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We present the findings of the electrically-detected nuclear magnetic resonance (NMR) and the spin polarization of the 29Si nuclei in the three-terminal Rashba gate-controlled ring embedded in the p-type self-assembled silicon quantum well that is prepared on the n-type Si (100) surface. The amplitude and phase sensitivity of the 0.7(2e2/h) feature of the hole quantum conductance staircase revealed by the quantum point contact inserted using the split-gate technique in the one of the arms of the double-slit ring are studied by varying the value of the external magnetic field and the top gate voltage that are applied perpendicularly to the plane of the double-slit ring and revealed by the Aharonov-Bohm (AB) and Aharonov-Casher (AC) conductance oscillations, respectively. The phase shift in the 0.7(2e2/h) structure revealed by the Aharonov-Bohm oscillations is found to be changed from π/2 to π by electrically-detected NMR of the 29Si nuclei thereby verifying the spin polarisation in the quantum point contact. This phase shift appeared to result from the Overhauser shift that is due to the regular magnetic field created by the 29Si nuclei. By varying the top gate voltage at the fixed value of the split-gate voltage, the transition from the positive magnetoresistance to the negative magnetoresistance is observed in very weak magnetic field, 0.005 mT thereby verifying a crossover from the weak antilocalization to the weak localization following the changes of the concentration of the 2D holes. Besides, the weak antilocalization caused by the scattering of heavy holes on the 29Si nuclei is found by the electrically-detected NMR in the weakest magnetic field, 0.001 mT. The amplitude and phase sensitivity of the 0.7(2e2/h) feature of the hole quantum conductance staircase revealed by verying the top gate voltage are shown to result from the interplay of the spontaneous spin polarization and the Rashba spin-orbit interaction (SOI). Finally, the values of the AC conductance oscillations caused by the Rashba SOI are found to take the fractional form with both the plateaus and steps as a function of the top gate voltage. |