Detecting end states of topological quantum paramagnets via spin Hall noise spectroscopy

We theoretically study the equilibrium spin current fluctuations and the corresponding charge noise generated by the inverse spin Hall effect (ISHE) in a metal with strong spin-orbit coupling deposited on top of a quantum paramagnet. It is shown that the charge noise power spectra measured along different spatial axes can directly probe the different spin components of the boundary dynamic spin correlations of the quantum paramagnet. We report the utility of this ISHE-facilitated spin noise probe as a tool to unambiguously detect topological phase transitions in an S = 1/2 quantum spin ladder that hosts a trivial ground state of singlet product states, but topologically protected fractional spin excitations localized at its ends. Our work demonstrates the general usefulness of ISHE-mediated spin noise spectroscopy for the detection of topological phases in quantum paramagnets.