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Majorana spin in magnetic atomic chain systems

Jian Li, Sangjun Jeon, Yonglong Xie, Ali Yazdani, and B. Andrei Bernevig
Phys. Rev. B 97, 125119 – Published 15 March 2018

Abstract

In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin-resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a hybrid model. By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes (BdG) particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to a ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included. We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy (STM) techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidental-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains. We further confirm our results with numerical simulations that address generic parameter settings.

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  • Received 25 September 2017

DOI:https://doi.org/10.1103/PhysRevB.97.125119

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jian Li1,2,3, Sangjun Jeon1, Yonglong Xie1, Ali Yazdani1, and B. Andrei Bernevig1,4,5,6

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 2Institute for Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang Province, China
  • 3Westlake University, Hangzhou, Zhejiang Province, China
  • 4Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
  • 5Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
  • 6Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris, France

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Issue

Vol. 97, Iss. 12 — 15 March 2018

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