Insulating phases induced by crossing of partially filled Landau levels in a Si quantum well

We study magnetotransport in a high-mobility Si two-dimensional electron system by in situ tilting of the sample relative to the magnetic field. A pronounced dip in the longitudinal resistivity is observed during the Landau-level crossing process for noninteger filling factors. Together with a Hall resistivity change which exhibits the particle-hole symmetry, this indicates that electrons or holes in the relevant Landau levels become localized at the coincidence where the pseudospin-unpolarized state is expected to be stable.

Figure 1

(a) Schematic of the Hall bars. The current direction is along the $x$ axis in HB-X and the $y$ axis in HB-Y. The magnetic field is tilted from the $z$ axis in the $x$ direction by an angle $\theta$. (b) Landau levels in a tilted magnetic field. The ratio of the Zeeman energy $E_z$ to the cyclotron energy $\hslash {\omega }_c$ increases with $\theta$. $E_z$ and $\hslash {\omega }_c$ are approximately proportional to the total magnetic field $B_{\text{tot}}$ and the perpendicular component $B_{\perp }=B_{\text{tot}}\text{cos}\theta$, respectively.

Figure 2

(Color online) $B_{\perp }$ dependence of ${\rho }_{xx}$ and ${\rho }_{yx}$ for different fixed values of $B_{\text{tot}}$. The data were obtained for HB-X by decreasing $B_{\perp }$ at 70 mK. The position of the peak or dip shifts to higher $B_{\perp }$ as $B_{\text{tot}}$ increases. The peak for $B_{\text{tot}}=4.42\text{T}$ and the dip for $B_{\text{tot}}=5.23\text{T}$ are indicated by arrows.

Figure 3

(Color online) [(a)–(d), (f), (g)] Longitudinal resistivities as functions of $B_{\text{tot}}$ for different fixed values of $\nu$. (e) Inverse of the Hall resistivity vs $B_{\text{tot}}/B_{\perp }$. All the data were obtained by decreasing $B_{\text{tot}}$ at 70 mK. HB-X was used for (a), (c), and (f). HB-Y was used for (b), (d), (e), and (g).

Figure 4

(Color online) (a) The full width at half maximum of the dip in ${\rho }_{xx}$ or ${\rho }_{yy}$ measured at 70 mK. Since hysteresis was observed, the mean values are plotted. (b) Hysteresis of $B_{\text{tot}}$ dependence of ${\rho }_{yy}$ at 70 mK and $\nu =2.67\left(B_{\perp }=2.21\text{T}\right)$. Solid curve (red): the downward sweep with $d{B}_{\text{tot}}/dt=-0.5\text{mT}/\text{s}$. Dashed curve (black): the upward sweep with $d{B}_{\text{tot}}/dt=+0.7\text{mT}/\text{s}$. (c) $B_{\text{tot}}$-dependence of ${\rho }_{yy}$ at $\nu =2.45\left(B_{\perp }=2.41\text{T}\right)$ for $T=50$,100, 200, 300, 400, 500, 600, and 800 mK (from bottom to top). The data were obtained by decreasing $B_{\text{tot}}$. (d) Logarithm plot of the ${\rho }_{yy}$ minimum, divided by the baseline value ${\rho }_b$, is shown as a function of the inverse temperature. The solid straight line represents an Arrhenius temperature dependence ${\rho }_{yy}/{\rho }_b\propto \text{exp}\left(-\Delta /2\text{T}\right)$, where $\Delta =1.0\text{K}$ is the energy gap. The dotted line is a guide for the eyes.