Theory predicts that double layer systems realize two-component composite fermions, which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layer-correlated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors $ u=3/7$, $4/9$, $6/11$, $4/7$, $3/5$, $2/3$, and $4/5$) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings $ u=3/7$ and $ u=3/5$ are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as $ u=3/7$, interlayer correlations are predicted to survive to surprisingly large interlayer separations.
Download