${\mathbb{Z}}_2$ topological quantum paramagnet on a honeycomb bilayer

Abstract

Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected ${\mathbb{Z}}_2$ topological quantum paramagnet ({\em topological triplon insulator}) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial ${\mathbb{Z}}_2$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the ${\mathbb{Z}}_2$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the ${\mathbb{Z}}_2$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d${}^4$ Mott insulators, and their potential applications.

10.5 pages; (v2) minor changes

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• Three-dimensional topological magnon systems
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Dirac cones and mass terms in bosonic spectra
• Weyl-triplons in SrCu2(BO3)2
• Dirac Hamiltonians for bosonic spectra
• Fragility of ${\mathcal{Z}}_2$ topological invariant characterizing triplet excitations in a bilayer kagome magnet
• Electric field induced thermal Hall effect of triplons in the quantum dimer magnets $X$CuCl${}_3$ ($X=$ Tl, K)
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• Tuning bulk topological magnon properties with light-induced magnons
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices
• Flavor Nernst effects in quantum paramagnets
• Pinch points and half moons encode Berry curvature
• Scattering Theory of Chiral Edge Modes in Topological Magnon Insulators
• Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions
• Fate of Bosonic Topological Edge Modes in the Presence of Many-Body Interactions