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What are some of the most controversial topics in condensed matter physics?
The low temperature metal-insulator transition in 2-dimensional electron gas in the absence of a magnetic field I am not sure if this can be considered 'most' controversial but the origin of the metal-insulator transition at very low temperature in very pure samples of semiconductors like Si is still highly disputed.The theory of localization [1] predicts that in 2 dimensions, all the electrons or holes states of the system are localized in the absence of a magnetic field in the limit of zero temperature, no matter how clean the 2D system is. So, for any 2D system, as you cool the system down towards K, the conductivity of the system approaches zero i.e. it becomes insulating. This was experimentally confirmed in the early eighties [2, 3] in electrical measurement taken in very high-quality Si MOSFETs (metal-oxide-silicon field effect transistors). The classic signature of an insulator is that its resistivity [math]rho[/math] increases as you lower the temperature. [Image of a Si MOSFET taken from http://www.learnabout-electronic...]However, in such structures, you can 'tune' the carrier (electron or hole) density by modulating the gate voltage or the electric field perpendicular to the 2D system. When you apply a positive gate voltage, the electrons get attracted to the area just beneath the gate, and the electron density increases. At a sufficiently high carrier density, the system undergoes a metal goes a transition from insulating to conducting. In a conducting (or metallic) system, the resistivity [math]rho[/math] decreases as you lower the temperature. This of course violates the predictions from the theory of localization [1].[Image taken from http://dx.doi.org/10.1590/S0103-...] The figure above shows the resistivity of a Si MOSFET in zero magnetic field as a function of temperature for electron densities [math]n_s[/math] =u00a0 8.58, 8.80, 9.02, 9.33, 9.52, 9.90, and 11.0E10 cm-2. The critical density for the metal-insulator transition is 9.02E10 cm-2. The controversy is over the origins of this 'transition'. Candidate explanations for this phenomenon include the formation of a metallic state in a strongly interacting 2D electron gas [4], strong spin-orbit interaction [5] as well as more conventional explanation along the lines of temperature-dependent screening of charged impurities [6]. This phenomenon was quite an active topic of research in the late 90's and early 2000's. However, with the discovery of graphene and other 2-dimensional layered crystals, a lot of attention was shifted away from the field since a lot of concepts and techniques developed for studying the metal-insulator transition could be more profitably applied to these newly discovered materials [7]. References:1. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)2. M J Uren et al., J. Phys. C: Solid State Phys. 14, 5737 (1981)3. D. J. Bishop, D. C. Tsui, and R. C. Dynes, Phys. Rev. Lett. 44, 1153 (1980)4. A. M. Finkelshtein, Z. Phys. B 56, 189 (1984)5. Y. Lyanda-Geller, Phys. Rev. Lett. 80, 4273. 6. S. He and X. C. Xie, Phys. Rev. Lett. 80, 3324 (1998); B. L. Altshuler and D. L. Maslov, Phys. Rev. Lett. 82, 145 (1999)7.u00a0 K. S. Novoselov et al., Science 306, 666 (2022)
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