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We discuss the excitation spectra around the Dirac node on a surface of athree-dimensional topological insulator. By using the diagrammatic expansion,we show that the coupling of an electron with the gauge field in the presenceof impurity scatterings opens a gap around the Dirac node. The results areconsistent with a recent experimental finding by T. Sato,et. al.[ Nature Phys.\textbf{7}, 840 (2011)]. We also discuss the consistency between the presentresults and the bulk-boundary correspondence of the topological insulator inthe presence of time reversal symmetry. The conclusion can be applied any twodimensional massless fermions.

Gapped energy spectra around the Dirac node at the surface of a 3D topological insulator in the presence of the time-reversal symmetry