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

TL;DR

This paper analytically studies how a charged impurity affects charge distribution, correlations, and thermodynamics in a 2D two-component plasma at coupling , revealing charge redistribution patterns and a topological term altering the system's conformal field theory properties.

Contribution

It provides a detailed analytical analysis of charge redistribution and thermodynamic effects caused by a charged impurity in a 2D plasma at  coupling, including a topological term in the grand potential.

Findings

Charges redistribute near the impurity depending on its sign.

A topological term proportional to n^2ln(mR) appears in the grand potential.

The central charge is modified from 1 to 1-6n^2 due to the impurity.

Abstract

We consider the thermodynamic effects of an electrically charged impurity immersed in a two-dimensional two-component plasma, composed by particles with charges $\pm e$, 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 analysis of the charge density, the correlation functions, and the grand potential. Our analytical results show how the charges are redistributed in the circular geometry considered here. When we consider a positively charged impurity, the negative ions accumulate close to the impurity leaving an excess of positive charge that accumulates at the boundary of the disk. Due to the symmetry under charge exchange, the opposite effect takes place when we place a negative impurity. Both the cases in which the impurity charge is an integer multiple of the particle charges in the plasma, $\pm e$, and a fraction of them are considered; both situations require a slightly different mathematical treatments, showing the effect of the quantization of plasma charges. The bulk and tension effects in the plasma described by the grand potential are not modified by the introduction of the charged particle. Besides the effects due to the collapse coming from the attraction between oppositely charged ions, an additional topological term appears in the grand potential, proportional to $-n^2\ln(mR)$, with $n$ the dimensionless charge of the particle. This term modifies the central charge of the system, from $c=1$ to $c=1-6n^2$, when considered in the context of conformal field theories.