Scanning gate imaging of the quantum Hall system

概要

Ⅰ. Introduction
Under a strong magnetic field, two- dimensional electron system (2DES) forms quantum Hall (QH) insulating incompressible (IC) and metallic compressible (C) phases [1]. The IC phase prevents backscattering between the C phase counter-propagating along both sides of the 2DES edges. This is the important microscopic aspect of nondissipative chiral transport of both the integer and fractional QH effects, which are characterized by macroscopic phenomena, i.e., a longitudinal resistance that vanishes and a universal quantized Hall conductance protected by a topological invariant [2]. The microscopic mechanism of the breakdown of topological protection is though to originate from backscattering through the IC region [3], and this has recently become a key issue in research on the quantum spin Hall effect [4]. Moreover, scattering of spin polarized electron in integer and fractional QH systems relies on interplay with the nuclear spin of the host material, giving strong impact on the microscopic structures of the IC phases and hence the QH transport properties. In this thesis, we address the microscopic aspects of electron scattering in the spin polarized QH systems by using scanning gate microscopy (SGM) incorporated with the nonequilibrium transport technique and/or nuclear resonance technique.

Ⅱ. Scanning gate imaging of the IC strip in the low-mobility sample
Firstly, using the nonequilibrium- transport-assisted SGM (Fig. 1(a)), we imaged the scattering region in integer QH system for the different mobility samples ensuring different density and strength of the potential disorder. We observed the line pattern along the sample edge that shows a robust QH behavior regardless of the mobility: the IC edge strip shifts from the Hall-bar edge to center as decreasing the filling factor (ν). In contrast, in the low- mobility sample alone, we found bright, dark, and annular patterns within the IC strip (Fig. 1(d)). These observed patterns are ascribed to inter-Landau level (LL) scattering assisted by resonance tunneling through an impurity bound state within the IC strip region.

Moreover, the scattering centers were pinpointed within the IC region near an exact integer filling factor. To examine the hyperfine interaction caused by inter-LL scattering near the spin-polarized QH ν = 1, we further incorporated nuclear resonance technique with the SGM measurement (scanning nuclear resonance microscopy: SMRM). We confirmed that nuclear spin polarization was driven by inter-LL scattering in the IC region.

Ⅲ. NER properties of the fractional quantum Hall system
We next explored the spin degenerate in the fractional quantum Hall ν = 2/3 system, in which the spin-polarized and unpolarized electron spin domains coexist in the bulk IC region [5]. Scattering between the neighbor domains involving spin flip is thought to induce nuclear spin polarization. Before applying SNRM based on electric nuclear resonance instead of conventional magnetic nuclear resonance, we tested to apply the radio frequency electric field over the entire 2DES region from the back gate mounted on the sample and performed the resistive detection. The obtained nuclear resonance spectrum showed the resonance peaks at fundamental and knight shift frequencies which respectively indicate formation of the spin unpolarized and polarized states (Fig. 2). This confirms the ability of the electric nuclear resonance to resolve the ν = 2/3 spin domain system.

Ⅳ. Scanning nuclear resonance imaging of fractional quantum Hall system
Using SNRM, the local electric nuclear resonance was applied to the ν = 2/3 spin domain system and provided an inhomogeneously distributed pattern of nuclear spin polarization intensity (Fig. 3). The result support the ability of SNRM to examine the spatial correlation between nuclear spin polarization and electron spin domains in the fractional quantum Hall system.

Ⅴ. Nuclear electric resonance of the QH system in a QPC
By using NER method at the lower side of νqpc = 1 under the nonequilibrium condition, we detected the nuclear resonance information, proved that NER method can be applied to the scanning gate to image the spatial distribution of the nuclear spin polarization in the quasi-one-dimensional system.

Ⅵ. Conclusion
Our results proved that the QH state is robustness to the disorder, and the disorder potential strongly modulates the QH IC phase. The scanning nuclear resonance microscopy imaging indicate the spatial distribution of the nuclear spin polarization is strongly correlated with the spin-flip scattering in both the integer and fractional QH system. These demonstrate that our SGM-based methods can directly revel the microscopic properties of the quantum Hall systems.

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