输运中对称性决定的Dirac费米子普适螺旋度重分布
Symmetry dictated universal helicity redistribution of Dirac fermions in transport
AI总结：
本文从理论上揭示Dirac费米子穿过静电势和质量势时由对称性决定的普适旋量变换与螺旋度重分布规则，并建立其与Lorentz推进、Klein隧穿及旋量Hilbert空间叶状结构的统一联系。
摘要：
螺旋度是Dirac费米子的一个基本性质。然而，关于它在输运中如何变化，目前仍缺乏一般规律。我们在理论上揭示了两类输运情形中的普适旋量态变换以及由此产生的螺旋度重分布规则，这两类情形分别是通过静电型势和质量型势的输运。前者由Lorentz推进及其在Klein隧穿区中的复对应所决定，这在螺旋度、Klein隧穿和Lorentz推进之间奇迹般地建立了一个统一而潜在的联系。后者则由我们构造的一个抽象旋转群支配；当该群作用于有效质量与动量构成的平面时，它退化为SO(2)。它们生成不变子流形，即叶，这些叶对Dirac旋量的Hilbert空间进行叶状化。我们的结果为统一理解螺旋度输运提供了基础，并可能为介观系统中基于螺旋度的新奇物理和应用打开一扇新窗口。
英文摘要：
Helicity is a fundamental property of Dirac fermions. Yet, the general rule of how it changes in transport is still lacking. We uncover, theoretically, the universal spinor state transformation and consequently helicity redistribution rule in two cases of transport through potentials of electrostatic and mass types, respectively. The former is dictated by Lorentz boost and its complex counterpart in Klein tunneling regime, which establishes miraculously a unified yet latent connection between helicity, Klein tunneling, and Lorentz boost. The latter is governed by an abstract rotation group we construct, which reduces to SO(2) when acting on the plane of effective mass and momentum. They generate invariant submanifolds, i.e., leaves, that foliate the Hilbert space of Dirac spinors. Our results provide a basis for unified understanding of helicity transport, and may open a new window for exotic helicity-based physics and applications in mesoscopic systems.
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