Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany.
Phys Rev Lett. 2013 Sep 20;111(12):126802. doi: 10.1103/PhysRevLett.111.126802. Epub 2013 Sep 17.
We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling. We find hierarchy multiplets of incompressible states at fillings ν = 1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as ν = 1/5, 2/7. These are accounted for by an analogy to Haldane pseudopotentials extracted from an analysis of the two-particle problem. Important distinctions to standard fractional quantum Hall physics are striking: in the absence of particle-hole symmetry in a single band, an interaction-induced single-hole dispersion appears, which perturbs and eventually destabilizes incompressible states as ν increases. For this reason, the nature of the state at ν = 2/3 is hard to pin down, while ν = 5/7, 4/5 do not seem to be incompressible in our system.
我们研究了无弥散 Chern 能带中相互作用电子的相图作为其填充的函数。我们在填充 ν = 1/3、2/5、3/7、4/9、5/9、4/7、3/5 以及 ν = 1/5、2/7 处发现了不可压缩态的层次多重态。这些可以通过与从双粒子问题分析中提取的 Haldane 赝势进行类比来解释。与标准分数量子霍尔物理的重要区别是明显的：在单个能带中没有粒子-空穴对称性的情况下，相互作用诱导的单空穴色散出现，这会干扰并最终使不可压缩态在 ν 增加时失稳。因此，在我们的系统中，ν = 2/3 处的状态性质难以确定，而 ν = 5/7、4/5 似乎不是不可压缩的。
