引力对量子霍尔效应影响的新认识
A fresh look at the influence of gravity on the quantum Hall effect
摘要：
研究了引力场中的量子霍尔效应。首先，我们回顾了地球引力场对量子霍尔效应的影响。假设地球的引力场沿垂直方向均匀分布，计算了受影响的量子化霍尔电阻率。然后，我们研究了在垂直于运动平面的恒定均匀磁场存在下，引力场如何改变在两个大质量半球之间运动的粒子的朗道能级。我们发现，熟悉的朗道能级的简并被删除，后者之间的间距变得依赖于半球的质量密度和引力常量$G$。我们用这个结果表明，在薄导体的量子霍尔效应，夹在两个巨大的半球，应产生一个略有不同的变化的霍尔电阻率与所施加的磁场。然后，我们认为，众所周知的问题的引力引起的电场，这可能是一个先验被认为是阻碍重力的影响，实际上有一个有益的作用，因为它放大了后者。最后讨论了利用量子霍尔效应探测引力平方反比定律的可能性。
英文摘要：
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical direction, we compute the affected quantized Hall resistivity. Then, we investigate how the gravitational field modifies the Landau levels of a particle moving between two massive hemispheres in the presence of a constant and uniform magnetic field perpendicular to the plane of motion. We find that the familiar degeneracy of the Landau levels is removed and the spacing between the latter becomes dependent on the mass density of the hemispheres and on the gravitational constant $G$. We use this result to show that the quantum Hall effect in a thin conductor, sandwiched between two massive hemispheres, should yield a slightly different variation of the Hall resistivity with the applied magnetic field. We then argue that the well-known problem of the gravitationally induced electric field, that might a priori be thought to hinder the effect of gravity, has actually a beneficial role as it amplifies the latter. We finally discuss whether there is a possibility of using the quantum Hall effect to probe the inverse-square law of gravity.
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