  Quantum spin-liquids are strongly correlated phases of matter displaying a
highly entangled ground state. Due to their unconventional nature, finding
experimental signatures of these states has proven to be a remarkable
challenge. Here we show that the effects of local impurities can provide strong
signatures of a Dirac quantum spin-liquid state. Focusing on a gapless Dirac
quantum spin-liquid state as realized in NaYbO$_2$, we show that single
magnetic impurity coupled to the quantum spin-liquid state creates a resonant
spinon peak at zero frequency, coexisting the original Dirac spinons. We
explore the spatial dependence of this zero-bias resonance, and show how
different zero modes stemming from several impurities interfere. We finally
address how such spinon zero-mode resonances can be experimentally probed with
inelastic spectroscopy and electrically-driven paramagnetic resonance with
scanning tunnel microscopy. Our results put forward impurity engineering as a
means of identifying Dirac quantum spin-liquids with scanning probe techniques,
highlighting the dramatic impact of magnetic impurities in a macroscopically
entangled many-body ground state.
