Scanning nuclear resonance imaging of a hyperfine-coupled quantum Hall system

Abstract

Nuclear resonance (NR) is widely used to detect and characterise nuclear spin polarisation and conduction electron spin polarisation coupled by a hyperfine interaction. While the macroscopic aspects of such hyperfine-coupled systems have been addressed in most relevant studies, the essential role of local variation in both types of spin polarisation has been indicated in 2D semiconductor systems. In this study, we apply a recently developed local and highly sensitive NR based on a scanning probe to a hyperfine-coupled quantum Hall (QH) system in a 2D electron gas subject to a strong magnetic field. We succeed in imaging the NR intensity and Knight shift, uncovering the spatial distribution of both the nuclear and electron spin polarisation. The results reveal the microscopic origin of the nonequilibrium QH phenomena, and highlight the potential use of our technique in microscopic studies on various electron spin systems as well as their correlations with nuclear spins.

Probing the breakdown of topological protection: Filling-factor-dependent evolution of robust quantum Hall incompressible phases

“…The observed ν evolution of the incompressible phases that shows agreement with the LSDA calculation indicates that the QH phases is microscopically robust against the local breakdown caused by inter-LL scattering under the nonequilibrium condition. The robustness of a QH state is supported by our previously reported scanning nuclear resonance imaging [43], where we demonstrated the spatial homogeneity of the fully polarized ν = 1 state maintained under similar nonequilibrium conditions near the onset of breakdown of the QH effect. We speculate that this robustness maintains at nonequiliblium I sd up to the limit above which the position of the incompressible pattern showed the I sd dependence (see the Supplementary Material [40]).…”

“…A distinct line-like pattern can be seen extending in the x direction along a Hall bar edge (left dashed line), which corresponds to the side with the higher chemical potential (µ chem ) across the y direction of the Hall bar. This µ chem dependency, confirmed by reversing the direction of the current [40], can be explained by the fact that µ chem mainly drops at the higher-µ chem incompressible strip in a nonequilibrium condition [42], where we expect a higher rate of inter-LL scattering [43] and thus more SGM sensitivity with respect to the corresponding incompressible strip. To minimize the influence of I sd on the incompressible patterns, I sd was limited to below the current in all measurements, at which the position of the strip shows no significant I sd dependence in the entire measurement region of ν.…”

“…4(e)), which correspond to the positions (crosses in Figs 4(c)) of the disorder-induced QH compressible puddles. These indicate that the filament pattern is correlated with the potential disorder whose potential slope may not be fully screened owing to less compressibility induced by the heating effect [48,49] in the dissipative QH breakdown regime [43,50]. This implies that inter-LL scattering arises along the potential disorder [51] over the sample in the deep QH breakdown regime.…”

Emergence of spin-active channels at a quantum Hall interface

“…One complication in our system is that only the nuclear spins near the interface will couple to the gapless chiral spin modes, so a local measurement of T 2 will be necessary. Some progress has been made in this direction recently [24,25].…”