Controllable Driven Phase Transitions in Fractional Quantum Hall States in Bilayer Graphene

Here we report from our theoretical studies that, in biased bilayer graphene, one can induce phase transitions from an incompressible fractional quantum Hall state to a compressible state by tuning the band gap at a given electron density. The nature of such phase transitions is different for weak and strong interlayer coupling. Although for strong coupling more levels interact there is a lesser number of transitions than for the weak coupling case. The intriguing scenario of tunable phase transitions in the fractional quantum Hall states is unique to bilayer graphene and has never before existed in conventional semiconductor systems.

Figure 1

A few lowest Landau levels of the conduction band (for two valleys) as a function of the bias potential, $\Delta U$, for different values of interlayer coupling: (a) $t=30\mathrm{meV}$, (b) $t=150\mathrm{meV}$, and (c) $t=300\mathrm{meV}$, and a magnetic field of 15 Tesla. The numbers next to the curves denote the corresponding Landau levels. The Landau levels where the $\frac{1}{3}$-FQHE can be observed are drawn as blue (dark gray) and green (light gray) filled dots. The green (light gray) dots correspond to the Landau levels where the FQHE states are identical to that of a monolayer of graphene. The red (medium gray) dots represent Landau levels with weak $\frac{1}{3}$-FQHE and the open dots for those where the FQHE is absent. In (a), the dashed lines labeled by (i) and (ii) illustrate two situations: (i) under a constant gate voltage and variable bias potential; (ii) under a constant bias potential and variable gate voltage.

Figure 2

Low-energy excitation spectra of the $\frac{1}{3}$-FQHE states (eight electrons) in the Landau levels (a) $1_{(2)}^{(+)}$, and (b) $1_{(1)}^{(+)}$, shown for different values of the bias potential (the numbers next to the lines are the values of $\Delta U$ in meV). The system is fully spin polarized. The interlayer hopping integral is set to 30 meV and the magnetic field is 15 Tesla. The flux quanta is $2S=21$. The solid dot at $L=0$ depicts the ground state. The energy unit is ${\epsilon }_c=e^2/\kappa {\ell }_0$.

Figure 3

The FQHE gaps are shown for different Landau levels. The labels next to the lines correspond to the labeling of Landau levels shown in Fig. 1. $\nu =\frac{1}{3}$-FQHE (eight electron) for (a) $\Delta U=10\mathrm{meV}$, and (b) $\Delta U=300\mathrm{meV}$. All systems are fully spin polarized.