Abstract
We describe Majorana edge states of a semi-infinite wire using the complex band structure approach. In this method the edge state at a given energy is built as a superposition of evanescent waves. It is shown that the superposition can not always satisfy the required boundary condition, thus restricting the existence of edge modes. We discuss purely 1D and 2D systems, focusing in the latter case on the effect of the Rashba mixing term.
Highlights
The realization of Majorana states as specific excitations of semiconductor quantum wires and of other condensed matter systems has attracted much interest recently.[1–28] Experimental evidences of these peculiar states in quantum wires and topological insulators have been presented in Refs. 23–26 and 27– 28, respectively
A Majorana state is a zero-energy mode, degenerate with the system ground state, that is localized on the system edges or interfaces
The subject of this work, such zero-energy modes can be induced by the combined action of the following three mechanisms: superconductivity, Rashba spin-orbit coupling, and Zeeman magnetic field
Summary
The realization of Majorana states as specific excitations of semiconductor quantum wires and of other condensed matter systems has attracted much interest recently.[1–28] Experimental evidences of these peculiar states in quantum wires and topological insulators have been presented in Refs. 23–26 and 27– 28, respectively. The subject of this work, such zero-energy modes can be induced by the combined action of the following three mechanisms: superconductivity, Rashba spin-orbit coupling, and Zeeman magnetic field. Waves with complex k cannot be physically realized for infinitely long distances from a given point in both directions due to the divergent behavior in one of them, but they can in a finite domain, or even in a semi-infinite one provided the infinite distance is in the direction of decaying amplitude The latter situation is precisely the one we expect for edge Majorana modes. We suggest robust numerical algorithms to obtain the complex band structure of 1D and 2D quantum wires in general, discussing the conditions for the existence of Majorana modes in the semi-infinite system. Being well understood,[1–22] the 1D system serves as a benchmark of the complex band structure method
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
