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Interlayer coherency and angular-dependent magnetoresistance oscillations in quasi-two-dimensional conductors
Synthetic Metals 133–134 (2003) 113–115
Interlayer coherency and angular-dependent magnetoresistance oscillations in quasi-two-dimensional conductors$ M. Kuraguchia,*, E. Ohmichia, T. Osadaa, Y. Shirakib a
Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan b Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
Abstract We have experimentally explored whether angular-dependent magnetoresistance oscillations (AMRO) could exist in multilayer systems with incoherent interlayer coupling. We have studied the interlayer transport of GaAs/AlGaAs semiconductor superlattices whose interlayer coupling is systematically changed. It is observed that AMRO exist in incoherent systems, while peak effects disappear. We also found that the angular dependence of the background magnetoresistance shows a non-classic behavior when the systems lose the interlayer coherence. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Angular-dependent magnetoresistance oscillation; Incoherent transport; Quasi-two-dimensional conductor; Semiconductor superlattice
1. Introduction Angular effects of the interlayer magnetoresistance have been extensively studied in organic conductors. These remarkable effects have been explained by the semiclassical magnetotransport theory considering three-dimensional Fermi surfaces. However, MacKenzie and Moses [1] claimed that the angular-dependent magnetoresistance oscillations (AMRO) could exist even in multilayer systems with incoherent interlayer coupling, where the in-plane scattering happens very often than the interlayer hopping and the three-dimensional Fermi surface no longer exists. On the other hand, existence of the resistance peak in a magnetic field parallel to the layers is not expected in incoherent systems [1]. They applied their theory to lowdimensional organic conductors and discussed the interlayer coherency of these compounds. However, no experimental confirmation of their prediction has been done since it is difficult to evaluate the interlayer coherency in organic conductors. In this study, instead of organic conductors, we have chosen GaAs/AlGaAs semiconductor superlattices as samples of quasi-two-dimensional (Q2D) conductors, since $
Yamada Conference LVI, the Fourth International Symposium on Crystalline Organic Metals, Superconductors and Ferromagnets, ISCOM 2001—Abstract Number B2Tue. * Corresponding author. Tel./fax: þ81-471-35-1221. E-mail address: [email protected] (M. Kuraguchi).
their interlayer coupling can be systematically controlled [2,3].
2. Experiment GaAs/AlGaAs superlattice samples were grown by molecular beam epitaxy on nþ-GaAs (1 0 0) conducting substrates. The parameters of the superlattice parts are shown in Table 1. The width 4tc of the lowest miniband was calculated by a simple Kronig–Penny model and the carrier density n and the in-plane scattering rate h=t were obtained from Shubnikov–de Haas oscillations. The doping density was controlled so as to locate the Fermi energy in the first minigap. In sample #2, h=t is about 10 times larger than 4tc, so that the interlayer coupling is incoherent. On the other hand, the interlayer coupling of sample #1 is coherent because 4tc > h=t. We fabricated the samples into devices for the measurement of the interlayer transport.
3. Results and discussion The measurements were carried out at rather high temperatures to suppress Shubnikov–de Haas oscillations, following the previous work [4]. Fig. 1(a) shows the angular dependence of the interlayer magnetoresistance of sample #1 with coherent interlayer coupling. A peak structure
0379-6779/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 ( 0 2 ) 0 0 3 2 2 - 3
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M. Kuraguchi et al. / Synthetic Metals 133–134 (2003) 113–115
Table 1 Sample parametersa
#1 #2
Well ˚) width (A
Barrier ˚) width (A
Al content
n (1011 cm2/layer)
4tc (meV)
h=t (meV)
Interlayer coupling
188 150
38 150
0.18 0.1
1.7 6.0
2.14 0.120
0.98 1.03
Coherent Incoherent
a 4tc, h=t and n are the first miniband width, the in-plane scattering rate and the carrier density per layer, respectively. In sample #1, 4tc is greater than h=t and vice versa in sample #2.
