Polarization of Nuclear Spins from the Conductance of Quantum Wire

We devise an approach to measure the polarization of nuclear spins via conductance measurements. Specifically, we study the combined effect of external magnetic field, nuclear spin polarization, and Rashba spin-orbit interaction on the conductance of a quantum wire. Nonequilibrium nuclear spin polarization affects the electron energy spectrum making it time dependent. Changes in the extremal points of the spectrum result in time dependence of the conductance. The conductance oscillation pattern can be used to obtain information about the amplitude of the nuclear spin polarization and extract the characteristic time scales of the nuclear spin subsystem.

Figure 1

Quantum wire with an applied magnetic field in the $x$-direction, and an effective nuclear hyperfine field initially pointing in the $y$-direction.

Figure 2

The lowest-energy subbands, in units of $\hslash \omega$, as functions of $p=\hslash k$, for three different times. Here $\eta \equiv \sqrt{2m^{*}\hslash \omega }$. The two sets of curves correspond to spin $\pm$.

Figure 3

Time dependence of the conductance at (a) zero temperature and (b) finite temperature, as a function of the reservoir chemical potential, $\mu$.

Figure 4

Time dependence of the conduction at a finite temperature and at the fixed value of $\mu =0.5\hslash \omega$.