- Email: [email protected]
AlGaAs single heterostructure
Physica B 298 (2001) 191}194
Longitudinal resistance anomaly around the 2/3 "lling factor observed in a GaAs/AlGaAs single heterostructure K. Hashimoto *, K. Muraki , T. Saku , Y. Hirayama NTT Basic Research Laboratories, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan CREST-JST, 4-1-8 Honmachi, Kawaguchi, Saitama 331-0012, Japan
Abstract A pronounced R enhancement near " is observed in a back-gated GaAs/AlGaAs single heterostructure when the VV magnetic "eld for " (B ) is set less than 6 T using the back gate, but it almost vanishes for B '8 T. This tendency is consistent with a model in which the mixed state consisting of two di!erent spin domains plays an important role for the anomalous R enhancement. By taking advantage of the back-gated operation, we "nd a quick recovery of the VV R enhancement in spite of prior electron depletion, and the long relaxation time of the R enhancement. These results VV VV support the argument that the R enhancement is not memorized by the electron system but by the alternative system VV such as the nuclear spin con"guration leading to a long relaxation time. 2001 Elsevier Science B.V. All rights reserved. PACS: 75.70.!i; 76.60.Es Keywords: Fractional quantum Hall e!ect; Back-gated GaAs/AlGaAs single heterostructure; Longitudinal resistance; Nuclear spin
The fractional quantum Hall states at some "lling factor (), for instance ", have two possible di!erent electron-spin states, unpolarized and polarized states. Which state appears depends on a competition between the Coulomb and Zeeman energies [1}3]. When the Zeeman term becomes dominant with increasing magnetic "eld, there is a transition from the unpolarized state to the polarized state. According to theoretical calculation [4], another di!erent state, a mixed state, is predicted to exist at " near the transition point between the
* Corresponding author. NTT Basic Research Laboratories, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan. Tel.: #81-46-240-3481; fax: #81-46-240-4727. E-mail address: [email protected] (K. Hashimoto).
unpolarized and polarized states. In the mixed state, there may be a domain structure of electron spins consisting of unpolarized and polarized domains. Actually, KronmuK ller et al. [5,6] have reported an interesting experimental result which suggests the existence of the " mixed state. In their result, anomalous enhancements in the longitudinal resistance (R ) appear around the "lling VV factor " for a narrow quantum well, when the magnetic "eld is scanned at a slow rate. In this paper, we study a similar R anomaly VV around " for a back-gated GaAs/AlGaAs single heterostructure. We show that a pronounced R enhancement near " appears when the VV magnetic "eld for " (B ) is set less than 6 T, but it almost vanishes for B '8 T. This tendency is consistent with a model in which the mixed state
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 0 2 9 9 - X
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K. Hashimoto et al. / Physica B 298 (2001) 191}194
consisting of two di!erent spin domains plays an important role leading to an anomalous R enVV hancement. We also investigate a relaxation of the R enhancement by taking advantage of the VV back-gated operation. We "nd a quick recovery of the R enhancement in spite of prior electron VV depletion, and the long relaxation time of the R enhancement. VV We perform the experiment using the back-gated GaAs/AlGaAs single heterostructure [7], which consists of a Si doped n-GaAs substrate, 820 nm barrier layers and a 500 nm GaAs top layer. The barrier layers contain an 800 nm GaAs/AlAs superlattice and 20 nm AlGaAs. In the back-gated system, the electron density (N ) of the two-dimensional Q electron gas (2DEG) is precisely controlled by the back-gate bias (< ) and the 2DEG is completely @E depleted for < (
Fig. 1. Magnetic "eld dependence of the R enhancement near VV " at the temperature of 100 mK. All data except for those in the inset of Fig. 1(a) are measured with scanning the magnetic "eld in a downward direction only. (a) shows the magnetresistance at < "1.90 V (N "8.7;10 m\) for B "5.5 T. @E Q The broken and solid lines show R measured with a normal VV scanning speed, 0.2 T/min and with a slow scanning speed, 0.003 T/min, respectively. The slow scan gives rise to a pronounced enhancement which is marked by an arrow. Inset shows hysteresis around " in up and down slow sweeps (the arrows indicate scanning direction) at < "1.60 V @E (N "6.7;10 m\). In contrast with (a), no enhancement can Q be seen when B "12.2 T on increasing < to 3.50 V @E (N "1.9;10 m\) in (b). In (c), the value of the R enhanceQ VV ment appearing at the peak marked by the arrow in (a) is plotted at several di!erent B values by changing < (N ). Below 5 T, @E Q the R minimum at " deviates from the ideal value VV R "0 . VV
measurements are performed in a dilution refrigerator without any illumination. A standard lowfrequency AC lock-in technique is used with a current of 100 nA. Figs. 1 (a) and (b) show the magnetic "eld dependence of R around " at di!erent values of VV
K. Hashimoto et al. / Physica B 298 (2001) 191}194
