We studied the Shubnikov-de Haas (SdH) oscillations in high-mobility Si-MOS samples over a wide range of carrier densities n ≃ (1 − 50) × 10 11 cm −2 , which includes the vicinity of the apparent metal-insulator transition in two dimensions (2D MIT). Using a novel technique of measuring the SdH oscillations in superimposed and independently controlled parallel and perpendicular magnetic fields, we determined the spin susceptibility χ * , the effective mass m * , and the g * -factor for mobile electrons. These quantities increase gradually with decreasing density; near the 2D MIT, we observed enhancement of χ * by a factor of ∼ 4.7.71. 30.+h, 73.40.Qv, 71.27.+a Many two-dimensional (2D) systems exhibit an apparent metal-insulator transition (MIT) at low temperatures as the electron density n is decreased below a critical density n c (for reviews see, e.g., Refs. [1][2][3]). The phenomena of the MIT and 'metallic' conductivity in 2D attract a great deal of interest, because it addresses a fundamental problem of the ground state of strongly correlated electron systems. The strength of electron-electron interactions is characterized by the ratio r s of the Coulomb interaction energy to the Fermi energy ǫ F . The 2D MIT is observed in Si MOSFETs at n c ∼ 1 × 10 11 cm −2 , which corresponds to r s ∼ 8 (for 2D electrons in (100)-Si, r s = 2.63 10 12 cm −2 /n).In the theory of electron liquid, the electron effective mass m * , the g * -factor, and the spin susceptibility χ * ∝ g * m * are renormalized depending on r s [4]. Though the quantitative theoretical results [5][6][7] vary considerably, all of them suggest enhancement of χ * , m * and g * with r s . Earlier experiments [8][9][10][11] have shown growth of m * and g * m * at relatively small r s values, pointing to a ferromagnetic type of interactions in the explored range 1 < ∼ r s < 6.5. Potentially, strong interactions might drive an electron system towards ferromagnetic instability [4]. Moreover, it has been suggested that the 'metallic' behavior in 2D is accompanied by a tendency to a ferromagnetic instability [12]. Thus, in relation to the still open question of the origin of the 2D MIT, direct measurements of these quantities in the dilute regime near the 2D MIT are crucial.In this Letter, we report the direct measurements of χ * , m * , and hence g * over a wide range of carrier densities (1 ≤ r s ≤ 8.4), which extends for the first time down to and across the 2D MIT. The data were obtained by a novel technique of measuring the interference pattern of Shubnikov-de Haas (SdH) oscillations in crossed magnetic fields. The conventional technique of measuring g * m * in tilted magnetic fields [8,10] is not applicable when the Zeeman energy is greater than the cyclotron energy [13]. The crossed field technique removes this restriction and allows us to extend measurements over the wider range of r s . We find that for small r s , the g * m *values increase slowly in agreement with the earlier data by Fang and Stiles [8] and Okamoto et al. [10]. For larger valu...
PHYSlCAL REVIEW LETTERS 20 DECEMBER 1982 measurement (such as a, study of the oscillation of a cylindrical cavity containing SPH), the b state will show a much smaller effective superfluid density and will produce a lot more damping than the a state. I thank Andrei Huckenstein and Eric Siggia for discussions. I also thank David Mermin for urging me to reformulate my original. presentation in a more general form. This work is supported by the National Science Foundation, Grant No. PH Y77-27084.
We compare the temperature dependence of resistivity rho(T) of Si-metal-oxide-semiconductor field-effect transistors with the recent theory by Zala et al. In this comparison, the effective mass m* and g* factor for mobile electrons have been determined from independent measurements. An anomalous increase of rho with temperature, which has been considered as a signature of the "metallic" state, can be described quantitatively by the interaction effects in the ballistic regime. The in-plane magnetoresistance rho(B(axially)) is only qualitatively consistent with the theory; the lack of quantitative agreement indicates that the magnetoresistance is more sensitive to sample-specific effects than rho(T).
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We have measured the conductivity of high-mobility (001) Si metal-oxide-semiconductor field effect transistors (MOSFETs) over wide ranges of electron densities n = (1.
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