Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
复制标题
半填充朗道能级的费米子-陈-西蒙斯和狄拉克描述中的粒子空穴对称性
DOI：
10.1103/physrevx.7.031029
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发表时间：
2016
影响因子：
12.5
通讯作者：
A. Stern
中科院分区：
文献类型：
--
作者：
Chong Wang;N. Cooper;B. Halperin;A. Stern
众所周知，在部分填充的朗道能级中，具有二体相互作用的自旋极化电子存在粒子空穴对称性，在回旋加速器能量与相互作用强度相比较大的极限下，这种对称性变得精确，因此可以忽略朗道能级之间的混合。这种对称性在 D. T. Son 最近使用狄拉克费米子引入的半满朗道能级的描述中是明确的，但人们认为在由 Halperin、Lee 和 Read 及后续作者开发的旧费米子-陈-西蒙斯方法中不存在这种对称性。然而，我们在这里表明，经过正确评估，Halperin，Lee，Read (HLR) 理论给出了长波长低能物理性质的结果，包括存在杂质时的霍尔电导以及接近半填充的分数量子化霍尔态的磁子光谱中的最小值位置，这与狄拉克公式的预测相同。事实上，HLR 理论预测，即使回旋加速器能量有限，也会在接近半填充时出现粒子空穴对称性。
It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the interaction strength, so one can ignore mixing between Landau levels. This symmetry is explicit in the description of a half-filled Landau level recently introduced by D. T. Son, using Dirac fermions, but it was thought to be absent in the older fermion-Chern- Simons approach, developed by Halperin, Lee, and Read and subsequent authors. We show here, however, that when properly evaluated, the Halperin, Lee, Read (HLR) theory gives results for long-wavelength low-energy physical properties, including the Hall conductance in the presence of impurities and the positions of minima in the magnetoroton spectra for fractional quantized Hall states close to half-filling, that are identical to predictions of the Dirac formulation. In fact, the HLR theory predicts an emergent particle-hole symmetry near half filling, even when the cyclotron energy is finite.