2012/03/31 by Bitan Roy
Materials Science · Mathematics · Physics and Astronomy · #Bilayer graphene #Condensed matter physics #Diamond and Carbon-based Materials Research #Ferromagnetism #Graphene #Graphene research and applications #Ground state #Magnetic field #Mathematics #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Scaling #Zeeman effect #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.89.201401
published as Phys. Rev. B, 89, 201401(R)(2014) · Published version: 5 pages, 2 figures (Supplementary: 6 pages, 2 figures); New references, typos corrected
openalex publication_date 2014/05/09 · arxiv created 2014/06/19 · arxiv updated 2014/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer antiferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the \ensuremathν=0 Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of recent experiments with realistic strengths for the ferromagnetic interaction. A component of the LAF order, parallel to the external magnetic field, gives birth to additional incompressible Hall states at filling \ensuremathν=\ifmmode±\else\textpm\fi2, whereas the remote hopping in BLG yields \ensuremathν=\ifmmode±\else\textpm\fi1 Hall states. Evolution of the LAF order in tilted magnetic fields, scaling of the gap at \ensuremathν=2, the effect of external electric fields on various Hall plateaus, and different possible hierarchies of fractional quantum Hall states are highlighted.