Thermal Hall Signatures of Distinct Schwinger-Boson Flux Sectors on the Honeycomb Lattice

Abstract

Thermal transport offers a bulk probe of charge-neutral excitations in frustrated magnets. It remains challenging, however, to determine whether such transport can distinguish different parton mean-field structures of the same spin system. This question is particularly relevant on the honeycomb lattice, where distinct $0$-flux, $\pi$-flux, and chiral $\pi /2$-flux sectors have been proposed. In this paper, we compare self-consistent saddle-point solutions in these three sectors for a frustrated $J_1-J_2$ Heisenberg model with a next-nearest-neighbor Dzyaloshinskii-Moriya interaction and a perpendicular magnetic field. Using finite-temperature Schwinger-boson mean-field theory and the Kubo formula for bosonic Bogoliubov-de Gennes systems, we evaluate the intrinsic spinon thermal Hall conductivity. At a common parameter point where all three branches remain gapped, the $0$-flux response is positive and the $\pi$-flux response is negative for $D>0$ and $h>0$ under the sign conventions used in this paper, whereas the $\pi /2$-flux response changes sign with increasing temperature. We further show that a projective symmetry combining a sixfold rotation with time reversal forces the zero-field response of a fixed chiral $\pi /2$-flux domain to vanish. Within the mean-field regime examined in this paper, the sign and temperature dependence of ${\kappa }_{xy}/T$ therefore provide a flux-sensitive transport signature.

main text: 14 pages, 9 figures; supplemental information: 6 pages, 3 figures