Robust zero-energy bound states around a pair-density-wave vortex core in locally noncentrosymmetric superconductors

Yoichi Higashi, Yuki Nagai, Tomohiro Yoshida, Yusuke Masaki, and Youichi Yanase

Phys. Rev. B 93, 104529 – Published 29 March 2016

Abstract

We numerically investigate the electronic structures around a vortex core in a bilayer superconducting system, with $s$ -wave pairing, Rashba spin-orbit coupling, and Zeeman magnetic field, with the use of the quasiclassical Green's function method. The BCS phase and the so-called pair-density-wave (PDW) phase appear in the temperature-magnetic-field phase diagram in a bulk uniform system [T. Yoshida et al., Phys. Rev. B 86, 134514 (2012)]. In the low magnetic field perpendicular to the layers, the zero-energy vortex bound states in the BCS phase are split by the Zeeman magnetic field. On the other hand, the PDW state appears in the high magnetic field, and the sign of the order parameter is opposite between the layers. We find that the vortex core suddenly shrinks and the zero-energy bound states appear by increasing the magnetic field through the BCS-PDW transition. We discuss the origin of the change in the vortex-core structure between the BCS and PDW states by clarifying the relation between the vortex bound states and the bulk energy spectra. In the high-magnetic-field region, the PDW state and vortex bound states are protected by the spin-orbit coupling. These characteristic behaviors in the PDW state can be observed by scanning tunneling microscopy/spectroscopy.

Received 25 February 2015
Revised 1 February 2016

DOI:https://doi.org/10.1103/PhysRevB.93.104529

Physics Subject Headings (PhySH)

Electronic structure Rashba coupling Superconductivity Vortices in superconductors s-wave

Superconductors

BCS theory Semiclassical methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yoichi Higashi^1,*, Yuki Nagai², Tomohiro Yoshida^3,†, Yusuke Masaki⁴, and Youichi Yanase^5,‡

¹Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan
²CCSE, Japan Atomic Energy Agency, 178-4-4, Wakashiba, Kashiwa, Chiba 277-0871, Japan
³Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
⁴Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
⁵Department of Physics, Niigata University, Niigata 950-2181, Japan

^*Present address: Department of Physics, Sungkyunkwan University, Suwon 16419, Korea; y.higashi@skku.edu
^†Present address: Department of Physics, Gakushuin University, Tokyo 171-8588, Japan.
^‡Present address: Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.

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Issue

Vol. 93, Iss. 10 — 1 March 2016

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