Probing one-dimensional systems via noise magnetometry with single spin qubits

The study of exotic one-dimensional states, particularly those at the edges of topological materials, demand new experimental probes that can access the interplay between charge and spin degrees of freedom. One potential approach is to use a single spin probe, such as a Nitrogen Vacancy center in diamond, which has recently emerged as a versatile tool to probe nanoscale systems in a non-invasive fashion. Here we present a theory describing how noise magnetometry with spin probes can directly address several questions that have emerged in experimental studies of 1D systems, including those in topological materials. We show that by controlling the spin degree of freedom of the probe, it is possible to measure locally and independently local charge and spin correlations of 1D systems. Visualization of 1D edge states, as well as sampling correlations with wavevector resolution can be achieved by tuning the probe-to-sample distance. Furthermore, temperature-dependent measurements of magnetic noise can clearly delineate the dominant scattering mechanism (impurities vs. interactions) -- this is of particular relevance to quantum spin Hall measurements where conductance quantization is not perfect. The possibility to probe both charge and spin excitations in a wide range of length scales opens new pathways to bridging the large gap between atomic scale resolution of scanning probes and global transport measurements.