Abstract

We study the electronic properties of a position-dependent effective mass electron on a bilayer graphene catenoid bridge. We propose a position-dependent mass (PDM) as a function of both Gaussian and mean curvature. The Hamiltonian exhibits parity and time-reversal steaming from the bridge symmetry. The effective potential contains the da Costa, centrifugal, and PDM terms which are concentrated around the catenoid bridge. For zero angular momentum states, the PDM term provides a transition between a reflectionless to a double-well potential. As a result, the bound states undergo a transition from a single state around the bridge throat into two states each one located at rings around the bridge. Above some critical value of the PDM coupling constant, the degeneracy is restored due to double-well tunneling resonance.

Graphic abstract

中文翻译：

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双层石墨烯链状桥的位置依赖质量效应

摘要

我们研究了双层石墨烯链状桥上位置相关的有效质量电子的电子特性。我们建议将位置相关质量 (PDM) 作为高斯曲率和平均曲率的函数。哈密​​顿量从桥对称性中表现出奇偶校验和时间反转。有效势包含集中在悬链桥周围的 da Costa、离心和 PDM 项。对于零角动量状态，PDM 项提供无反射到双阱势之间的过渡。结果，束缚态从围绕电桥喉部的单一状态转变为两个状态，每个状态都位于围绕电桥的环处。高于 PDM 耦合常数的某个临界值，由于双井隧道共振，简并性恢复。

图形摘要