< (di!erent electron densities), which give di!er@E ent B values. All curves are measured at the temperature of 100 mK. The scanning direction of these curves except for the one in the inset is downward. In Fig. 1 (a), < is set to 1.90 V @E (N "8.7;10 m\) giving B "5.5 T. The broQ ken line depicts R measured with a normal scannVV ing speed, 0.2 T/min. It shows normal fractional quantum Hall e!ect and well-developed minimum at ". When we decrease the scanning speed to 0.003 T/min, R indicated by a solid line shows an VV anomalous enhancement which is marked by an arrow near B . It is about 1.3 times larger than the R measured with the normal scanning speed. VV The value of the R enhancement reaches 1460 . VV The R enhancement shows the hysteretic behavVV ior in up and down slow scans. For instance, in the inset of Fig. 1(a), the R curves for < "1.60 V VV @E (N "6.7;10 m\) depict the hysteretic behavQ ior for the slow scan in the up and down scanningdirections represented by the arrows. In contrast to Fig. 1(a), as shown in Fig. 1(b), we can see no enhancement at B "12.2 T on increasing < to @E 3.50 V (N "1.9;10 m\). To investigate the Q magnetic "eld dependence of the R enhancement, VV we measure the value of the R enhancement VV marked by an arrow [see Fig. 1(a)] at other several di!erent B values by changing < (N ). The re @E Q sult is shown in Fig. 1(c). Almost no enhancement is observed when B '8 T. However, we observed a pronounced R enhancement on decreasing VV B to 5.5 T. Although the enhancement develops with the further reduction of B , the R min VV imum at " deviates from the ideal value R of VV 0 for B (5 T. The magnetic "eld where we observed a clear R enhancement is below that VV observed by KronmuK ller et al., namely B "8}9 T [5,6]. This di!erence can be under stood as follows. In our experiment, we use a single heterostructure, while KronmuK ller et al. use a narrow quantum well. The thickness of the 2DEG layer in our single heterostructure is about twice as thick as their narrow quantum well. Since the Coulomb term in our thicker layer is weaker than that in their thinner structure, the Zeeman term starts dominant at a lower magnetic "eld in our single heterostructure [8]. This fact gives rise to a shifting of the "eld where the " mixed state
193
appears to lower magnetic "eld in a single heterostructure. Therefore, our results are consistent with the model in which the mixed state plays an important role for the anomalous R enhancement. VV Fig. 2 illustrates the development and relaxation of the R enhancement. In this experiment, we "rst VV set < "1.94 V (N "9.0;10 m\) for the "xed @E Q magnetic "eld of 5.8 T, where the R enhancement VV clearly appears with a well-developed R minVV imum at " (B "5.6 T). R develops with VV time and saturates after about 30 min with a R enhancement of 1610 . Then, we completely VV deplete the 2DEG for a given depletion time by setting < "0 V. Finally, we apply < "1.94 V @E @E again to re"ll the 2DEG and measure how much the R enhancement has relaxed (R ). For 30 s VV VV depletion, R "301 which corresponds to VV 19% of the saturated R enhancement. This small VV
Fig. 2. The development and relaxation of the R enhancement VV at < "1.94 V (N "9.0;10 m\), the magnetic "eld of @E Q 5.8 T (B "5.6 T) and the temperature of 140 mK. R evolves VV with time and saturates after about 30 min. The 2DEG is then completely depleted for a given depletion time, 30 s, by setting < "0 V. Finally, < "1.94 V is applied again to re"ll the @E @E 2DEG, and how much the R enhancement has relaxed (R ) VV VV is measured. The inset shows R versus some depletion time. VV
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K. Hashimoto et al. / Physica B 298 (2001) 191}194
R implies the following process. The R enVV VV hancement may strongly relate to the " mixed state. In the mixed state, it is reasonable to consider that R mainly re#ects scattering by the electron VV spin domains. Although the electrons are completely depleted, the electron spin domains return quickly back to the initial situation just before depleting on re"lling with electrons. The inset shows R versus depletion time. From this plot, VV we estimate the relaxation time of the R enhanceVV ment to be approximately 30 min which is the same order of typical relaxation time of nuclear spin [9]. These two results: the quick recovery of the R enVV hancement in spite of the electron depletion, and the long relaxation time, is evidence that the R enhancement is not memorized by the electron VV system but by some other systems providing the long relaxation time. The most plausible candidate is the nuclear spin con"guration as KronmuK ller et al. [5,6] have already demonstrated experimentally. These results and our discussion suggest that it may be possible to write and read nuclear spin information by using the 2DEG near ". In conclusion, we report a R anomaly around VV " for a back-gated GaAs/AlGaAs single hetero structure. The pronounced R enhancement near VV " is observed at B (6 T, but it almost van ishes at B '8 T. In the relaxation experiment of the R enhancement, we "nd a quick recovery of VV the R enhancement in spite of the prior electron VV depletion, and the long relaxation time of the R enhancement. These results support the arguVV ment that the R enhancement is not memorized VV
by the electron system but by the alternative system such as the nuclear spin con"guration leading to a long relaxation time.
