Abstract
The two-dimensional electron gas (2DEG) in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor even in the absence of tunneling between the layers. This system, which can be described as a quantum Hall pseudospin ferromagnet, has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor , 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 , Zeeman coupling , or electrical bias , these textured crystal states can involve spin, pseudospin, or both intertwined. This last case is a “ skyrmion crystal.” In this paper, we present a comprehensive numerical study of the collective excitations of these textured crystals using the generalized random-phase approximation. 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 four gapless modes. In contrast, a pure pseudospin-skyrme crystal at finite tunneling has only the phonon mode. For , the state evolves into a meron crystal and supports an extra gapless [U(1)] mode in addition to the phonon. For a skyrmion crystal, we find a U(1) gapless mode in the presence of nonvanishing symmetry-breaking fields , , and . In addition, a second mode with a very small gap is present in the spectrum. We present dispersion relations for the different low-energy modes of these various crystals as well as their physical interpretations.
5 More- Received 31 July 2007
DOI:https://doi.org/10.1103/PhysRevB.76.125320
©2007 American Physical Society