Electrical Readout of the Local Nuclear Polarization in the Quantum Hall Effect: A Hyperfine Battery

It is demonstrated that the now well-established “flip-flop” mechanism of spin exchange between electrons and nuclei in the quantum Hall effect can be reversed. We use a sample geometry which utilizes separately contacted edge states to establish a local nuclear spin polarization—close to the maximum value achievable—by driving a current between electron states of different spin orientation. When the externally applied current is switched off, the sample exhibits an output voltage of up to a few tenths of a mV, which decays with a time constant typical for the nuclear spin relaxation. The surprising fact that a sample with a local nuclear spin polarization can act as a source of energy and that this energy is well above the nuclear Zeeman splitting is explained by a simple model which takes into account the effect of a local Overhauser shift on the edge state reconstruction.

Figure 1

Schematic of the sample geometry. Contacts (1)–(4) are positioned along the etched edges (thick lines) of the ring-shaped mesa. The gray area represents the gate electrode, the hatched area indicates the interaction region of the edge states, where the nuclear spin polarization is induced. Arrows indicate the direction of electron drift in the edge states for the chosen magnetic field direction. The filling factors are $\nu =2$ in the ungated regions and $g=1$ under the gate. The gate gap width is $2\mu \mathrm{m}$.

Figure 2

Time-dependent output voltage between inner and outer contacts after establishing a nuclear polarization for ten minutes at different currents $I_{\mathrm{pump}}$. The filling factors are $\nu =2$ and $g=1$ in the ungated and gated regions, respectively. The inset shows the nonlinear $I\mathrm{\text{−}}V$ characteristic used to determine $\Delta E_z$ (see text).

Figure 3

Schematic representation of the local energy structure of (a) noninteracting electron states and (b) edge states in local equilibrium. The gray area indicates the gate gap region with polarized nuclear spins, where an Overhauser field $B_{\mathrm{Ov}}>0$ is present. The bottom inset shows the edge reconstruction inside (center) and outside (left and right) of the gate gap region. Half filled circles represent electronic states at the Fermi energy.

Figure 4

Output voltage $V_{\mathrm{out}}$ as a function of the pumping current, for different times after switching off $I_{\mathrm{pump}}$. Pumping is most effective around $I_{\mathrm{pump}}=+50\mathrm{nA}$. At this current the resulting bias allows for resonant electron transfer between the different spin systems, as schematically shown in the middle inset.