Oscillatory Hall effect in high-mobility two-dimensional electron gases

We report an unexpected anomaly in the zero-field Hall coefficient of two-dimensional electron systems in high-mobility GaAs/AlGaAs heterostructures. Our device layout allows the investigation of mesoscopic systems with variable Fermi energy as well as with tunable Hall probes. At very low temperature, both positive and negative deviations from the noninteracting Hall coefficient ${\gamma }_{\text{H}}^0$ are observed, which can be twice as large as ${\gamma }_{\text{H}}^0$ itself. A distinct regularity in the deviations and their temperature dependence are interpreted as the spontaneous formation of localized spins and their indirect exchange interaction.

Figure 1

(Color online) Mesoscopic Hall device: (a) Scanning electron microscopy image of a device with electrical setup. Negative $V_{\text{G}}^{\text{QPC}1}$ and $V_{\text{G}}^{\text{QPC}2}$ confine a $4–5\mu \text{m}$ wide mesa. $V_{\text{G}}^{\text{FG}}$ varies the Fermi energy in the central region. (b) ${\sigma }_{xx}$ as a function of $V_{\text{G}}^{\text{FG}}$. The gray region indicates the voltage range investigated in the measurements. (c) Asymmetric Hall resistance up to 5 mT at several Fermi energies. (d) The resulting ${\gamma }_{\text{H}}$ and the theoretical Hall coefficient ${\gamma }_{\text{H}}^0$ shown as dashed green/gray line. The colored (grayscale) dots correspond to the colored (grayscale) lines in Fig. 1c.

Figure 2

(Color online) Hall coefficient at different temperatures: Asymmetric zero-field ${\gamma }_{\text{H}}$ (range 5 mT) over $V_{\text{G}}^{\text{FG}}$ and $2k_{\text{F}}R$ shows periodic fluctuations that vanish with increasing $T$ (orange/gray dashed line corresponds to ${\gamma }_{\text{H}}^0$). Inset: ${\gamma }_{\text{H}}$ over $V_{\text{G}}^{\text{FG}}$ and $n_{2\text{D}}$. The blue/dark gray squares were recorded at $T=75\text{mK}$ with 50 mT range and the red/gray dots were recorded at $T=1.7\text{K}$ in the active region of $n_{2\text{D}}$ (gray box) with 5 mT range. Both sets of data combine to a smooth function of $n_{2\text{D}}$ over the full range.

Figure 3

(Color online) (a) The temperature dependence of M points is monotonic. The solid lines are a guide to the eyes. (b) $T$-dependence of ${\rho }_{xx}/\left({\gamma }_{\text{H}}-{\gamma }_{\text{H}}^0\right)$ shows three distinct regimes over $T$. (c) Nonequilibrium transport spectroscopy shows three distinct $T$ regimes as well.

Figure 4

(Color online) (a) The temperature dependence of P points is nonmonotonic. The upturn exceeds the noninteracting high-$T$ value (see also Fig. 2). (b) An enlargement of the Fermi surface can lead to a change in sign in the effective mass and thus the nature of the quasiparticles. (c) Nonequilibrium transport spectroscopy shows a resonance in $\text{d}I/\text{d}V$ at $E_{\text{F}}$, recorded at a P point.