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Radiation-induced zero-resistance states with resolved Landau levels R. G. Mani1 1Harvard University, Gordon McKay Laboratory of Applied Science, 9 Oxford Street, Cambridge, MA 02138, USA (Dated: February 2, 2008) The microwave-photoexcited high mobility GaAs/AlGaAs two-dimensional electron system ex- 5 hibits an oscillatory-magnetoresistance with vanishing resistance in the vicinity of magnetic fields 0 0 B = [4/(4j +1)]Bf, where Bf = 2πfm∗/e, m∗ is an the effective mass, e is the charge, f is the 2 microwave frequency, and j =1,2,3... Here, we report transport with well-resolved Landau levels, and some transmission characteristics. n a Journal Reference: Appl. Phys. Lett. 85, 4962 (2004). J 5 TheexperimentalstudyofquantizedHalleffect(QHE) lower-B minimum, near (4/9)B , which follow the series f ] has shown that a two-dimensional electron system B = (4/[4j +1])B , with j = 1,2,3...[2] A remarkable l f l a (2DES) can exhibit zero-resistance states in the vicinity feature in these zero-resistance states is the absence of h of integral and mostly odd-denominator fractional fill- concomitant plateau formation in the Hall effect,[2, 3] - ing factors, at low temperatures, T, and high magnetic as in typical quantum Hall systems.[1] The R data of s xy e fields, B. These (quantum Hall) zero - resistance states Fig 1(a) show, for example, that the Hall resistance in- m are initially approached, at finite T, following an acti- creaseslinearlyvs. the magneticfieldandcoincideswith . vation law, which is understood as a manifestation of theR thatisobservedwithoutradiationovertheB in- t xy a a gap in the electronic spectrum.[1] Recent observations tervalcorrespondingtothe(4/5)B zero-resistancestate. f m of radiation-induced zero-resistance states in the 2DES Yet, a carefulcomparisonof the photoexcited(w/ radia- - areparticularlyinterestingbecausetheyhaveshownthat tion)Halleffectwiththedark(w/oradiation)Halleffect d theabovementionedcharacteristics,i.e.,activatedtrans- reveals some definite modifications in R upon irradi- n xy o port and zero-resistance states, can also be obtained in ation. For example, at the Rxx maxima, there appear c a photo-excited high mobility 2DES, without realizing to be reductions in the magnitude of the irradiatedR . xy [ at the same time a QHE.[2, 3] In such a situation, one In addition, well above B , i.e., B ≥ 0.2 Tesla, where f 1 wonders whether the observedcharacteristicscould once Rxy exhibits QHE plateaus, a given filling factor QHE v again be indicative of a spectral gap, as in the quantum appears shifted to higher B under the influence of radi- 1 Hall limit.[1] ation. These effects could, however, be reversed simply 9 The zero-resistance states of interest here are in- by switching off the microwave excitation. 0 duced by microwave excitation of a high mobility As suggested by Fig. 1, radiation-induced zero- 1 0 GaAs/AlGaAs 2DES, at low T, in a large filling factor resistance states are typically observed over a range of 5 limit.[2,3,4]Experimentsindicatevanishingdiagonalre- magnetic fields corresponding to weak- or non-existent 0 sistance,followinganactivationlaw,aboutB =(4/5)B SdH oscillations (in the dark) at easily accessible mi- f / ∗ ∗ t andB = (4/9)Bf, where Bf = 2πfm /e,m is aneffec- crowave frequencies and temperatures. A question that a tive mass,e is the electroncharge,andf isthe radiation we wish to address is whether radiation-induced zero- m frequency.[2] In this report, we illustrate transport with resistancestatescanalsooccurovertherangeofB where - d resolved Landau levels and transmission characteristics, theamplitudeofSdHoscillationsinthedarkisrelatively n as we refer the reader to the literature for discussions of large,saysubstantiallygreaterthanone-halfoftheback- o theory.[5, 6] ground dc resistance in the absence of microwaveexcita- c Experiments were performed, as indicated tion, at the same B. : v elsewhere,[2] on standard devices fabricated from Weshowhereresultswhichindicatethat,indeed,these i X GaAs/AlGaAs heterostructure junctions with an elec- radiation-inducedzero-resistancestatescanalsooccurin tron mobility up to 1.5 × 107 cm2/Vs. Typically, a the B limit, where giant Shubnikov-de Haas oscillations r a specimen was mounted inside a waveguide, immersed are observable in the specimen. That is, where the Lan- in pumped liquid Helium, and irradiated with elec- dau level spacing, h¯ω , exceeds both the thermal en- C tromagnetic (micro-) waves over the frequency range ergy, k T, and a broadening parameter, Γ, defined from B 27 ≤ f ≤ 170 GHz. Reported electrical measure- the transport relaxation time i.e., Γ << k T < ¯hω , B C ments were carried out using low frequency ac lock-in whichmay be viewedas a quantumHall threshold. This techniques, as usual. is a regime of consequence because theory has some- Figure 1 shows the low-B transport under photoex- times identified observed effects with the limit where citation at 60 GHz. Fig. 1(a) indicates a wide R Γ<<k T ≈¯hω .