Anomalous Hall Resistance in Bilayer Quantum Hall Systems

Abstract

We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the emergence of the phase current in a system where the interlayer phase coherence develops spontaneously. The phase current arranges itself to minimize the total energy of the system, as induces certain anomalous behaviors in the Hall current in the counterflow geometry and also in the drag experiment. They explain the recent experimental data for anomalous Hall resistances due to Kellogg et al. [M. Kellogg, I.B. Spielman, J.P. Eisenstein, L.N. Pfeiffer and K.W. West, Phys. Rev. Lett. \textbf{88} (2002) 126804; M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer and K.W. West, Phys. Rev. Lett. \textbf{93} (2004) 036801] and Tutuc et al. [E. Tutuc, M. Shayegan and D.A. Huse, Phys. Rev. Lett. \textbf{93} (2004) 036802] at $\nu =1$.

11 pages, 3 figures

References in corpus (11)

• Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Counterflow measurements in strongly correlated GaAs hole bilayers: evidence for electron-hole pairing
• Vanishing Hall Resistance at High Magnetic Field in a Double Layer Two-Dimensional Electron System
• Observation of Quantized Hall Drag in a Strongly Correlated Bilayer Electron System
• Double-layer quantum Hall antiferromagnetism at filling fraction nu=2/(odd integer)
• Canted antiferromagnetic and spin singlet quantum Hall states in double-layer systems
• Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems
• Ground-State Structure in $\nu =2$ Bilayer Quantum Hall Systems
• Topological Solitons in Noncommutative Plane and Quantum Hall Skyrmions
• Microscopic Theory of Skyrmions in Quantum Hall Ferromagnets

Cited by in corpus (2)

• Spin Supercurrent in the Canted Antiferromagnetic Phase
• Nambu-Goldstone modes and the Josephson supercurrent in the bilayer quantum Hall system