Magnetic field driven redistribution between extended and localized electronic states in high-mobility Si MOSFETs at low temperatures

In the study of oscillatory electron transport in high-mobility Si MOSFETs at low temperatures we observe two correlated effects in weak in-plane magnetic fields: a steep decrease of the magnetic susceptibility ${\chi }^{*}\left(H\right)$ and an increase of the concentration of mobile carriers $n\left(H\right)$. We suggest a phenomenological model of the magnetic field driven redistribution between the extended and localized electronic states that qualitatively explains both effects. We argue that the redistribution is mainly caused by magnetization of the large-spin $S\approx 2$ localized states with energies close to the Fermi energy $E_F$, coexisting with the majority Fermi liquid state. Our findings also resolve a long-standing disagreement between the experimental data on ${\chi }^{*}$ obtained in weak ($H\sim k_{B}T/{\mu }_B$) and strong ($H\sim E_F/g{\mu }_B$) magnetic fields.

Figure 1

Summary of ${\chi }^{*}\left(H_{\parallel }\right)/{\chi }^{*}\left(0\right)$ data versus $H_{\parallel }$ for both samples and for several densities. For the lowest density $n=0.99$, the ${\chi }^{*}\left(H\right)/{\chi }^{*}\left(0\right)$ variations are scaled down by two times. The density is indicated in units of ${10}^{11}{\mathrm{cm}}^{-2}$, $T=0.1$ K. The dashed line is a guide to the eye.

Figure 2

Correlation between the in-plane field dependence of (a) ${\chi }^{*}\left(H\right)/{\chi }^{*}\left(0\right)$, (b) density $n_{\mathrm{SdH}}$, and (c) spin magnetization $M\left(H_{\parallel }\right)$ (reproduced from Ref. [31]). Red curve shows $tanh({\mu }_{B}H/k_{B}T)$-fitting of the experimental $M\left(H\right)$ data, blue curve shows $H\partial M/\partial H$ calculated from the fitting curve. The zero-field density $n_0=1.61\times {10}^{11}{\mathrm{cm}}^{-2}$ for (a) and (b), and $1.4\times {10}^{11}{\mathrm{cm}}^{-2}$ for (c). Temperature $T=0.1$ K for (a) and (b) and 1.7 K for (c).

Figure 3

Evolution of the ${\chi }^{*}\left(H\right)/{\chi }_b$ dependencies with density, from the (a) lowest density $0.99\times {10}^{11}{\mathrm{cm}}^{-2}$ to higher densities (b) $2\times {10}^{11}{\mathrm{cm}}^{-2}$, (c) $6.16\times {10}^{11}{\mathrm{cm}}^{-2}$, and at the highest studied density (d) $10.0\times {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 4

Density variations as a function of the in-plane magnetic field $H_{\parallel }$ for the zero-field densities $n_{\mathrm{SdH}}\left(0\right)$: (a) 1.153, (b) 1.265, (c) 1.64, (d) 2.0, and (e) $9.8\times {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 5

Comparison of the magnetic field dependences of ${\chi }^{*}\left(H\right)/{\chi }_b$ and $n\left(H\right)$ at high carrier density $n\approx 10\times {10}^{11}{\mathrm{cm}}^{-2}$. Sample Si3-10.

Figure 6

(a) $dM/dN$ versus $H_{\parallel }$. Symbols are the data from Ref. [31] for $n=1.4\times {10}^{11}{\mathrm{cm}}^{-2}$. (b), (c) Schematic spatial arrangement of the two-phase state and the energy band diagram of the two-phase system.

Figure 7

Model curve $\delta N_1\left(H_{\parallel }\right)$ calculated from experimental data as described in the text.

Figure 8

Example of the magnetic field dependence of $dN\left(H\right)/dH$ calculated from Fig. 4. Sample Si6-14. $N\left(0\right)=1.61\times {10}^{11}{\mathrm{cm}}^{-2}$.