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arXiv 2109.07355cond-mat.mes-hall
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1+1维Dirac佯谬及其自旋轨道耦合纳米线的实现

The Dirac paradox in 1+1 dimensions and its realization with spin-orbit coupled nanowires

Leonid Gogin, Lorenzo Rossi, Fausto Rossi, Fabrizio Dolcini

摘要:

在两个具有相反螺旋度的无质量狄拉克模型之间的界面处,出现了一种矛盾的情况:由于自旋和动量之间的锁定,横向撞击的电子似乎既不能被透射也不能被反射。在这里,我们调查这个悖论在一个空间维度,不同的高维实现,电子不能泄漏沿界面。我们表明,模型只涉及无质量狄拉克模式导致要么没有解决方案或平凡的解决方案的悖论,这取决于如何跨接口的螺旋度变化的建模。然而,非平凡的散射解决方案的悖论存在时,额外的大量狄拉克模式考虑。虽然这些模式在它们的间隙内不携带能量的电流,但是它们与无质量模式的界面耦合可以引起有限的和可调谐的传输。最后,我们表明,这种无质量+大规模狄拉克模型可以实现在适当的门控自旋轨道耦合纳米线暴露于外部塞曼场,其中的传输系数可以控制电。

英文摘要:

At the interface between two massless Dirac models with opposite helicity a paradoxical situation arises: A transversally impinging electron can seemingly neither be transmitted nor reflected, due to the locking between spin and momentum. Here we investigate this paradox in one spatial dimension where, differently from higher dimensional realizations, electrons cannot leak along the interface. We show that models involving only massless Dirac modes lead to either no solutions or to trivial solutions to the paradox, depending on how the helicity change across the interface is modeled. However, non trivial scattering solutions to the paradox are shown to exist when additional massive Dirac modes are taken into account. Although these modes carry no current for energies within their gap, their interface coupling with the massless modes can induce a finite and tunable transmission. Finally, we show that such massless+massive Dirac model can be realized in suitably gated spin-orbit coupled nanowires exposed to an external Zeeman field, where the transmission coefficient can be controlled electrically.

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