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Leakage of Majorana bound states in an inhomogeneous topological nanowire
Journal of Physics: Condensed Matter ( IF 2.7 ) Pub Date : 2020-07-31 , DOI: 10.1088/1361-648x/aba154
Wei Fu 1 , Na Yao , Sha-Sha Ke , Yong Guo , Hai-Feng Lü
Affiliation  

We present an exact solution of the continuum Bogolyubov-de-Gennes (BdG) Hamiltonian for MBSs generated in a superconductor-semiconductor hybrid topological nanowire. The full energy spectra that include the band states and in-gap states could be obtained. We show that for relatively short wire length, the zero energy mode could be induced even in the topological trivial regime, which also indicates oscillatory dependence on the chemical potential. With the increase of the Zeeman eld, the MBSs are almost fully spin-polarized and do not localize in the wire ends gradually. We also extend our discussion to the property of Majorana modes in an inhomogeneous nanowire, in which a local gate voltage is applied to one end of the nanowire. It is found that the local potential barrier or well could modulate the Majorana energy splitting periodically. The leakage of MBSs to the potential region is exponentially suppressed for the barrier case. A potential well could induce near-zero energy bound states and these states merge with MBSs, leading to the delocalization of MBSs. In the potential well region, both the spin-up and spin-down components of the trivial states account for a signicant proportion, which can be detected experimentally.

中文翻译:

非均匀拓扑纳米线中 Majorana 束缚态的泄漏

我们提出了超导体-半导体混合拓扑纳米线中生成的 MBS 的连续谱 Bogolyubov-de-Gennes (BdG) 哈密顿量的精确解。可以获得包括带态和带隙态的全能谱。我们表明,对于相对较短的导线长度,即使在拓扑微不足道的情况下也可以诱导零能量模式,这也表明对化学势的振荡依赖性。随着塞曼场的增加,MBSs 几乎完全自旋极化并且逐渐不在线端定位。我们还将讨论扩展到非均匀纳米线中马约拉纳模式的特性,其中局部栅极电压施加到纳米线的一端。发现局部势垒或阱可以周期性地调节Majorana能量分裂。对于势垒情况,MBS 向潜在区域的泄漏受到指数抑制。势阱可以诱导接近零的能量束缚态,这些态与 MBS 合并,导致 MBS 离域。在势阱区,平凡状态的自旋向上和自旋向下分量都占很大比例,这可以通过实验检测到。
更新日期:2020-07-31
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