Merons in a finite quantum Hall system

Abstract

We study quasiparticle states in a finite $\ensuremath{\nu}=1$ spin (as an additional degree of freedom) quantum Hall system. The skyrmion (topological) quasiparticle states are well established in the infinite system, but in finite systems, in the effective mean-field pictures that we have, as a rule, they are not eigenstates of hamiltonian and some other generators of the system symmetries. We present a class of states, which are eigenstates of certain combinations of the generators and are similar in structure to the orbital angular momentum eigenstates of the Laughlin quasihole in the same system. We refer to the states as states of a meron. They have an upper limit on the mean orbital angular momentum, and the limit defines an effective edge, at a distance less than the system radius, in an effective quasiparticle description of the meron. Remarkably, the meron edge (as the usual quasihole edge) is characterized by a power-law decay of the single-particle, static correlator defined between positional coherent states of the meron.