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We consider the thermodynamic effects of an electrically charged impurityimmersed in a two-dimensional two-component plasma, composed by particles withcharges $\pm e$, at temperature $T$, at coupling $\Gamma=e^2/(k_B T)=2$,confined in a large disk of radius $R$. Particularly, we focus on the analysisof the charge density, the correlation functions, and the grand potential. Ouranalytical results show how the charges are redistributed in the circulargeometry considered here. When we consider a positively charged impurity, thenegative ions accumulate close to the impurity leaving an excess of positivecharge that accumulates at the boundary of the disk. Due to the symmetry undercharge exchange, the opposite effect takes place when we place a negativeimpurity. Both the cases in which the impurity charge is an integer multiple ofthe particle charges in the plasma, $\pm e$, and a fraction of them areconsidered; both situations require a slightly different mathematicaltreatments, showing the effect of the quantization of plasma charges. The bulkand tension effects in the plasma described by the grand potential are notmodified by the introduction of the charged particle. Besides the effects dueto the collapse coming from the attraction between oppositely charged ions, anadditional topological term appears in the grand potential, proportional to$-n^2\ln(mR)$, with $n$ the dimensionless charge of the particle. This termmodifies the central charge of the system, from $c=1$ to $c=1-6n^2$, whenconsidered in the context of conformal field theories.

Screening of an electrically charged particle in a two-dimensional two-component plasma at $\Gamma=2$