Optical Probing of Spin Polarization of Electrons in Quantum Dot Edge Channels

We propose an optical method for the investigation of the quantum dot edge channels by utilizing circularly polarized photoluminescence in the integer-quantum-Hall-effect regime. One of the advantages of our method is that the degree of the spin-polarization of the electrons in the inner- and outer- compressible liquids can be probed separately. The observed polarized photoluminescence spectra can be explained by the calculated electron spin-dependent optical transition probabilities based on the local-spin density approximation.

Figure 1

(a) PL spectra at the bulk filling factor $\nu =3$ (5 T) between $V_B=0$ and $-2.0\mathrm{V}$ for ${\sigma }^{-}$ polarization. Zero points of the $y$ axis are shifted for clarity. Dashed curves are a guide for eyes. (b) Optical transition energy of the peaks in PL for ${\sigma }^{-}$ (solid circles) and ${\sigma }^{+}$ (open circles) polarization. (c) Bias voltage dependence of degree of polarization $P$ of the peaks in PL for LL0 (solid circles), LL1 (open circles), SU0 (crosses), LL0-1 (solid squares) and LL0-2 (solid triangles). The estimated spin-polarization $\eta$ is also shown.

Figure 2

(a) Single-particle energy plotted against $\langle {\rho }_i^2\rangle$ at $V_g=-0.6\mathrm{V}$ for down- (solid circles) and up- (open circles) spin electrons. (inset) Density of states for down- (solid lines) and up- (dashed lines) spin electrons. (b) Electron density distribution of down-spin electron (i), up-spin electron (ii), and potential of down-spin electron (iii) and up-spin electron (iv) at $V_g=-0.6\mathrm{V}$, along the horizontal direction parallel to the side of the square mesh through the center of the QD. Potential is offset for clarity.

Figure 3

(a) Calculated optical transition probability $J_{\sigma }$ at (i) $V_g=-0.4$, (ii) $-0.5$, (iii) $-0.6$, (iv) $-0.8$, (v) $-1.0$, and (vi) $-1.2\mathrm{V}$. Solid and dashed lines depict $J_{\sigma }$ for the down and up spins, respectively. (b) $V_g$ dependence of the peak energies in $J_{\sigma }$ for up- (solid circles) and down-spin (open circles) electrons, respectively.