Superconducting order parameter for the even-denominator fractional quantum Hall effect
Superconducting order parameter for the even-denominator fractional quantum Hall effect
复制标题
偶分母分数量子霍尔效应的超导序参数
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Kwon Park
中科院分区：
文献类型：
--
作者：
Hantao Lu;S. Sarma;Kwon Park
自然界中最有趣的现象之一是在半填充的第二朗道能级中观察到的分数量子霍尔效应（FQHE），它出现在偶数分母填充因子中，$
u=5/2$ 和 $7/2$ 与其他 FQHE 的起源完全不同，除了这两个填充因子之外，所有这些 FQHE 都出现在奇分母分数中。目前的主流理论通常用称为摩尔-里德普法夫波函数的试验波函数来表述，当前的主流理论将 5/2 FQHE 的起源归因于库珀对的形成，库珀对不是电子，而是称为复合费米子的系统的真正准粒子的形成。这种库珀配对产生的超导性的性质特别令人费解，因为它显然与强磁场共存，这造成了一个有趣的困境，因为迈斯纳效应是超导性最重要的定义属性。这种明显的困境是通过以下事实解决的：复合费米子在偶数分母填充因子下不响应外部磁场。为了提供直接证据证明复合费米子实际上形成了超导凝聚体，在这里，我们开发了一种数值精确的方法来创建复合费米子的库珀对，并显式计算作为真实空间坐标函数的超导序参数。结果，除了超导性的直接证据之外，我们还获得了超导相干长度的定量预测。获得这样的理论预测可以作为实现容错拓扑量子计算的重要一步。
One of the most intriguing phenomena in nature is the fractional quantum Hall effect (FQHE) observed in the half-filled second Landau level which, arising in even-denominator filling factors, $
u=5/2$ and $7/2$, is completely different from other FQHEs in its origin, all of which, except for those two filling factors, occur in odd-denominator fractions. Usually formulated in terms of a trial wave function called the Moore-Read Pfaffian wave function, current leading theories attribute the origin of the 5/2 FQHE to the formation of Cooper pairs, not of electron, but of the true quasi-particle of the system known as composite fermion. The nature of superconductivity resulting from such Cooper pairing is particularly puzzling in the sense that it apparently coexists with strong magnetic fields, which poses an interesting dilemma since the Meissner effect is {it the} most important defining property of superconductivity. This apparent dilemma is resolved by the fact that composite fermions do not respond to external magnetic field at even-denominator filling factors. To provide direct evidence that it is composite fermions that actually form the superconducting condensate, here, we develop a numerically exact method of creating a Cooper pair of composite fermions and explicitly compute the superconducting order parameter as a function of real space coordinates. As results, in addition to direct evidence for superconductivity, we obtain quantitative predictions for superconducting coherence length. Obtaining such theoretical predictions can serve as an important step toward fault-tolerant topological quantum computation.