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首页> 外文期刊>Physical review >Distinguishing particle-hole conjugated fractional quantum Hall states using quantum-dot-mediated edge transport
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Distinguishing particle-hole conjugated fractional quantum Hall states using quantum-dot-mediated edge transport

机译：使用量子点介导的边缘传输区分粒子-空穴共轭分数量子霍尔态

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摘要

We study theoretically edge transport of a fractional quantum Hall liquid, in the presence of a quantum dot inside the Hall bar with well-controlled electron density and Landau-level filling factor v and show that such transport studies can help reveal the nature of the fractional quantum Hall liquid. In our first example we study the v = 1/3 and v = 2/3 liquids in the presence of a v = 1 quantum dot. When the quantum dot becomes large, its edge states join those of the Hall bar to reconstruct the edge states configuration. Taking randomness around the edges into account, we find that in the disorder-irrelevant phase the two-terminal conductance of the original v = 1/3 system vanishes at zero temperature, while that of the v = 2/3 case remains finite. This distinction is rooted in the fact that the v = 2/3 state is built on the v = 1 state. In the disorder-dominated phase, the two-terminal conductance of v = 1/3 system is (1/5)e~2/h and that of v = 2/3 system is (1/2)e~2/h. We further apply the same idea to the v = 5/2 system, which realizes either the Pfaffian state or the anti-Pfaffian state. In this case, we study the edge transport in the presence of a central v = 3 quantum dot. If the quantum dot is large enough for its edge states joining those of the Hall bar, in the disorder-irrelevant phase the total two-terminal conductance in the Pfaffian case is G_(tot)~(Pf) → 2e~2/h while that of anti-Pfaffian case is higher but not universal, G_(tot)~(aPf) > 2e~2/h. This difference can be used to determine which one of these two states is realized at v = 5/2. In the disorder-dominated phase, however, the total two-terminal conductances in these two systems are exactly the same, G_(tot)~(Pf/aPf) = (7/3)e~2/h.
机译：我们在霍尔棒内部存在量子点且具有良好控制的电子密度和朗道能级填充因子v的情况下，从理论上研究了分数量子霍尔液体的边缘传输，并证明了这种传输研究可以帮助揭示分数原子的性质量子霍尔液体。在我们的第一个示例中，我们在存在v = 1量子点的情况下研究v = 1/3和v = 2/3的液体。当量子点变大时，其边缘状态会与霍尔棒的边缘状态合并，以重建边缘状态配置。考虑到边缘周围的随机性，我们发现在无序无关阶段，原始v = 1/3系统的两端电导在零温度下消失，而v = 2/3情况的电导仍然有限。这种区别源于v = 2/3状态建立在v = 1状态的事实。在无序控制阶段，v = 1/3系统的两端电导为（1/5）e〜2 / h，v = 2/3系统的两端电导为（1/2）e〜2 / h 。我们进一步将相同的想法应用于v = 5/2系统，该系统实现了Pfaffian态或反Pfaffian态。在这种情况下，我们研究存在中心v = 3量子点时的边缘传输。如果量子点足够大以使其边缘状态与霍尔棒的边缘状态相结合，则在无序无关相中，在Pfaffian情况下，总的两端电导为G_（tot）〜（Pf）→2e〜2 / h，而反Pfaffian情况的G_（tot）〜（aPf）> 2e〜2 / h较高，但不是通用的。该差异可用于确定在v = 5/2时实现这两种状态中的哪一种。然而，在无序控制阶段，这两个系统的总的两个末端电导完全相同，G_（tot）〜（Pf / aPf）=（7/3）e〜2 / h。

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