Session M2: Invited Session: Interaction-Driven Quantum Hall States in Graphene

Unconventional Sequence of Fractional Quantum Hall States in Graphene

Electronic compressibility is a powerful tool for the study of correlated electron phases in two-dimensional electron systems. Using a scanning single-electron transistor, we have measured the local electronic compressibility of suspended graphene in the quantum Hall regime. The local nature of the measurement technique allows us to probe exceptionally clean regions of graphene, revealing delicate many-body effects that are obscured by disorder in global transport studies. In this talk, I will review recent measurements of the fractional quantum Hall effect (FQHE) in graphene. We observe a multitude of FQH states that follow the standard composite fermion sequence between $\nu =$ 0 and 1, but only occur at even-numerator fractions between $\nu =$ 1 and 2, suggesting that an underlying symmetry remains. Moreover, we observe a series of phase transitions in the FQH states between $\nu =$ 0 and 1 that are marked by a decreased energy gap and a narrow region of negative compressibility that cuts across the FQH state. We use a simple model based on crossing composite fermion Landau levels with different internal degrees of freedom to reproduce much of the experimental behavior. Our results provide insight into the interplay between electron-electron interactions and the spin and valley symmetries of graphene.   

Phase diagram and edge excitations of the $\nu=0$ quantum Hall state in graphene

The interaction-induced broken-symmetry incompressible quantum Hall states in graphene at integer and fractional filling factors have by now been firmly established in transport and compressibility measurements. However, identifying their precise nature (e.g., how the symmetry is broken) still remains a tough challenge: on the experimental side, transport and compressibility probes do not provide direct information about the physical order; on the theoretical side, the presence of additional to spin discrete degrees of freedom, valleys, results in a variety of competing phases in this multicomponent system. As the prime example of this rich behavior, I will present a generic phase diagram for the intriguing $\nu=0$ state, obtained within the framework of quantum Hall ``ferromagnetism.'' The diagram consists of the canted antiferromagnetic, ferromagnetic, charge-density-wave (charge-layer-polarized), and Kekul\'{e} (interlayer-coherent) phases in monolayer (bilayer). I will then discuss the edge excitations of the $\nu=0$ state. Remarkably, the edge excitations are nonuniversal (e.g., can be gapped or gapless) and crucially depend on which phase is realized in the bulk of the system. Besides being of considerable theoretical interest, these unprecedented properties simultaneously allow one to infer about the nature of the phases from the transport experiments. I will present arguments based on this analysis and existing data why the insulating $\nu=0$ state realized in real bilayer (and possibly, monolayer) graphene is likely to be canted antiferromagnetic. Finally, I will mention how this theoretical framework can be generalized to fractional quantum Hall states in graphene, which could shed light on some of the puzzling features of the recent experiments.   

Tunable electron interactions and robust non-Abelian quantum Hall states in graphene and other Dirac materials

Discovery of the fractional quantum Hall effect inspired a concept of quasiparticles with non-Abelian exchange statistics. However, a major limitation for experimental studies of non-Abelian quasiparticles in traditional GaAs-based 2d systems is their lack of tunability: the effective electron interactions in such systems are fixed at values which make non-Abelian states either absent of very fragile. Therefore it is desirable to find alternative, tunable 2d systems that host robust non-Abelian quantum Hall states. In this talk, we will discuss the phase diagram of fractional quantum Hall states in recently discovered 2d Dirac materials (graphene, bilayer graphene, topological insulators). We will show that the effective interactions in these materials can be naturally tuned in a broad range, in contrast to GaAs. This tunability is achieved by external fields that control the mass gap of Dirac fermions. Alternatively, the effective interactions can be controlled by engineering the dielectric environment of the 2d Dirac electron gas. We will demonstrate that the tunability of interactions in Dirac materials allows one to stabilize non-Abelian states, as well as to drive phase transitions between various correlated phases (quantum Hall states, Fermi-liquid-like states, and states with broken translational symmetry) in a controlled manner. Connecting to experiments, we will argue that a very promising candidate material for tuning interactions and stabilizing non-Abelian states is bilayer graphene, where the gap can be naturally controlled by perpendicular electric field. Our study provides a realistic route towards engineering robust fractional and non-Abelian quantum Hall states in graphene and other Dirac materials. \\[4pt] [1] Z. Papic, R. Thomale, D. A. Abanin,Phys. Rev. Lett. 107, 176602 (2011).\\[0pt] [2] Z. Papic, D. A. Abanin, Y. Barlas, R. N. Bhatt, Phys. Rev. B 84, 241306(R) (2011).\\[0pt] [3] D. Abanin, Z. Papic, Y. Barlas, R. N. Bhatt, New J. Phys. 14, 025009 (2012).   

Superconducting states in graphene

In spite of the remarkable electronic properties of graphene, which include the existence of massless Dirac quasiparticles, the low density of states near the Dirac points seems to conspire against the formation of new many body ground states. In this context, the search for intriscic superconductivity in graphene has involved either combining graphene with other materials [1], or else exploring ways to modify the electronic density of states at the Fermi level. In this talk, after discussing the classification of symmetry states in the honeycomb lattice and analysing the general thermodynamic properties for Dirac fermion superconductors [2], I will describe a few promissing mechanisms to induce superconductivity in graphene. In particular, I will show that in the situation where strain effects lead to a reconstruction of the vacuum into a discrete spectrum of Landau levels due to pseudo magnetic fields, which preserve overall time reversal symmetry, superconductivity is quantum critical at integer filling of the Landau levels, when the system is incompressible. At partial filling, the quenching of the kinetic energy due to the Landau levels leads to a crossover to a non-Fermi liquid regime, where the critical temperature scales linearly with the coupling in the weak coupling limit. I will show that the critical temperature can be orders of magnitude larger than in conventional weak coupling superconductors, and may be triggered by phonons.\\[4pt] [1] B. Uchoa, A. H. Castro Neto, Physical Review Letters 98, 146801 (2007);\\[0pt] [2] V. N. Kotov, B. Uchoa et al., Reviews of Modern Physics 84, 1067 (2012).