# Recent Developments in the Field of the Metal-Insulator Transition in Two Dimensions
## 4 Spin Susceptibility; \(g\)-Factor; the Effective Mass  
In [28], the Shubnikov-de Haas oscillations in a 2D electron system in silicon were studied at low electron densities, and it was shown that near the metal-insulator transition, only \"spin\" minima  
Figure 3: Temperature dependence of the resistivity of a Si MOSFET at different electron densities near the MIT in zero magnetic field (**a**) and in a parallel magnetic field of 4 Tesla (**b**). The electron densities are indicated in units of \(10^{11}\) cm\({}^{-2}\). Dashed curves correspond to \(n_{\rm s}=n_{\rm c}^{*}\), which is equal to \(0.795\times 10^{11}\) cm\({}^{-2}\) in zero field and to \(1.155\times 10^{11}\) cm\({}^{-2}\) in \(B=4\) Tesla. Adapted from [17]. Figure 2: (**a**) Resistivity vs. parallel magnetic field measured at \(T=0.29\) K in a Si MOSFET. Densities are indicated in units of \(10^{11}\) cm\({}^{-2}\); from [20]. (**b**) Resistivity as a function of \(B_{\parallel}\) in a 10 nm-wide \(p\)-type GaAs quantum well at 20 mK; from [21]. of the resistance at Landau-level filling factors \(\
u=2\), 6, 10, and 14 are seen, while the \"cyclotron\" minima at \(\
u=4\), 8, and 12 disappear. A simple explanation of the observed behavior requires a giant enhancement of the ratio between the spin and cyclotron splittings near the metal-insulator transition. Indeed, it turned out that with decreasing electron density (increasing interaction strength), the Pauli spin susceptibility, \(\chi\), measured by several independent methods [29; 30], grows by as much as a factor of seven compared to its non-interacting value, \(\chi_{0}\), with a tendency to diverge at a disorder-independent density \(n_{\chi}\) (see Figure 4a). A similar increase of the spin susceptibility near the metal-insulator transition has been observed in single-crystalline ZnO-based heterostructures [31]. In principle, this behavior can be due to either the increase of the effective electron mass or that of the Lande \(g\)-factor (or both). In [32], these two values have been measured separately, and it has been shown that the dramatic increase of the spin susceptibility is due to the strongly-enhanced effective mass, while the \(g\)-factor remains almost constant and close to its value in bulk silicon (see Figure 4b). The strong increase of the effective mass has been later independently confirmed by the analysis of the temperature dependence of Shubnikov-de Haas oscillations [33] and magnetization measurements in perpendicular magnetic fields [34]. In measurements of the thermopower in Si MOSFETs, data obtained for electron densities that are much closer to the critical point than the earlier measurements confirm that the critical density \(n_{\mathrm{m}}\) lies close to, but is consistently below the critical density \(n_{\mathrm{c}}\) for the MIT [35]. The results indicate the occurrence of an interaction-induced transition to a new phase at low density that may be a precursor phase or a direct transition to the Wigner solid. It has been found recently that in contrast to previous experiments on lower-mobility samples, in ultra-high mobility SiGe/Si/SiGe quantum wells, the critical electron density \(n_{\mathrm{c}}\) of the MIT becomes smaller than the density \(n_{\mathrm{m}}\), where the effective mass at the Fermi level tends to diverge [8]. Figure 4: (**a**) Dependence of the Pauli spin susceptibility on electron density in a silicon MOSFET obtained by three independent methods: thermodynamic measurements of the magnetization (dashed line), the magnetic field of the full spin polarization (circles), and magnetocapacitance (squares). The dotted line is a guide to the eye. Also shown by a solid line are the transport data of [29]. The inset shows the polarization field as a function of the electron density determined from the magnetization (circles) and magnetocapacitance (squares) data. The symbol size for the magnetization data reflects the experimental uncertainty. The dependence extrapolates linearly to zero field at a density \(n_{\chi}\) just below \(n_{\mathrm{c}}\).