Collective modes of CP^{3} skyrmion crystals in quantum Hall ferromagnets
Abstract
The twodimensional electron gas (2DEG) in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor ν=1 even in the absence of tunneling between the layers. This system, which can be described as a quantum Hall pseudospin ferromagnet, has lowenergy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor ν=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 (Δ_{SAS}) , Zeeman coupling (Δ_{Z}) , or electrical bias (Δ_{b}) , these textured crystal states can involve spin, pseudospin, or both intertwined. This last case is a “ CP^{3} skyrmion crystal.” In this paper, we present a comprehensive numerical study of the collective excitations of these textured crystals using the generalized randomphase 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 pseudospinskyrme crystal at finite tunneling has only the phonon mode. For Δ_{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 nonvanishing symmetrybreaking fields Δ_{SAS} , Δ_{Z} , and Δ_{b} . In addition, a second mode with a very small gap is present in the spectrum. We present dispersion relations for the different lowenergy modes of these various crystals as well as their physical interpretations.
 Publication:

Physical Review B
 Pub Date:
 September 2007
 DOI:
 10.1103/PhysRevB.76.125320
 arXiv:
 arXiv:0708.0029
 Bibcode:
 2007PhRvB..76l5320C
 Keywords:

 73.21.b;
 73.22.Lp;
 73.20.Qt;
 Electron states and collective excitations in multilayers quantum wells mesoscopic and nanoscale systems;
 Collective excitations;
 Electron solids;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 16 pages and 12 eps figures