实际样品中$ν=1/3$和$ν=7/3$的磁子形状
Shape of the magnetoroton at $ν=1/3$ and $ν=7/3$ in real samples
摘要：
我们重新讨论了朗道能级填充分数$ν=1/3$和$ν=7/3$下分数量子霍尔效应中集体中性激发模的理论。我们包括有限厚度的二维电子气的效果，并使用广泛的精确对角化的环面几何。在最低朗道能级，集体能隙模即磁子总是在长波长极限的连续谱中融合。在第二朗道水平的模式是定义良好的波矢量小于临界值，并消失在连续超过这一点。它在零动量附近的曲率与LLL相反。即使在零动量下，它也能很好地与连续谱分离，并且高阶态连续谱的能隙是$k=0$集体模能隙的两倍。的形状的色散关系生存的朗道能级混合的微扰处理。
英文摘要：
We revisit the theory of the collective neutral excitation mode in the fractional quantum Hall effect at Landau level filling fractions $ν=1/3$ and $ν=7/3$. We include the effect of finite thickness of the two-dimensional electron gas and use extensive exact diagonalizations in the torus geometry. In the lowest Landau level the collective gapped mode i.e. the magnetoroton always merges in the continuum in the long-wavelength limit. In the second Landau level the mode is well-defined only for wavevectors smaller than a critical value and disappears in the continuum beyond this point. Its curvature near zero momentum is opposite to that of the LLL. It is well separated from the continuum even at zero momentum and the gap of the continuum of higher-lying states is twice the collective mode gap at $k=0$. The shape of the dispersion relation survives a perturbative treatment of Landau level mixing.
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