Acknowledgements The authors acknowledge T. Fujisawa and S. Miyashita for their supports in experiments and sample preparation. The authors also wish to thank G. Austing for the critical reading of the manuscript. This work is partly supported by NEDO NTDP-98 program.
References [1] R.G. Clark, S.R. Haynes, A.M. Suckling, J.R. Mallett, P.A. Wright, J.J. Harris, C.T. Foxon, Phys. Rev. Lett. 62 (1989) 1536. [2] R. Clark, P. Maksym, Physics World 2, (1989) 39. [3] T. Chakraborty, P. Pietilainen, The Quantum Hall E!ects, Springer, Berlin, 1995. [4] T. Chakraborty, Surf. Sci. 229 (1990) 16. [5] S. KronmuK ller, W. Dietsche, J. Weis, K. von Klitzing, W. Wegscheider, M. Bichler, Phys. Rev. Lett. 81 (1998) 2526. [6] S. KronmuK ller, W. Dietsche, K. von Klitzing, G. Denninger, W. Wegscheider, M. Bichler, Phys. Rev. Lett. 82 (1999) 4070. [7] T. Saku, K. Muraki, Y. Hirayama, Jpn. J. Appl. Phys. 37 (1998) L765. [8] J.P. Eisenstein, H.L. Stormer, L.N. Pfei!er, K.W. West, Phys. Rev. B 11 (1990) 7910. [9] A. Berg, M. Dobers, R.R. Gerhardts, K. von Klitzing, Phys. Rev. Lett. 64 (1990) 2563.
Longitudinal resistance anomaly around the 2/3 "lling factor observed in a GaAs/AlGaAs single heterostructure K. Hashimoto *, K. Muraki , T. Saku , Y. Hirayama NTT Basic Research Laboratories, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan CREST-JST, 4-1-8 Honmachi, Kawaguchi, Saitama 331-0012, Japan
Abstract A pronounced R enhancement near " is observed in a back-gated GaAs/AlGaAs single heterostructure when the VV magnetic "eld for " (B ) is set less than 6 T using the back gate, but it almost vanishes for B '8 T. This tendency is consistent with a model in which the mixed state consisting of two di!erent spin domains plays an important role for the anomalous R enhancement. By taking advantage of the back-gated operation, we "nd a quick recovery of the VV R enhancement in spite of prior electron depletion, and the long relaxation time of the R enhancement. These results VV VV support the argument that the R enhancement is not memorized by the electron system but by the alternative system VV such as the nuclear spin con"guration leading to a long relaxation time. 2001 Elsevier Science B.V. All rights reserved. PACS: 75.70.!i; 76.60.Es Keywords: Fractional quantum Hall e!ect; Back-gated GaAs/AlGaAs single heterostructure; Longitudinal resistance; Nuclear spin
The fractional quantum Hall states at some "lling factor (), for instance ", have two possible di!erent electron-spin states, unpolarized and polarized states. Which state appears depends on a competition between the Coulomb and Zeeman energies [1}3]. When the Zeeman term becomes dominant with increasing magnetic "eld, there is a transition from the unpolarized state to the polarized state. According to theoretical calculation [4], another di!erent state, a mixed state, is predicted to exist at " near the transition point between the
* Corresponding author. NTT Basic Research Laboratories, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan. Tel.: #81-46-240-3481; fax: #81-46-240-4727. E-mail address: [email protected] (K. Hashimoto).