[6] xx B C radiation-induced zero-resistance state about (4/5)B , Fig. 2(a)showsthatthedarkspecimenexhibitsstrong f and a close approach to vanishing resistance at the next SdH oscillations over the range of B−1 given by 13 ≤ 2 0.5 B B f f 12 (a) 0.5 K 10 0.6 60 GHz w/o radiation 46 δ 0.7 K 8 8 54 Ω) SdH[Dark] ( 0.4 R xx4 -60 dB Ω)6 Ω) ( (a) (k 0 Rxx4 R xy 12 (b) 0.2 w/ radiation 2 8 ) Ω ( 4/5 B x 0 f 0.0 Rx4 10 0 -10 dB 8 0 Ω)6 Ω) 12 (c ) 163.5 GHz R (xx4 (b) R (xy ∆ ) 8 Ω 2 ( w/ radiation R xx 0 -30 4 0.0 0.1 0.2 0.3 -2 dB B (T) 0 20 B-1/δ 30 FIG.1: (Coloronline)ThefigureexhibitstheHallresistance SdH[Dark] Rxy observed both with (w/) and without (w/o) microwave radiation at f = 60 GHz, along with Rxx under radiation. Here, Rxx vanishes about (4/5)Bf, and this zero-resistance FIG. 2: (Color online) This figureshows theevolution of the state does not produce a plateau in Rxy. Note the remark- diagonal resistance Rxx underradiation, intheregime where able shift of QHE plateaus, i.e., plateaus with Rxy = h/ie2, largeamplitudeShubnikov-deHaas(SdH)oscillationsareob- for46 ≤i≤54, tohigherBundertheinfluenceofradiation. servable in Rxx. Top: This panel shows the SdH oscillations (b): The radiation induced correction to the Hall resistance, in the absence of radiation (-60 dB). The abscissa has been ∆Rxy, is shown along with Rxx. Notably, the ∆Rxy oscilla- normalizedbytheperiodδSdH[Dark]oftheseSdHoscillations. tionscorrespondtoadecreaseinthemagnitudeofRxy,while Center: Here, Rxx under 163.5 GHz excitation has been ex- the slope in ∆Rxy (dotted line) indicates a change in the hibitedwiththeradiationintensityattenuatedto-10dB.The slopeoftheRxy curveuponirradiation. Thelatterfeatureis radiation produces a strong modulation in the amplitude of qualitativelyconsistentwiththeshiftoftheQHEplateausto the SdH oscillations, which is a signature of the radiation- higher B underradiation, see (a). induced oscillatory magnetoresistance. Bottom: Rxx under photoexcitation,withtheradiationintensityattenuatedto-2 dB. Note the radiation induced zero-resistance states about 17 ≤ B−1/δ ≤ 23 and 34 < B−1/δ , where B−1/δSdH[Dark] ≤ 38. This correspondsto filling factors theSdHosciSlldaHt[iDonasrka]lso vanish. AsthecolorSeddH[dDisakrks]mark a 26≤ν≤76becauseafactor-of-twooccursbetweenνand fixed filling factor, their shift along the abscissa between (a) B−1/δ , i.e., ν = 2B−1/δ , when spin - (c) is interpreted as a change in the cross sectional area of SdH[Dark] SdH[Dark] splitting is not resolved in the SdH oscillations. Here, theFermi surface underradiation. at the examined temperature, T = 0.5 K, hf = 0.676 meV easily exceeds k T = 0.043 meV. Estimates of the B broadening parameter indicate that Γ<<k T.[2] tivity, and that in turn suppresses the amplitude of SdH B oscillations. Here,weimaginethatthebackgroundresis- Photoexcitation of the specimen with f = 163.5 GHz tance (and resistivity) could be defined (and extracted) radiation initially produces a modulation in the ampli- from the midpoints of the SdH oscillations. tude of the SdH oscillations (see Fig. 2(b)), which is the signature of the radiation-induced resistance oscillations A further increase in the radiation intensity, see Fig. in this separated Landau level limit. One might plausi- 2(c),leadstozero-resistancestatesoverbroadB−1 inter- bly explain this SdH modulation feature, at least about vals. For example, the (4/5)B state occurs here about f the radiation induced resistance minima, by suggesting B−1/δ = 20, and it looks similar to the effect SdH[Dark] thattheradiationreducesthebackgrounddiagonalresis- that is observed at lower f (see Fig. 1). Note that 3 4/5 B B B−1/δ = 29 in Fig. 2(c), the amplitude of the f f SdH[Dark] SdH oscillations is not also increased, and this suggests -9 dB a break in the correlationbetween the backgroundresis- tance and the SdH amplitude at the maxima, unlike the casewiththe minima. Anoteworthypointhereseemsto ) s t -3 dB be that in Fig. 2 (b) and (c), the SdH oscillations seem i n u not to increase in amplitude under the influence of mi- b. (b) crowaves. The SdH amplitude either stays the same or r a it is reduced under microwaveexcitation. This mightin- R (S 0 dB dicate a role for electron heating. Parenthetically, there microwaves is also some evidence that the threshold radiation inten- B = 2πf m*/e f sity for realizing zero-resistance increases, as one moves 12 to higher f. Thus, heating could be more influential at 1.3 K higher excitation frequencies. This feature is attributed R here to the point that, as the photon energy increases S sample with f, more power needs to be delivered to the speci- 8 waveguide men in order to maintain a constant photon number per ) Ω unit of time, which could be the essentialunderlying pa- ( -9 dB R xx (a) -3 dB rameter, at a higher f. A subtle feature of interest in 4 0 dB Fig. 2 is that the SdH extrema seem to shift to lower B−1 (or higher B) under microwaveexcitation, in quali- tative agreement with the behavior observed in the Hall f = 108 GHz effect in Fig. 1(a).