Weyl semimetals with short-range interactions

Joseph Maciejko and Rahul Nandkishore
Phys. Rev. B 90, 035126 – Published 18 July 2014

Abstract

We construct a low-energy effective field theory of fermions interacting via short-range interactions in a simple two-band model of a Weyl semimetal on the cubic lattice and investigate possible broken-symmetry ground states through a one-loop renormalization group (RG) analysis. Using the symmetries of the noninteracting Hamiltonian to constrain the form of the interaction term leads to four independent coupling constants. We investigate the stability of RG flows towards strong coupling and find a single stable trajectory. In order to explore possible broken-symmetry ground states, we calculate susceptibilities in the particle-hole and particle-particle channels along this trajectory and find that the leading instability is towards a fully gapped spin-density wave (SDW) ground state. The sliding mode of this SDW couples to the external electromagnetic fields in the same way as the Peccei-Quinn axion field of particle physics. We also study the maximally symmetric version of our model with a single independent coupling constant. Possible ground states in this case are either gapless ferromagnetic states where the spin waves couple to the Weyl fermions like the spatial components of a (possibly chiral) gauge field, or a fully gapped spin-singlet Fulde-Ferrell-Larkin-Ovchinnikov superconducting state.

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  • Received 5 December 2013
  • Revised 12 June 2014

DOI:https://doi.org/10.1103/PhysRevB.90.035126

©2014 American Physical Society

Authors & Affiliations

Joseph Maciejko1,2 and Rahul Nandkishore1

  • 1Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1

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Issue

Vol. 90, Iss. 3 — 15 July 2014

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