appears at about y ¼ 40 . These peak positions are almost independent of the field strength and satisfy the following Yamaji’s condition [5]: ckF tan y ¼ pði 14Þ
(1)
where c, kF and i are the spacing between adjacent layers, the Fermi wave number in a layer and an integer, respectively. Therefore, these structures seem to correspond to the AMRO. However, we note that sample #1 has the low carrier density so that the electron system is in the quantum limit, where the conventional AMRO is not expected. To explain this novel AMRO, we might take into account the finite layer thickness. In addition to AMRO, peak effects are visible at the field orientation parallel to the layers (y ¼ 90 ). On the other hand, no peak effect was observed up to 13 T in sample #2, as shown in Fig. 1(b). This fact is consistent with McKenzie’s prediction that incoherent systems show no peak effect. In contrast to the peak effect, AMRO are seen clearly at about y ¼ 25 and 458. We can conclude that AMRO appear even in the incoherent systems in the same
way as in the coherent systems. This result strongly supports McKenzie’s theory that the tunneling probability between neighboring layers oscillates when the magnetic fields are rotated, even if the tunneling events are uncorrelated. Next, we note the angular dependence of the background magnetoresistance. In the semiclassical picture, the maximum values of the background magnetoresistance are expected at y ¼ 90 because the Lorentz force should affect the electron motion most effectively. The behavior of samples #1 and #2 in the low magnetic field region is accordant to the above expectation. However, the background magnetoresistance of sample #2 shows the opposite angular dependence in the high magnetic field region and it seems that the normal component of the magnetic fields dominantly contributes to the magnetoresistance. The magnetic field dependence of the interlayer magnetoresistance is shown in Fig. 1(c) and (d). We observed resistance dips at B ¼ 6 and B ¼ 10 T in samples #1 and #2, respectively. It is expected that the magnetic fields parallel to the layers cause the orbital confinement into a single well under the condition that the diameter of the classic cyclotron
Fig. 1. Angular dependence of the interlayer magnetoresistance of (a) sample #1 and (b) sample #2. Vertical dotted lines indicate calculated Yamaji’s angles. The field dependence of (c) sample #1 and (d) sample #2.
M. Kuraguchi et al. / Synthetic Metals 133–134 (2003) 113–115
orbit becomes smaller than the well width. In fact, the calculated confinement fields indicated by the arrows almost coincide with the positions of the dip structures.
Acknowledgements This work was financially supported by the Toray Science Foundation.
115
References [1] R.H. MacKenzie, P. Moses, Phys. Rev. Lett. 81 (1998) 4492. [2] T. Osada, H. Nose, M. Kuraguchi, Physica B 294–295 (2001) 402. [3] M. Kuraguchi, E. Ohmichi, T. Osada, Y. Shiraki, in: Proceedings of the 25th International Conference on the Physics of Semiconductors, p. 803. [4] R. Yagi, Y. Iye, Y. Hashimoto, T. Odagiri, H. Noguchi, H. Sakaki, T. Ikoma, J. Phys. Soc. Jpn. 60 (1991) 3784. [5] K. Yamaji, J. Phys. Soc. Jpn. 58 (1989) 1520.
Interlayer coherency and angular-dependent magnetoresistance oscillations in quasi-two-dimensional conductors$ M. Kuraguchia,*, E. Ohmichia, T. Osadaa, Y. Shirakib a
Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan b Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
Abstract We have experimentally explored whether angular-dependent magnetoresistance oscillations (AMRO) could exist in multilayer systems with incoherent interlayer coupling. We have studied the interlayer transport of GaAs/AlGaAs semiconductor superlattices whose interlayer coupling is systematically changed. It is observed that AMRO exist in incoherent systems, while peak effects disappear. We also found that the angular dependence of the background magnetoresistance shows a non-classic behavior when the systems lose the interlayer coherence. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Angular-dependent magnetoresistance oscillation; Incoherent transport; Quasi-two-dimensional conductor; Semiconductor superlattice
1. Introduction Angular effects of the interlayer magnetoresistance have been extensively studied in organic conductors. These remarkable effects have been explained by the semiclassical magnetotransport theory considering three-dimensional Fermi surfaces. However, MacKenzie and Moses [1] claimed that the angular-dependent magnetoresistance oscillations (AMRO) could exist even in multilayer systems with incoherent interlayer coupling, where the in-plane scattering happens very often than the interlayer hopping and the three-dimensional Fermi surface no longer exists. On the other hand, existence of the resistance peak in a magnetic field parallel to the layers is not expected in incoherent systems [1]. They applied their theory to lowdimensional organic conductors and discussed the interlayer coherency of these compounds. However, no experimental confirmation of their prediction has been done since it is difficult to evaluate the interlayer coherency in organic conductors. In this study, instead of organic conductors, we have chosen GaAs/AlGaAs semiconductor superlattices as samples of quasi-two-dimensional (Q2D) conductors, since $
Yamada Conference LVI, the Fourth International Symposium on Crystalline Organic Metals, Superconductors and Ferromagnets, ISCOM 2001—Abstract Number B2Tue. * Corresponding author. Tel./fax: þ81-471-35-1221. E-mail address: [email protected] (M. Kuraguchi).
their interlayer coupling can be systematically controlled [2,3].
