Lee Sung-Sik, Ryu Shinsei, Nayak Chetan, Fisher Matthew P A
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA.
Phys Rev Lett. 2007 Dec 7;99(23):236807. doi: 10.1103/PhysRevLett.99.236807. Epub 2007 Dec 6.
We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.
我们讨论了在形成配对量子霍尔态的半填充朗道能级中近似粒子-空穴对称性的影响。我们注意到Pfaffian态不是粒子-空穴对称的。因此，在朗道能级混合消失的极限情况下，其中粒子-空穴变换是一种精确对称性，Pfaffian态自发地打破了这种对称性。存在一个粒子-空穴共轭态，我们称之为反Pfaffian态，在这个极限下它与Pfaffian态简并。我们观察到强朗道能级混合应该有利于Pfaffian态，但对于实验中存在的中等朗道能级混合情况，哪种态更受青睐仍是一个未解决的问题。我们讨论了反Pfaffian态的体相和边缘物理。我们分析了一个简化模型，在其中可以详细研究两种态的类似物之间的跃迁。最后，我们讨论了实验意义。
