Collective modes of CP(3) Skyrmion crystals in quantum Hall ferromagnets

TL;DR

This paper investigates the collective excitations of CP(3) Skyrmion crystals in quantum Hall ferromagnets, revealing various gapless modes and their dependence on system parameters through comprehensive numerical analysis.

Contribution

It provides the first detailed numerical study of collective modes in CP(3) Skyrmion crystals, highlighting the effects of symmetry-breaking fields and different energy scales.

Findings

Identifies gapless phonon and Goldstone modes in spin Skyrmion crystals.

Demonstrates the breakup of Skyrmions into merons at zero Zeeman coupling.

Discovers a U(1) gapless mode and a nearly gapless mode in CP(3) Skyrmion crystals.

Abstract

The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseudospin, or both intertwined. In this article, we present a comprehensive numerical study of the collective excitations of these textured crystals using the GRPA. For the pure spin case, at finite Zeeman coupling the state is a Skyrmion crystal with a gapless phonon mode, and a separate Goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent Skyrmions break up, and the resulting state is a meron crystal with 4 gapless modes. In contrast, a pure pseudospin Skyrme crystal at finite tunneling has only the phonon mode. For Delta_SAS=0, the state evolves into a meron crystal and supports an extra gapless U(1) mode in addition to the phonon. For a CP(3) Skyrmion crystal, we find a U(1) gapless mode in the presence of the symmetry-breaking fields. In addition, a second mode with a very small gap is present in the spectrum.