倾斜磁场中量子霍尔系统的哈密顿理论：激活能隙的鲁棒性
Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: robustness of activation gaps
摘要：
我们利用Shankar和Murthy发展的哈密顿理论研究了倾斜磁场中的量子霍尔系统。由于系统在$z$方向上的有限宽度，磁场的平行分量将各向异性引入到有效的二维相互作用中。这种各向异性的影响可以有效地捕获最近提出的广义赝势。我们发现赝势的非对角分量导致了复合费米子朗道能级的混合，这是对复合费米子理论中填充$p$朗道能级图像的扰动.通过改变复合费米子的内部几何形状，这样的扰动可以最小化，可以找到相应的激活间隙为不同的倾斜角，我们计算出相关的最佳度量。我们的研究结果表明，激活间隙是显着鲁棒的面内磁场在最低的朗道水平。
英文摘要：
We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the $z$ direction, the parallel component of the magnetic field introduces anisotropy into the effective two-dimensional interactions. The effects of such anisotropy can be effectively captured by the recently proposed generalized pseudo-potentials. We find that the off-diagonal components of the pseudo-potentials lead to mixing of composite fermions Landau levels, which is a perturbation to the picture of $p$ filled Landau levels in composite-fermion theory. By changing the internal geometry of the composite fermions, such a perturbation can be minimized and one can find the corresponding activation gaps for different tilting angles, and we calculate the associated optimal metric. Our results show that the activation gap is remarkably robust against the in-plane magnetic field in the lowest Landau level.
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