Cubic hastatic order in the two-channel Kondo-Heisenberg model

Abstract

Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel symmetry breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with ${\Gamma }_3$ non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic order necessarily breaks time-reversal symmetry, but the spatial arrangement of the hybridization spinor can be either uniform (ferrohastatic) or break additional lattice symmetries (antiferrohastatic). The experimental signatures of both orders are presented in detail, and include tiny conduction electron magnetic moments. Interestingly, there can be several distinct antiferrohastatic orders with the same moment pattern that break different lattice symmetries, revealing a potential experimental route to detect the spinorial nature of the hybridization. We employ an SU(N) fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields.

arXiv comment28 pages, 32 figures

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• Critical theory of non-Fermi liquid fixed point in multipolar Kondo problem
• Large-N Approach to the Two-Channel Kondo Lattice
• Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field
• Field-induced Ferrohastatic Order in Cubic Non-Kramers Doublet Systems
• Emergent Spinon Dispersion and Symmetry Breaking in Two-Channel Kondo Lattices
• Mutual information, quantum phase transition, and phase coherence in Kondo systems
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• Signatures of hidden octupolar order from nonlinear Hall effects
• Development of long-range phase coherence on the Kondo lattice
• Dynamic mass generation and topological order in overscreened Kondo lattices
• Unconventional orbital ordering and emergent dimensional reduction in fulleride superconductors
• Evolution of non-Kramers Doublets in Magnetic Field PrNi${}_2$Cd${}_{20}$ and PrPd${}_2$Cd${}_{20}$
• Quantum Criticality Enabled by Intertwined Degrees of Freedom
• Topological ground state degeneracy of the two-channel Kondo lattice
• Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice
• Antiferromagnetism and Stripe Channel Order in the $\mathrm{SU}(N)$-Symmetric Two-Channel Kondo Lattice Model
• Unified Theory of Hastatic order and Antiferromagnetism in URu${}_2$Si${}_2$
• Higher-Dimensional Chirally Stabilized Fixed Points and Their Deformations