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

Abstract

The integer quantum Hall (QH) effects characterized by topologically quantized and nondissipative transport are caused by an electrically insulating incompressible phase that prevents backscattering between chiral metallic channels. We probed the incompressible area susceptible to the breakdown of topological protection using a scanning gate technique incorporating nonequilibrium transport. The obtained pattern revealed the filling-factor (ν)-dependent evolution of the microscopic incompressible structures located along the edge and in the bulk region. We found that these specific structures, respectively attributed to the incompressible edge strip and bulk localization, show good agreement in terms of ν-dependent evolution with a calculation of the equilibrium QH incompressible phases, indicating the robustness of the QH incompressible phases under the nonequilibrium condition. Further, we found that the ν dependency of the incompressible patterns is, in turn, destroyed by a large imposed current during the deep QH effect breakdown. These results demonstrate the ability of our method to image the microscopic transport properties of a topological two-dimensional system. PACS numbers: Valid PACS appear hereA two-dimensional electron system (2DES) subjected to strong magnetic fields forms a quantum Hall (QH) insulating phase with a state lying in a gap between quantized Landau levels (LLs). This gapped phase, the socalled incompressible phase, prevents backscattering between the metallic gapless (compressible) phase counterpropagating along both sides of the 2DES edges [1]. This is the key microscopic aspect of nondissipative chiral transport of the integer QH effect, which is characterized by a longitudinal resistance that vanishes and a universal quantized Hall conductance protected by a topological invariant [2,3]. Topological phases are attracting renewed attention due to the recent discovery of exotic topological materials such as insulators [4][5][6][7], superconductors [8], and Weyl semimetals [9].The formation of incompressible and compressible phases in the QH regime originates from the interplay between Landau quantization and the Coulomb interaction [10], which drives nonlinear screening [11,12]. The spatial configuration depends on the potential landscape. For example, the edge confinement potential, accompanied by strong bending of the LLs, forms spatially alternating unscreening and screening regions due to the Fermi-level pinning at the gap and LLs. These regions respectively result in alternating incompressible and compressible strips near the 2DES edge. The innermost incompressible strip moves and spreads to the bulk as the LL filling factor ν reduces to an integer i from a higher ν. This ν dependency of the edge strips has been microscopically investigated using various imaging techniques such as single-electron transistor imaging [13], Hall-potential imaging [14,15], microwave impedance imaging [16], ca-pacitance imaging [17], and scanning gate imaging [18][19][20][21][22][23][24], and it has bee...

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“…1 c–e. Note that these SGM signatures do not originate from a direct coupling of the counterpropagating QHECs induced by the tip potential alone: this would yield iso-resistance stripes following the edge topography 24 , 29 . The absence of such stripes in SGM maps (Fig.…”

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“…A competing process due to elastic inter-LL interactions at high currents also give rise to Hall field-induced oscillations (HIRO) which have been investigated in QWs composed of GaAs [10][11][12], Ge/SiGe [13], and MgZnO/ZnO [14]. It is interesting to note that in GaAs QWs inter-LL processes can also manifest themselves as a breakdown of the integer quantum Hall effect [15][16][17][18][19].…”

Real space imaging of the quantum-Hall incompressible states influenced by the strong disorder

“…This disorder-induced QH effect has been microscopically confirmed through scanning probe measurement [2,3] that showed compressible paddles interspersed with the IC bulk phase, namely, localized states. On the other hand, the IC along the edge of the 2DEG governed by edge confinement potential [4] and its robust ν-dependence have recently been microscopically demonstrated for the high mobility Hall bar device by our nonequilibrium-transport assisted scanning gate imaging [5].…”

“…Hence, the tip (a nanoscale top gate) could perturb a microscopic landscape of the potential, resulting in a modification of the inter-LL tunneling. In the case of a high-mobility sample, the nanoscale top gate reduces the width of the IC region by bending the LLs locally and enhancing the inter LL tunneling, particularly through the innermost IC [5], leading to a further enhancement in the longitudinal resistance. Here, the tip-induced resistance change was measured as the longitudinal voltage (V xx ) at the constant source-drain current (I sd ) by a DC amplifier during scanning.…”

“…Here, the tip-induced resistance change was measured as the longitudinal voltage (V xx ) at the constant source-drain current (I sd ) by a DC amplifier during scanning. This scanning gate microscopy technique enables robust imaging of the QH IC strip in the non-equilibrium condition [5]. By using a dilution refrigerator and a superconductor magnet, measurements were performed at a temperature of 100-300 mK, while varying ν near ν = 1 by tuning the electron density of the 2DEG via back gating at a constant magnetic field B = 8 T. The experimental results obtained for high-and low-mobility samples were then compared.…”