Abstract
The metallic behaviour of the resistivity observed at low temperatures in low-disorder, dilute, two-dimensional (2D) carrier systems is of considerable interest as it defies the scaling theory of localization in two dimensions1. Although the origin of the metallic behaviour remains unknown and controversial, there is widespread evidence that the spin degree of the freedom plays a crucial role. Here, we directly probe the role of another discrete electronic degree of freedom, namely the valley polarization. Using symmetry-breaking strain together with an in-plane magnetic field to tune the valley and spin polarizations of an AlAs 2D electron system at fixed density, we map out a spin–valley phase diagram for its metal–insulator transition. The insulating phase occurs in the quadrant where the system is sufficiently spin and valley polarized. This observation establishes the equivalent roles of spin and valley degrees of freedom in the 2D metal–insulator transition.
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References
Abrahams, E., Anderson, P. W., Licciardello, D. C. & Ramakrishnan, T. V. Scaling theory of localization: Absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979).
Kravchenko, S. V., Kravchenko, G. V., Furneaux, J. E., Pudalov, V. M. & D’Iorio, M. Possible metal-insulator transition at B=0 in two dimensions. Phys. Rev. B 50, 8039–8042 (1994).
Kravchenko, S. V. & Sarachik, M. P. Metal-insulator transition in two-dimensional electron systems. Rep. Prog. Phys. 67, 1–44 (2004).
Das Sarma, S. & Hwang, E. H. The so-called two dimensional metal-insulator transition. Solid State Commun. 135, 579–590 (2005).
Zala, G., Narozhny, B. N. & Aleiner, I. L. Interaction corrections at intermediate temperatures: Magnetoresistance in a parallel field. Phys. Rev. B 65, R20201 (2001).
Papadakis, S. J. & Shayegan, M. Apparent metallic behavior at B=0 of a two-dimensional electron system in AlAs. Phys. Rev. B 57, R15068–R15071 (1998).
Hanein, Y. et al. Observation of the metal-insulator transition in two-dimensional n-type GaAs. Phys. Rev. B 58, R13338–R13340 (1998).
Lai, K., Pan, W., Tsui, D. C. & Xie, Y.-H. Observation of the apparent metal-insulator transition of high mobility two-dimensional electron system in SiGe heterostructure. Appl. Phys. Lett. 84, 302–304 (2004).
Lai, K. et al. Two-dimensional metal insulator transition and in-plane magnetoresistance in a high-mobility strained Si quantum well. Phys. Rev. B 72, R81313 (2005).
Okamoto, T., Ooya, M., Hosoya, K. & Kawaji, S. Spin polarization and metallic behavior in a silicon two-dimensional electron system. Phys. Rev. B 69, R41202 (2004).
Hanein, Y. et al. The metallic-like conductivity of a two-dimensional hole system. Phys. Rev. Lett. 80, 1288–1291 (1998).
Simmons, M. Y. et al. Metal-insulator transition at B=0 in a dilute two dimensional GaAs–AlGaAs hole gas. Phys. Rev. Lett. 80, 1292–1295 (1998).
Murzin, S. S., Dorozhkin, S. I., Landwehr, G. & Gossard, A. C. Effect of hole-hole scattering on the conductivity of the two-component 2D hole gas in GaAs/(AlGa)As heterostructures. JETP Lett. 67, 113–119 (1998).
Lam, J., D’Iorio, M., Brown, D. & Lafontaine, H. Scaling and the metal-insulator transition in Si/SiGe quantum wells. Phys. Rev. B 56, R12741–R12743 (1997).
Coleridge, P. T., Williams, R. L., Feng, Y. & Zawadzki, P. Metal-insulator transition at B=0 in p-type SiGe. Phys. Rev. B 56, R12764–R12767 (1997).
Papadakis, S. J., De Poortere, E. P., Manoharan, H. C., Shayegan, M. & Winkler, R. The effect of spin splitting on the metallic behavior of a two-dimensional system. Science 283, 2056–2058 (1999).
Yaish, Y. et al. Effect of hole-hole scattering on the conductivity of the two-component 2D hole gas in GaAs/(AlGa)As heterostructures. Phys. Rev. Lett. 84, 4954–4957 (2000).
Simonian, D., Kravchenko, S. V., Sarachik, M. P. & Pudalov, V. M. Magnetic field suppression of the conducting phase in two dimensions. Phys. Rev. Lett. 79, 2304–2307 (1997).
Okamoto, T., Hosoya, K., Kawaji, S. & Yagi, A. Spin degree of freedom in a two-dimensional electron liquid. Phys. Rev. Lett. 82, 3875–3878 (1999).
Yoon, J., Li, C. C., Shahar, D., Tsui, D. C. & Shayegan, M. Parallel magnetic field induced transition in transport in the dilute two-dimensional hole system in GaAs. Phys. Rev. Lett. 84, 4421–4424 (2000).
Papadakis, S. J., De Poortere, E. P., Shayegan, M. & Winkler, R. Anisotropic magnetoresistance of two-dimensional holes in GaAs. Phys. Rev. Lett. 84, 5592–5595 (2000).
Tutuc, E., De Poortere, E. P., Papadakis, S. J. & Shayegan, M. In-plane magnetic field-induced spin polarization and transition to insulating behavior in two-dimensional hole systems. Phys. Rev. Lett. 86, 2858–2861 (2001).
Das Sarma, S. & Hwang, E. H. Low-density finite-temperature apparent insulating phase in two-dimensional semiconductor systems. Phys. Rev. B 72, 205303 (2005).
Punnoose, A. & Finkelstein, A. M. Metal-insulator transition in disordered two-dimensional electron system. Science 310, 289–291 (2005).
De Poortere, E. P. et al. Enhanced electron mobility and high order fractional quantum Hall states in AlAs quantum wells. Appl. Phys. Lett. 80, 1583–1585 (2002).
Shayegan, M. et al. Low-temperature, in situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator. Appl. Phys. Lett. 83, 5235–5237 (2003).
Gunawan, O. et al. Valley susceptibility of an interacting two-dimensional electron system. Phys. Rev. Lett. 97, 186404 (2006).
Dolgopolov, V. T. & Gold, A. Magnetoresistance of a two-dimensional electron gas in a parallel magnetic field. JETP Lett. 71, 27–30 (2000).
Shkolnikov, Y. P., Vakili, K., De Poortere, E. P. & Shayegan, M. Dependence of spin susceptibility of a two-dimensional electron system on the valley degree of freedom. Phys. Rev. Lett. 92, 246804 (2004).
Tutuc, E., Melinte, S., De Poortere, E. P., Shayegan, M. & Winkler, R. Role of finite layer thickness in spin polarization of GaAs two-dimensional electrons in strong parallel magnetic fields. Phys. Rev. B 67, R241309 (2003).
Acknowledgements
We thank the NSF and ARO for support and Y. P. Shkolnikov, E. Tutuc and K. Lai for illuminating discussions.
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Gunawan, O., Gokmen, T., Vakili, K. et al. Spin–valley phase diagram of the two-dimensional metal–insulator transition. Nature Phys 3, 388–391 (2007). https://doi.org/10.1038/nphys596
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DOI: https://doi.org/10.1038/nphys596
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