Fu Wei, Yao Na, Ke Sha-Sha, Guo Yong, Lü Hai-Feng
School of Physics and State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China.
College of Optoelectronics Technology, Chengdu University of Information Technology, Chengdu 610225, People's Republic of China.
J Phys Condens Matter. 2020 Jul 30;32(43). doi: 10.1088/1361-648X/aba154.
We present an exact solution of the continuum Bogolyubov-de-Gennes Hamiltonian for Majorana bound states (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 field, the MBSs are almost fully spin-polarized and do not localize at 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 significant proportion, which can be detected experimentally.
我们给出了超导体-半导体混合拓扑纳米线中产生的马约拉纳束缚态（MBSs）的连续体博戈留波夫-德热纳哈密顿量的精确解。可以获得包括能带态和能隙态在内的完整能谱。我们表明，对于相对较短的线长，即使在拓扑平凡区域也能诱导出零能模，这也表明其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，并且不会逐渐定域在线端。我们还将讨论扩展到非均匀纳米线中马约拉纳模的性质，其中在纳米线的一端施加局部栅极电压。发现局部势垒或势阱可以周期性地调制马约拉纳能隙。对于势垒情况，MBSs向势垒区域的泄漏被指数抑制。势阱可以诱导近零能束缚态，并且这些态与MBSs合并，导致MBSs的非定域化。在势阱区域，平凡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。
