We present systematic investigations of the electrically induced breakdown of the integer quantum Hall effect (QHE) in (Al,Ga)As-based Hall bars of different widths ranging from 7 to 70 $\mu \mathrm{m}$. It is striking that, for the narrow Hall bars, the threshold values for the applied voltage that induces the breakdown of the longitudinal zero-resistance state differ appreciably between the upper and lower sides of a quantum Hall (QH) plateau. When moving from the low magnetic field side of the QH plateau to higher magnetic fields, the threshold rises in a strongly superlinear manner until—at the expected integer value for the Landau level (LL) filling factor in the bulk of the two-dimensional electron system (2DES)—the threshold value abruptly drops to low values for the rest of the plateau. With increasing widths of the Hall bars, the zero-resistance state extends slightly further to higher magnetic field values. The threshold values on the low-magnetic field side are almost independent of the Hall bar width, whereas the threshold values on the high magnetic field side scale linearly with the Hall bar width. These observations correspond perfectly with the microscope picture of the QHE where the biased current flows in a dissipationless manner in electrically incompressible regions of the 2DES of locally the same LL filling factor, driven by the respective drop of the Hall voltage over the width of these incompressible regions. Owing to the self-consistent evolution of the electrically incompressible/compressible landscape within the 2DES as a function of magnetic field, a transition from an edge- to a bulk-dominated QH regime is described within a QH plateau. This microscopic picture was derived from sophisticated, long-lasting scanning probe experiments measuring Hall potential profiles on typically 15-$\mu$m-wide Hall bars. Conversely, performing systematic electrically induced breakdown measurements like those presented here would allow us to identify the presence of edge- and bulk-dominated regimes of the QHE in a wider variety of samples.

中文翻译：

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在不同霍尔杆宽度下的电感应击穿量子霍尔效应：可视化量子霍尔高台内的边缘和体为主的状态

我们目前对（Al，Ga）As基宽度为7到70的霍尔棒中的整数量子霍尔效应（QHE）的电致击穿进行系统研究 $\mu \mathrm{米}$。令人惊讶的是，对于窄的霍尔棒，在量子霍尔（QH）平稳区的上侧和下侧之间引起纵向零电阻状态击穿的施加电压的阈值明显不同。当从QH平稳区的低磁场侧移到较高磁场时，阈值以强烈的超线性方式上升，直到-在二维电子主体中的Landau能级（LL）填充因子的预期整数值处系统（2DES）-对于高原的其余部分，阈值突然下降到较低值。随着霍尔棒宽度的增加，零电阻状态会进一步扩展到更高的磁场值。低磁场侧的阈值几乎与霍尔棒宽度无关，而高磁场侧的阈值与霍尔棒宽度成线性比例。这些观察结果与QHE的显微镜图片非常吻合，在该图片中，偏置电流以无耗散的方式流经局部具有相同LL填充因子的2DES的电不可压缩区域，这是由霍尔电压在这些不可压缩区域的相应下降引起的地区。由于2DES内电不可压缩/可压缩景观随磁场的自洽演变，因此在QH平稳期内描述了从边缘占主导的QH态到整体占优势的QH态的过渡。这张显微图片来自复杂，持久的扫描探针实验，该实验测量了通常在15-$\mu$米宽的大厅酒吧。相反，执行此处介绍的系统性电击穿测量，将使我们能够识别出在各种样品中QHE的边沿和体相主导制度的存在。