unpolarized and polarized states. In the mixed state, there may be a domain structure of electron spins consisting of unpolarized and polarized domains. Actually, KronmuK ller et al. [5,6] have reported an interesting experimental result which suggests the existence of the " mixed state. In their result, anomalous enhancements in the longitudinal resistance (R ) appear around the "lling VV factor " for a narrow quantum well, when the magnetic "eld is scanned at a slow rate. In this paper, we study a similar R anomaly VV around " for a back-gated GaAs/AlGaAs single heterostructure. We show that a pronounced R enhancement near " appears when the VV magnetic "eld for " (B ) is set less than 6 T, but it almost vanishes for B '8 T. This tendency is consistent with a model in which the mixed state
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 0 2 9 9 - X
192
K. Hashimoto et al. / Physica B 298 (2001) 191}194
consisting of two di!erent spin domains plays an important role leading to an anomalous R enVV hancement. We also investigate a relaxation of the R enhancement by taking advantage of the VV back-gated operation. We "nd a quick recovery of the R enhancement in spite of prior electron VV depletion, and the long relaxation time of the R enhancement. VV We perform the experiment using the back-gated GaAs/AlGaAs single heterostructure [7], which consists of a Si doped n-GaAs substrate, 820 nm barrier layers and a 500 nm GaAs top layer. The barrier layers contain an 800 nm GaAs/AlAs superlattice and 20 nm AlGaAs. In the back-gated system, the electron density (N ) of the two-dimensional Q electron gas (2DEG) is precisely controlled by the back-gate bias (< ) and the 2DEG is completely @E depleted for < (
Fig. 1. Magnetic "eld dependence of the R enhancement near VV " at the temperature of 100 mK. All data except for those in the inset of Fig. 1(a) are measured with scanning the magnetic "eld in a downward direction only. (a) shows the magnetresistance at < "1.90 V (N "8.7;10 m\) for B "5.5 T. @E Q The broken and solid lines show R measured with a normal VV scanning speed, 0.2 T/min and with a slow scanning speed, 0.003 T/min, respectively. The slow scan gives rise to a pronounced enhancement which is marked by an arrow. Inset shows hysteresis around " in up and down slow sweeps (the arrows indicate scanning direction) at < "1.60 V @E (N "6.7;10 m\). In contrast with (a), no enhancement can Q be seen when B "12.2 T on increasing < to 3.50 V @E (N "1.9;10 m\) in (b). In (c), the value of the R enhanceQ VV ment appearing at the peak marked by the arrow in (a) is plotted at several di!erent B values by changing < (N ). Below 5 T, @E Q the R minimum at " deviates from the ideal value VV R "0 . VV
measurements are performed in a dilution refrigerator without any illumination. A standard lowfrequency AC lock-in technique is used with a current of 100 nA. Figs. 1 (a) and (b) show the magnetic "eld dependence of R around " at di!erent values of VV
K. Hashimoto et al. / Physica B 298 (2001) 191}194
< (di!erent electron densities), which give di!er@E ent B values. All curves are measured at the temperature of 100 mK. The scanning direction of these curves except for the one in the inset is downward. In Fig. 1 (a), < is set to 1.90 V @E (N "8.7;10 m\) giving B "5.5 T. The broQ ken line depicts R measured with a normal scannVV ing speed, 0.2 T/min. It shows normal fractional quantum Hall e!ect and well-developed minimum at ". When we decrease the scanning speed to 0.003 T/min, R indicated by a solid line shows an VV anomalous enhancement which is marked by an arrow near B . It is about 1.3 times larger than the R measured with the normal scanning speed. VV The value of the R enhancement reaches 1460 . VV The R enhancement shows the hysteretic behavVV ior in up and down slow scans. For instance, in the inset of Fig. 1(a), the R curves for < "1.60 V VV @E (N "6.7;10 m\) depict the hysteretic behavQ ior for the slow scan in the up and down scanningdirections represented by the arrows. In contrast to Fig. 1(a), as shown in Fig. 1(b), we can see no enhancement at B "12.2 T on increasing < to @E 3.50 V (N "1.9;10 m\). To investigate the Q magnetic "eld dependence of the R enhancement, VV we measure the value of the R enhancement VV marked by an arrow [see Fig. 1(a)] at other several di!erent B values by changing < (N ). The re @E Q sult is shown in Fig. 1(c). Almost no enhancement is observed when B '8 T. However, we observed a pronounced R enhancement on decreasing VV B to 5.5 T. Although the enhancement develops with the further reduction of B , the R min VV imum at " deviates from the ideal value R of VV 0 for B (5 T. The magnetic "eld where we observed a clear R enhancement is below that VV observed by KronmuK ller et al., namely B "8}9 T [5,6]. This di!erence can be under stood as follows. In our experiment, we use a single heterostructure, while KronmuK ller et al. use a narrow quantum well. The thickness of the 2DEG layer in our single heterostructure is about twice as thick as their narrow quantum well. Since the Coulomb term in our thicker layer is weaker than that in their thinner structure, the Zeeman term starts dominant at a lower magnetic "eld in our single heterostructure [8]. This fact gives rise to a shifting of the "eld where the " mixed state
