Theory of NMR in semiconductor quantum point contact devices

We describe how a local nonequilibrium nuclear polarization can be generated and detected by electrical means in a semiconductor quantum point contact device. We show that measurements of the nuclear-spin-relaxation rate will provide clear signatures of the interaction mechanism underlying the “0.7” conductance anomaly. Our analysis illustrates how nuclear-magnetic-resonance methods, which are used extensively to study strongly correlated electron phases in bulk materials, can be made to play a similarly important role in nanoscale devices.

Figure 1

(Color online) The sensitivity of the QPC device to small changes in the nuclear polarization at fixed gate voltage is conveniently represented by ${\phantom{|}\frac{dG}{d{Z}_e}|}_n$. This is plotted as a function of the conductance (which varies with gate voltage) for a noninteracting electron gas with subband spacing $\hslash {\omega }_y$ and $Z_e=0.03\hslash {\omega }_y$.

Figure 2

(Color online) Conductance (top panels) and nuclear-spin-relaxation rate (bottom panels) for a quasi-1D electron gas on the first conductance riser. (a) Noninteracting electron gas with small Zeeman energy, $Z_e=0.001\hslash {\omega }_y$. (b) Noninteracting electron gas with larger Zeeman energy, $Z_e=0.05\hslash {\omega }_y$. (c) Electron gas with exchange-enhanced spin splitting [Eq. (7)] with $Z_e=0.001\hslash {\omega }_y$ and $\gamma =0.1\hslash {\omega }_y/n_0$. The electron density $n$ is in units of $n_0\equiv \sqrt{m{\omega }_y/\pi h}$. A typical quantum wire has subband spacing $\hslash {\omega }_y=20\text{K}$ (Ref. 20), for which the illustrated temperatures are $T=40$, 100, 200, and 400 mK.