Phase diagram for quantum Hall states in graphene

Abstract

We investigate integer and half-integer filling states (uniform and unidimensional stripe states respectively) for graphene using the Hartree-Fock approximation. For fixed filling factor, the ratio between the scales of the Coulomb interaction and Landau level spacing $g=(e^2/\epsilon \ell )/(\hslash v_F/\ell )$, with $\ell$ the magnetic length, is a field-independent constant. However, when $B$ decreases, the number of filled negative Landau levels increases, which surprisingly turns out to decrease the amount of Landau level mixing. The resulting states at fixed filling factor $\nu$ (for $\nu$ not too big) have very little Landau level mixing even at arbitrarily weak magnetic fields. Thus in the density-field phase diagram, many different phases may persist down to the origin, in contrast to the more standard two dimensional electron gas, in which the origin is surrounded by Wigner crystal states. We demonstrate that the stripe amplitudes scale roughly as $B$, so that the density waves ``evaporate'' continuously as $B\to 0$. Tight-binding calculations give the same scaling for stripe amplitude and demonstrate that the effect is not an artifact of the cutoff procedure used in the continuum calculations.

9 pages, 6 figures, 3 tables, submitted to Physical Review B

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Cited by in corpus (4)

• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• The effect of electron dielectric response on the quantum capacitance of graphene in a strong magnetic field
• Local density of states of electron-crystal phases in graphene in the quantum Hall regime
• A Hartree-Fock study of the $\nu =0$ quantum Hall state of monolayer graphene with short range interactions