193
appears to lower magnetic "eld in a single heterostructure. Therefore, our results are consistent with the model in which the mixed state plays an important role for the anomalous R enhancement. VV Fig. 2 illustrates the development and relaxation of the R enhancement. In this experiment, we "rst VV set < "1.94 V (N "9.0;10 m\) for the "xed @E Q magnetic "eld of 5.8 T, where the R enhancement VV clearly appears with a well-developed R minVV imum at " (B "5.6 T). R develops with VV time and saturates after about 30 min with a R enhancement of 1610 . Then, we completely VV deplete the 2DEG for a given depletion time by setting < "0 V. Finally, we apply < "1.94 V @E @E again to re"ll the 2DEG and measure how much the R enhancement has relaxed (R ). For 30 s VV VV depletion, R "301 which corresponds to VV 19% of the saturated R enhancement. This small VV
Fig. 2. The development and relaxation of the R enhancement VV at < "1.94 V (N "9.0;10 m\), the magnetic "eld of @E Q 5.8 T (B "5.6 T) and the temperature of 140 mK. R evolves VV with time and saturates after about 30 min. The 2DEG is then completely depleted for a given depletion time, 30 s, by setting < "0 V. Finally, < "1.94 V is applied again to re"ll the @E @E 2DEG, and how much the R enhancement has relaxed (R ) VV VV is measured. The inset shows R versus some depletion time. VV
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R implies the following process. The R enVV VV hancement may strongly relate to the " mixed state. In the mixed state, it is reasonable to consider that R mainly re#ects scattering by the electron VV spin domains. Although the electrons are completely depleted, the electron spin domains return quickly back to the initial situation just before depleting on re"lling with electrons. The inset shows R versus depletion time. From this plot, VV we estimate the relaxation time of the R enhanceVV ment to be approximately 30 min which is the same order of typical relaxation time of nuclear spin [9]. These two results: the quick recovery of the R enVV hancement in spite of the electron depletion, and the long relaxation time, is evidence that the R enhancement is not memorized by the electron VV system but by some other systems providing the long relaxation time. The most plausible candidate is the nuclear spin con"guration as KronmuK ller et al. [5,6] have already demonstrated experimentally. These results and our discussion suggest that it may be possible to write and read nuclear spin information by using the 2DEG near ". In conclusion, we report a R anomaly around VV " for a back-gated GaAs/AlGaAs single hetero structure. The pronounced R enhancement near VV " is observed at B (6 T, but it almost van ishes at B '8 T. In the relaxation experiment of the R enhancement, we "nd a quick recovery of VV the R enhancement in spite of the prior electron VV depletion, and the long relaxation time of the R enhancement. These results support the arguVV ment that the R enhancement is not memorized VV
by the electron system but by the alternative system such as the nuclear spin con"guration leading to a long relaxation time.
Acknowledgements The authors acknowledge T. Fujisawa and S. Miyashita for their supports in experiments and sample preparation. The authors also wish to thank G. Austing for the critical reading of the manuscript. This work is partly supported by NEDO NTDP-98 program.
References [1] R.G. Clark, S.R. Haynes, A.M. Suckling, J.R. Mallett, P.A. Wright, J.J. Harris, C.T. Foxon, Phys. Rev. Lett. 62 (1989) 1536. [2] R. Clark, P. Maksym, Physics World 2, (1989) 39. [3] T. Chakraborty, P. Pietilainen, The Quantum Hall E!ects, Springer, Berlin, 1995. [4] T. Chakraborty, Surf. Sci. 229 (1990) 16. [5] S. KronmuK ller, W. Dietsche, J. Weis, K. von Klitzing, W. Wegscheider, M. Bichler, Phys. Rev. Lett. 81 (1998) 2526. [6] S. KronmuK ller, W. Dietsche, K. von Klitzing, G. Denninger, W. Wegscheider, M. Bichler, Phys. Rev. Lett. 82 (1999) 4070. [7] T. Saku, K. Muraki, Y. Hirayama, Jpn. J. Appl. Phys. 37 (1998) L765. [8] J.P. Eisenstein, H.L. Stormer, L.N. Pfei!er, K.W. West, Phys. Rev. B 11 (1990) 7910. [9] A. Berg, M. Dobers, R.R. Gerhardts, K. von Klitzing, Phys. Rev. Lett. 64 (1990) 2563.