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Detection of topological states in two-dimensional Dirac systems by the dynamic spin susceptibility

We discuss dynamic spin susceptibility (DSS) in two-dimensional (2D) Dirac electrons with spin-orbit interactions to characterize topological insulators. The imaginary part of the DSS appears as an absorption rate in response to a transverse ac magnetic field, just as in an electron spin resonance experiment for localized spin systems. We found that when the system is in a static magnetic field, the topological state can be identified by an anomalous resonant peak of the imaginary part of the DSS as a function of the frequency of the transverse magnetic field $ω$. In the absence of a static magnetic field, the imaginary part of the DSS becomes a continuous function of $ω$ with a threshold frequency $ω_{\rm c}$. In this case, the topological and the trivial phases can also be distinguished by the values of $ω_{\rm c}$ and by the line shapes. Thus the DSS is an experimentally observable physical quantity to characterize a topological insulator directly from bulk properties, without observing a topological transition.