Itinerant fermions on a triangular lattice: unconventional magnetism and other ordered states

Abstract

We consider a system of 2D fermions on a triangular lattice with well separated electron and hole pockets of similar sizes, centered at certain high-symmetry-points in the Brillouin zone. We first analyze Stoner-type spin-density-wave (SDW) magnetism. We show that SDW order is degenerate at the mean-field level. Beyond mean-field, the degeneracy is lifted and is either $120^{\circ }$ "triangular" order (same as for localized spins), or a collinear order with antiferromagnetic spin arrangement on two-thirds of sites, and non-magnetic on the rest of sites. We also study a time-reversal symmetric directional spin bond order, which emerges when some interactions are repulsive and some are attractive. We show that this order is also degenerate at a mean-field level, but beyond mean-field the degeneracy is again lifted. We next consider the evolution of a magnetic order in a magnetic field starting from an SDW state in zero field. We show that a field gives rise to a canting of an SDW spin configuration. In addition, it necessarily triggers the directional bond order, which, we argue, is linearly coupled to the SDW order in a finite field. We derive the corresponding term in the Free energy. Finally, we consider the interplay between an SDW order and superconductivity and charge order. For this, we analyze the flow of the couplings within parquet renormalization group (pRG) scheme. We show that magnetism wins if all interactions are repulsive and there is little energy space for pRG to develop. However, if system parameters are such that pRG runs over a wide range of energies, the system may develop either superconductivity or an unconventional charge order, which breaks time-reversal symmetry.

24 pages, 9 figures; comments are welcome

References in corpus (20)

• High-temperature superconductivity in iron-based materials
• Near-degeneracy of several pairing channels in multiorbital models for the Fe-pnictides
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• To What Extent Iron-Pnictide New Superconductors Have Been Clarified: A Progress Report
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Unusual ordered phases of highly frustrated magnets: a review
• The key ingredients of the electronic structure of FeSe
• Superconductivity and spin-density-waves in multi-band metals
• The origin of nematic order in FeSe
• Quantum stabilization of 1/3-magnetization plateau in Cs_2CuBr_4
• Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
• Competing orders in FeAs layers
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• Electronic correlations stabilizing time-reversal broken chiral superconductivity in single-trilayer TiSe${}_2$
• Interplay between magnetism, superconductivity, and orbital order in a 5-pocket model for iron-based superconductors - a parquet renormalization group study
• Competing instabilities, orbital ordering and splitting of band degeneracies from a parquet renormalization group analysis of a 4-pocket model for iron-based superconductors: application to FeSe
• Spontaneous quantum Hall effect via thermally induced quadratic Fermi point
• Half-magnetization plateau in a Heisenberg antiferromagnet on a triangular lattice
• Orbital loop currents in iron-based superconductors
• Half-metallic magnetization plateaux

Cited by in corpus (2)

• Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe${}_2$
• Helical spin liquid in a triangular XXZ magnet from Chern-Simons theory