Incommensurate spin density wave as a signature of spin-orbit coupling and precursor of topological superconductivity

Aaron Farrell, P.-K. Wu, Y.-J. Kao, and T. Pereg-Barnea
Phys. Rev. B 94, 214424 – Published 22 December 2016

Abstract

On a square lattice, the Hubbard model at half filling reduces to the Heisenberg model and exhibits antiferromagnetism. When doped away from half filling this model gives rise to d-wave superconductivity. This behavior is reminiscent of the phenomenology of the cuprate family with their high Tcd-wave superconductivity and their antiferromagnetic parent compound. It is therefore interesting to study an extension of the Hubbard model which includes spin orbit coupling. We have previously studied this model away from half filling [see, for example, Farrell and Pereg-Barnea, Phys. Rev. B 89, 035112 (2014)] and found that the addition of spin-orbit coupling and Zeeman field leads to topological superconductivity with d+id pairing function. In this paper we are interested in the ‘parent compound’ of this state. Namely, we study the half filling, strong coupling limit of the square lattice Hubbard model with spin orbit coupling and Zeeman field. The strong coupling expansion of the model is a spin model which contains compass anisotropy and Dzyaloshinsky-Moriya interaction on top of the usual Heisenberg term. We analyze this spin model classically and find an incommensurate spin density wave (ISDW) for low Zeeman fields. This ISDW has a wave vector Q which deviates from (π,π) by an amount which is proportional to the spin-orbit coupling and can therefore serve as a signature. We study the stability of the ISDW phase using spin wave theory and find a stable and an unstable region. At higher but moderate Zeeman fields we find a tilted antiferromagnet and a ferromagnet at high Zeeman fields.

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  • Received 24 February 2014
  • Revised 28 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.214424

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Aaron Farrell1, P.-K. Wu2, Y.-J. Kao2,3,4, and T. Pereg-Barnea1

  • 1Department of Physics and Center for the Physics of Materials, McGill University, Montreal, QC, H3A 2T8, Canada
  • 2Department of Physics and Center of Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan
  • 3Center for Advanced Study in Theoretical Science, National Taiwan University, Taipei 10607, Taiwan
  • 4National Center of Theoretical Sciences, National Tsinghua University, Hsinchu 30013, Taiwan

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Issue

Vol. 94, Iss. 21 — 1 December 2016

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