Resistively-detected NMR lineshapes in a local filling $\nu <1$ quantum Hall breakdown

Resistively-detected NMR (RDNMR) is a unique characterization method enabling highly-sensitive NMR detection for a single quantum nanostructure, such as a quantum point contact (QPC). In many studies, we use dynamic nuclear polarization and RDNMR detection in a quantum Hall breakdown regime of a local QPC filling factor of 1 (${\nu }_{\mathrm{q}\mathrm{p}\mathrm{c}}=1$). However, the lineshapes of RDNMR signal are proved to be complicated and still not fully understood yet. Here, we systematically polarize the nuclear spins by current-pumping from the close vicinity of ${\nu }_{\mathrm{q}\mathrm{p}\mathrm{c}}=1$ conductance plateau all the way down to pinch-off point, providing a clear evidence that the spin-flip scattering between two edge channels at the lowest Landau level still occurs in the constriction even when it is close to the pinch off point ($G\approx {10}^{-2}$ $2e^2\mathrm{/}h$). The collected RDNMR spectra reveal two sets of distinguished features. First, in a strong to intermediate tunneling regime, we observe an ordinary resistance dip lineshape but interestingly its transition frequency follows a snake-like pattern, an indicative of spatial modulation of electron density in the QPC. Second, in a weak tunneling regime, the spectrum turns into a dispersive lineshape which we interpret due to the build up of two sets of nuclear spin polarization that are in contact with different electron spin polarization.