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Two-dimensional (2D) disordered superconductor (SC) in class D exhibits adisorder-induced quantum multicritical phenomenon among diffusive thermal metal(DTM), topological superconductor (TS), and conventional localized (AI) phases.To characterize the quantum tricritical point where these three phases meet, wecarry out a two-loop renormalization group (RG) analysis for 2D Dirac fermionwith random mass in terms of the $\epsilon$-expansion in the spatial dimension$d=2-\epsilon$. In 2D ($\epsilon=0$), the random mass is marginally irrelevantaround a clean-limit fixed point of the gapless Dirac fermion, while thereexists an IR unstable fixed point at finite disorder strength that correspondsto the tricritical point. The critical exponent, dynamical exponent, andscaling dimension of the (uniform) mass term are evaluated around thetricritical point by the two-loop RG analysis. Using a mapping between aneffective theory for the 2D random-mass Dirac fermion and the (1+1)-dimensionalGross-Neveu model, we further deduce the four-loop evaluation of the criticalexponent, and the scaling dimension of the uniform mass around the tricriticalpoint. Both the two-loop and four-loop results suggest that criticalities of aAI-DTM transition line as well as TS-DTM transition line are controlled byother saddle-point fixed point(s) at finite uniform mass.

Renormalization group analysis of Dirac fermions with random mass