Freezing of an unconventional two-dimensional plasma

TL;DR

This paper investigates phase transitions in an unconventional two-dimensional two-component plasma on a sphere, revealing a freezing transition and a BKT transition, with implications for quantum Hall states and plasma crystallization.

Contribution

It introduces a model with two Coulomb interactions and identifies distinct melting and binding transitions, expanding understanding of plasma phase behavior.

Findings

Freezing transition at Q_1^2 ≈ 140 indicating Wigner crystal formation.

BKT transition at Q_2^2 ≈ 4 leading to molecule formation.

The phase diagram features two independent transitions, forming a rectangular phase space.

Abstract

We study an unconventional two-dimensional, two-component classical plasma on a sphere, with emphasis on detecting signatures of melting transitions. This system is relevant to Ising-type quantum Hall states, and is unconventional in the sense that it features particles interacting via two different two-dimensional Coulomb interactions. One species of particles in the plasma carries charge of both types (Q_1,Q_2), while the other species carries only charge of the second type (0,-Q_2). We find signatures of a freezing transition at Q_1^2 approximately 140. This means that the species with charge of both types will form a Wigner crystal, whereas the species with charge of the second type also shows signatures of being a Wigner crystal, due to the attractive inter-component interaction of the second type. Moreover, there is also a Berezinskii-Kosterlitz-Thouless phase transition at Q_2^2 approximately 4, at which the two species of particles bind to form molecules that are neutral with respect to the second Coulomb interaction. These two transitions appear to be independent of each other, giving a rectangular phase diagram. As a special case, Q_2=0 describes the (conventional) two-dimensional one-component plasma. Our study is consistent with previous studies of this plasma, and sheds new light on the freezing transition of this system.