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

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