Detecting Quantum Spin Liquid Phases via Spin Hall Effect

In a quest to develop experimental probes to characterize exotic materials, we theoretically investigate the AC conductivity of a strongly spin-orbit coupled metal deposited atop a quantum spin liquid (QSL). In this bilayer setup, the transversely flowing spin current leads to a renormalization of the AC conductivity via Spin Hall effect. This elicits probing of the spin response function of the QSL adjacent to the metal. We illustrate this technique with the Kitaev honeycomb model ⏤ an exactly solvable QSL model ⏤ and study the evolution of the AC conductivity as the ground state changes from the gapped A phase to the gapless B phase of the model. The AC conductivity measurement is shown to be a viable probe of the phase diagram of the Kitaev model. This work lays a foundation for a broadband dynamical probe of QSLs based on electrical signals that complements existing spectroscopic techniques such as inelastic neutron and Raman scattering, and nuclear magnetic resonance.