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The nuclear spin relaxation time $T_1$ is calculated taking account of thecontributions from orbital currents of Dirac electrons. We consider a simplemodel of non-interacting Dirac electron gas in the three-dimensional bulksystem. The obtained result shows $T^3$ dependence of $1/T_1$ at temperatures$T$ above the energy gap. This temperature dependence agrees qualitatively withthe recent $\beta$-NMR experiment on the bulk of the topological insulator$\mathrm{Bi}_{0.9}\mathrm{Sb}_{0.1}$.

Nuclear Spin Relaxation Time due to the Orbital Currents in Dirac Electron Systems