## Phase diagram for quantum Hall states in graphene

##### Date

##### Authors

Wang, Jianhui

Iyengar, A.

Fertig, H. A.

Brey, L.

##### Journal Title

##### Journal ISSN

##### Volume Title

##### Publisher

##### Abstract

##### Description

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 $g=(e^2/\epsilon \ell)/(\hbar
v_F/\ell)$, 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.

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

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

##### Keywords

Condensed Matter - Mesoscale and Nanoscale Physics