2. Experiment GaAs/AlGaAs superlattice samples were grown by molecular beam epitaxy on nþ-GaAs (1 0 0) conducting substrates. The parameters of the superlattice parts are shown in Table 1. The width 4tc of the lowest miniband was calculated by a simple Kronig–Penny model and the carrier density n and the in-plane scattering rate h=t were obtained from Shubnikov–de Haas oscillations. The doping density was controlled so as to locate the Fermi energy in the first minigap. In sample #2, h=t is about 10 times larger than 4tc, so that the interlayer coupling is incoherent. On the other hand, the interlayer coupling of sample #1 is coherent because 4tc > h=t. We fabricated the samples into devices for the measurement of the interlayer transport.
3. Results and discussion The measurements were carried out at rather high temperatures to suppress Shubnikov–de Haas oscillations, following the previous work [4]. Fig. 1(a) shows the angular dependence of the interlayer magnetoresistance of sample #1 with coherent interlayer coupling. A peak structure
0379-6779/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 ( 0 2 ) 0 0 3 2 2 - 3
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M. Kuraguchi et al. / Synthetic Metals 133–134 (2003) 113–115
Table 1 Sample parametersa
#1 #2
Well ˚) width (A
Barrier ˚) width (A
Al content
n (1011 cm2/layer)
4tc (meV)
h=t (meV)
Interlayer coupling
188 150
38 150
0.18 0.1
1.7 6.0
2.14 0.120
0.98 1.03
Coherent Incoherent
a 4tc, h=t and n are the first miniband width, the in-plane scattering rate and the carrier density per layer, respectively. In sample #1, 4tc is greater than h=t and vice versa in sample #2.
appears at about y ¼ 40 . These peak positions are almost independent of the field strength and satisfy the following Yamaji’s condition [5]: ckF tan y ¼ pði 14Þ
(1)
where c, kF and i are the spacing between adjacent layers, the Fermi wave number in a layer and an integer, respectively. Therefore, these structures seem to correspond to the AMRO. However, we note that sample #1 has the low carrier density so that the electron system is in the quantum limit, where the conventional AMRO is not expected. To explain this novel AMRO, we might take into account the finite layer thickness. In addition to AMRO, peak effects are visible at the field orientation parallel to the layers (y ¼ 90 ). On the other hand, no peak effect was observed up to 13 T in sample #2, as shown in Fig. 1(b). This fact is consistent with McKenzie’s prediction that incoherent systems show no peak effect. In contrast to the peak effect, AMRO are seen clearly at about y ¼ 25 and 458. We can conclude that AMRO appear even in the incoherent systems in the same
way as in the coherent systems. This result strongly supports McKenzie’s theory that the tunneling probability between neighboring layers oscillates when the magnetic fields are rotated, even if the tunneling events are uncorrelated. Next, we note the angular dependence of the background magnetoresistance. In the semiclassical picture, the maximum values of the background magnetoresistance are expected at y ¼ 90 because the Lorentz force should affect the electron motion most effectively. The behavior of samples #1 and #2 in the low magnetic field region is accordant to the above expectation. However, the background magnetoresistance of sample #2 shows the opposite angular dependence in the high magnetic field region and it seems that the normal component of the magnetic fields dominantly contributes to the magnetoresistance. The magnetic field dependence of the interlayer magnetoresistance is shown in Fig. 1(c) and (d). We observed resistance dips at B ¼ 6 and B ¼ 10 T in samples #1 and #2, respectively. It is expected that the magnetic fields parallel to the layers cause the orbital confinement into a single well under the condition that the diameter of the classic cyclotron
Fig. 1. Angular dependence of the interlayer magnetoresistance of (a) sample #1 and (b) sample #2. Vertical dotted lines indicate calculated Yamaji’s angles. The field dependence of (c) sample #1 and (d) sample #2.
M. Kuraguchi et al. / Synthetic Metals 133–134 (2003) 113–115
orbit becomes smaller than the well width. In fact, the calculated confinement fields indicated by the arrows almost coincide with the positions of the dip structures.
Acknowledgements This work was financially supported by the Toray Science Foundation.
115
References [1] R.H. MacKenzie, P. Moses, Phys. Rev. Lett. 81 (1998) 4492. [2] T. Osada, H. Nose, M. Kuraguchi, Physica B 294–295 (2001) 402. [3] M. Kuraguchi, E. Ohmichi, T. Osada, Y. Shiraki, in: Proceedings of the 25th International Conference on the Physics of Semiconductors, p. 803. [4] R. Yagi, Y. Iye, Y. Hashimoto, T. Odagiri, H. Noguchi, H. Sakaki, T. Ikoma, J. Phys. Soc. Jpn. 60 (1991) 3784. [5] K. Yamaji, J. Phys. Soc. Jpn. 58 (1989) 1520.