  Quantum impurities serve as in-situ probes of the frustrated quantum magnets,
and Dirac spin liquids are an important class of quantum spin liquids. Here, we
present a general method, a combination of the Chern-Simons fermionization and
the Wess-Zumino-Witten theory, to study the quantum impurity in Dirac spin
liquids. Under the Chern-Simons fermionization, the gauge fluctuations are
apparently suppressed and the low-energy physics is described by a number of
Dirac valleys with valley-dependent pseudospin-momentum locking. The (2+1)D
effective theory can be further reduced into the (1+1)D Wess-Zumino-Witten
theory by rotational symmetry, where the pseudospin-exchange between Dirac
fermions and the impurity can then be solved by the non-Abelian bosonization.
Consequently, fixed points of Fermi liquid and non-Fermi liquid are identified,
respectively, depending on the relevance of the impurity scattering among the
Dirac valleys. This leads to experimental fingerprints for Dirac spin liquids,
including a Kondo-induced magneto-thermal effect, a non-monotonous thermal
conductivity during the crossover, and an anisotropic spin correlation
function.