[2] 0 0.0 0.1 0.2 B 0.3 0.4 The characteristic field scale for the radiation induced f effect, B ,[2] suggests a possible relation to cyclotron B (T) f resonance,which one might investigate through simulta- neous transmission and transport measurements in the same high mobility specimen, see Fig. 3. Here (see FIG. 3: (Color online) This figure illustrates the transmis- Fig. 3(inset)), a resistance sensor placed immediately sion characteristics of the 2DES under irradiation. Inset: A below the sample served to gauge the relative transmit- resistancesensorbelowthesampleservesastheradiationde- tector. (a)Rxx ofthe2DESvs. B. Theoscillationamplitude ted power. Fig. 3(a)illustrates the specimen Rxx vs. B, decreases with increasing radiation intensity when the power while Fig. 3(b) exhibits the B-dependent sensor resis- attenuationfactorexceeds-9dB,signifying”breakdown”. (b) tance, R . In this GaAs/AlGaAs specimen, the optimal S Themagnetoresistance oftheradiation sensor. Thisdetector radiation induced R response occurred in the vicinity xx response suggests nonmonotonic transmission above B . f of -9 dB, see Fig. 3(a). That is, the amplitude of the radiation-inducedresistanceoscillationsincreasedmono- tonically with increasing power up to -9 dB. A further at (4/5)Bf, h¯ωC [= (4/5)hf] is noticeably greater than increase of the radiation intensity (dB → 0) produced a kBT. A remarkable feature in these data of Fig. 2(c) is ”breakdown”orareductionintheRxx peakheightalong that the SdH oscillations disappear as Rxx −→ 0 under withanincrease intheresistanceattheminima(seeFig. the influence of radiation. It appears worthpointing out 3(a)). The response of the transmission sensor, R , (see S thatwehavenotobservedanyevidence of”chopping”of Fig. 3(b)) suggests structure at magnetic fields about- the SdH minima on the approach to zero-resistance, as and mostly above- B , which becomes more pronounced f might be expected if the amplitude of the SdH oscilla- with increased excitation. The feature correlates with a tions did not appropriately follow the background Rxx, strongradiation-induceddistortionofthe Rxx peak that or if the SdH amplitude somehow stayedconstant as the is centered about 0.3 Tesla. One might interpret some backgroundresistivity went to zero under microwaveex- of these features about B as a signature of cyclotron f citation. resonance, although further supplementary evidence ap- It is also worth considering the SdH behavior out- pears necessary to confirm this hypothesis. Remarkably, side of the domain of zero-resistance states. For exam- the observedoscillationsin Rxx below Bf appearimper- ple, on either side of the (4/5)B zero-resistance state ceptible in the sensor response (cf. Fig. 3(a) and Fig. f (aboutB−1/δ =20),ontheadjacentR max- 3(b)). SdH[Dark] xx ima, SdH oscillations continue to be observable, even as In summary, we have emphasized the possibility of re- theyhavedisappearedonthezero-resistancestatesthem- alizing radiation induced zero-resistance states, see Fig. selves. Note that as the background resistance is en- 2, in a range of B where R exhibits giant SdH oscil- xx hancedwith respect to the darkvalue near,for example, lations due to separated Landau levels. This result indi- 4 cates that radiation-induced zero-resistance states occur (tobepublished);Advances inSolidState Physics,edited even outside a so-called quasi-classical limit. Transmis- by B. Kramer (Springer, Heidelberg, 2004), Vol. 44, pp. sion measurements also indicate non-monotonic features 135-146. [3] M. A. Zudov, R. R. Du, L. N. Pfeiffer, and K. W. West, in the transmitted signal about and above B , some of f Phys. Rev.Lett. 90, 046807 (2003). which could be indicative of cyclotron resonance. [4] S.A.Studenikin,M.Potemski,P.T.Coleridge,A.Sachra- The authors acknowledge discussions with K. von Kl- jda,andZ.R.Wasilewski,Sol.St.Comm.129,341(2004). itzing, V. Narayanamurti, J. H. Smet, and W. B. John- [5] R. Fitzgerald, Phys. Today 56, 24 (2003); V. I. Ryzhii, son. 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