In this talk, we consider unboundedness and concentration phenomenon of solutions to a degenerate drift-diffusion equation with the mass critical exponent. We proved that solutions does not remain bounded in time when the initial data has negative free energy under non-weight condition. Moreover, we show that the mass concentration phenomenon of radially symmetric solutions to our problem occurswith the sharp lower constant related to the best constant of the Hardy-Littlewood-Sobolev inequality and the concentration rate of the total mass. We note that the sharp lower constant can be estimated by the well-known value 8π when we take the limit with respect to the dimension to 2.

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