phys . lett . _ * 88 * 106801 ( 2002 ) z. f. ezawa , _ quantum hall effects - field theoretical approach and related topics _ , 2nd edition ( world scientific , 2008 ) m. kellogg , j. p. eisenstein , l. n. pfeiffer and k. w. west , _ phys . lett . _ * 93 * 036801 ( 2004 ) e. tutuc , m. shayegan and d. a. huse , _ phys . lett . _ * 93 * 036802 ( 2004 ) y.yoon , l. tiemann , w. dietsche and k. von klitzing , to be submitted r. d. wiersma , j. g. s lok , s. kraus , w. dietsche , k. von klitzing , d. schuh , m. bichler , h .- tranitz and w. wegscheider _ phys . rev . lett . _ * 93 * 266805 ( 2004 )
we will discuss the relevant conditions to observe a critical tunneling current [ new j. phys . 
 10 , 045018 ( 2008 ) ] in electron - double layer systems at a total filling factor of one and find they are related to the effective layer separation and the temperature . 
 our studies suggest that the intensity of the critical tunneling behavior is also directly linked to the area of the sample .