@article{434eee64e50c4370a3c3e0f497441086,

title = "On the nature of the Hall insulator",

abstract = "We have conducted an experimental study of the linear transport properties of the magnetic-field induced insulating phase which terminates the quantum Hall (QH) series in two dimensional electron systems. We found that a direct and simple relation exists between measurements of the longitudinal resistivity, pxx, in this insulating phase and in the neighboring QH phase. In addition, we find that the Hall resistivity, pxy, can be quantized in the insulating phase. Our results indicate that a close relation exists between the conduction mechanism in the insulator and in the QH liquid.",

keywords = "D. phase transitions, D.quantum Hall effect",

author = "D. Shahar and Tsui, {D. C.} and Mansour Shayegan and Cunningham, {J. E.} and E. Shimshoni and Sondhi, {Shivaji Lal}",

note = "Funding Information: regimes[ 8,18,19]I.t is thereforein terestingto look for the symmetryn ear transitionsf rom FQHE statest o the insulator.I n Fig. 3a we plot two pXXt races( solid curves)v s. Av, obtainedn earthe v = 1/ 3 to insulator transition,a t T = 24 and 99 mK. Similarly to Fig. 1, we alsop lot 1/ p,, traces( dashedc urves)v s.a reversed Av axis. Although very close to the transitionp oint we againo btain the pXX= 1/ pXXs ymmetryt,h e range in termso f pXr appearst o be muchm ore limited.W e now recall that, in the KLZ descriptiono f the transitions in the FQHE regime,t he electronics ystemi s mapped,u singa Chern-Simonst ransformationo, nto a superconductor-insulatotrr ansitionso f an equivalent compositeb oson (CB) system[ 20].A similar transformationw as usedb y Jain [21]t o map the v = l/3 FQHE stateo nto a v = 1 IQHE stateo f composite fermions (CF{\textquoteright}s). We will next show that, by mapping our v = 1 / 3 to insulatort ransitiono nto a v = 1 to insulator transition of CF, the pXX= l/p, symmetry greatlyi mprovesa, nd the correspondingv {\textquoteright}s are againr elatedb y particle-holes ymmetryA. lternatively, it is possiblet o use the CB{\textquoteright}s mapping,a nd the corre-spondingv {\textquoteright}s are then relatedb y duality-symmetryo f the CB{\textquoteright}s [22]. Using the CF mapping,w e replot in Fig. 3b the samed ata as in Fig. 3a, only with the fillings of CF, v{\textquoteright} = &, as the abscissaA. much-improveds ymme-try is obtaineda t both T'se,x tendingto - 6 timest he transition value at 24 mK and N 4 times at 99 mK, beforea ppreciables ystematicd eviationsa re observed. In view of the data in Fig. 3, it is reasonableto as-sumet hat for the v = l/3 to insulatort ransition,t he symmetryi s that of the underlyingc ompositep articles,r athert han that of the electrons. Although we can not give a definitea nswert o the questiono f the range of validity of the pXX-l/p, symmetrya, n illuminatinge xperimentapl oint can be made by consideringt he current dependenceo f the pXu traces.I n Fig. 4, we again plot pXXa nd l/p, traces,s imilar to those in Fig. 3, taken at T = 24 mK, but measureda t two differentc urrents.C learly, the systematicd eviationo f the pXXt races( solid lines) from the 1/ pxx traces( dashedl ines) is much larger, and startsc loser to v:,, for the 100p A trace.O n the otherh and,t he 1/ p, tracesa t both currentsa ppeart o overlap( for the l/p, > 1 range),i ndicatingt hat the pxx in the FQHE regimei s independenot f currenti n the ranges hown.I t thereforea ppearst hatb y lowering them easuringc urrentt he rangeo f applicabilityo f the symmetryis significantlyin creasede, vena t thesev ery low currentsA. naturalc onclusionw ould be that the symmetryh olds only in the strictly ohmic regimeo f transport.W e wish to emphasizeh ere,t hat this is not the case,a nd that the symmetryi s maintainedm uch beyond the ohmic regime.H owever,s ince for higher currentso utsidet he ohmicr egimep, xx is ill-defined,a generalizeds ymmetrys houldb e invoked.T his can be done by consideringt he pxx - l/p, symmetrya s a symmetryu ndert he exchangeo f the currenta nd volt-agec oordinatesI.n a separatep ublication,w e demon-stratet hatthis generalizeds ymmetryin deedh olds for a broad rangeo f currentsa nd voltages[ 14]. From the discussionin the previousp aragraphw, e concludet hati t is essentiaflo r a quantitativec ompari-son of pxx on both sideso f thet ransitiont hatt hem ea-suremenct urrentw ill be keptt o a minimumt o prevent non-ohmic effectsw hich,f or a constant-currenmt ea-surementa, risep redominantlyin the insulator.W ith the exceptiono f Fig. 4, we usea n AC currento f IO-{\textquoteright} {\textquoteright} A and monitor the voltageb y a lock-in phases ensi-tive techniqueW. e also usev ery slow B sweepr ates( > 15m in/T) to maintainT stabilitya t dilution temperatures2 20 mK. We found that usingt heses low sweep rates,o ur Oxford 200T LM refrigeratorm aintainedT stabilityo f bettert han 2% throughouto ur T range. The resultsp resentedin this letter pose a rather strict constrainto n any theoreticalm odel aiming at describingt he QHE to insulatort ransitions.W e wish to outlineh eres omeo f thef eaturesre quiredf rom such a model.F irst, them odelh ast o be particle-holes ym-metric (Av - -Av), as is evidentf rom the v values of the correspondings tatesi n the insulator and the QHE statesF. or the v = 1 / 3 to insulatort ransition, the symmetrys hould be that of the compositep articles.S econd,t hem odelh ast o allow for the symmetry under pxx - 1f pxx exchangei,. e. an exchangeo f the measuredc urrentsa nd voltagesT. his symmetryc an be convenientlyd escribeda s symmetryu nder duality transformationa, nd is further discussedin a separate paper [23]. While our experimendt oesn ot directlyi dentifyt he mechanismfo r ohmic transporti n the Hall insulator, it does show that this mechanismis very closely related to that governingt he conductionp rocessi n the IQHE and FQHE regimes,o ver a surprisinglyw ide rangeo f v. It would be interestingto look for a similar symmetryn ear other transitionss, ucha s the QHE plateaut o plateaut ransitions,t ransitionst o an insulating phasei n double-layerQ HE systemsa, nd per-hapse vent he superconductor-insulatotrr ansitionsin thin metalf ilms and in Josephsonj unction arrays. Acknowledgements- We thank S. A. Kivelson for in-structived iscussionsT. his work has been supported by the NSF, the BeckmanI nstitute( ES) and the A. P Sloan Foundation (SLS).",

year = "1997",

month = jun,

doi = "10.1016/S0038-1098(97)00069-0",

language = "English (US)",

volume = "102",

pages = "817--821",

journal = "Solid State Communications",

issn = "0038-1098",

publisher = "Elsevier Limited",

number = "11",

}