Session Z27: Invited Session: Interaction Driven Broken Symmetry States in Bilayer Graphene

Theoretical Approach to Many-body Instabilities in Bilayer Graphene

I will review current theoretical approach to electron-electron interaction driven many-body instabilities in bilayer graphene at the neutrality point. The role of competing interactions and the dependence of different ordering tendencies on the range of the interaction will be examined. In particular, I will argue that within the renormalization group approach, for longer range interaction giving predominantly forward scattering, the leading ordering tendency is towards a gapless electronic nematic state. For shorter range interactions giving additional back scattering comparable to the forward scattering, the leading ordering tendency is towards a gapped Neel antiferromagnet. These results will be discussed in the context of recent experiments reporting signatures of broken symmetry states in suspended bilayer graphene.   

Interaction-Driven Spectrum Reconstruction in Bilayer Graphene

The nematic phase transition in various two-dimensional electronic systems is a fascinating subject of an ongoing investigation. Driven by electron-electron interactions it represents a new class of strongly correlated electronic ground states. Thus it is extremely important and interesting to expand the list of materials where such transitions are observed to those with particularly unusual electronic dispersion. Here we show indications that bilayer graphene -- a truly two-dimensional material with complex chiral electronic spectrum -- undergoes such transition. This is especially surprising as no interaction effects have been observed so far in either mono- or bilayer graphene without a help of magnetic field. Gaining access to low-energy physics in bilayer graphene devices (by suspending our samples and achieving quasiparticle mobilities larger than 10$^{6}$ cm$^{2}$/V$\cdot $s) allowed us to observe strong spectrum reconstructions and electron topological transitions which we attribute being due to such nematic transition.   

Spontaneous Quantum Hall Liquids

Driven by electron-electron interactions, bilayer graphene and its thicker cousins, chirally (ABC) stacked multilayers, exhibit a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers, because of their flat touching bands and large pseudospin chiralities. These gapped states are accompanied by large momentum space Berry curvatures and different types of topological orders. These competing ground states are distinguished by their flavor Hall conductivities, orbital magnetizations, edge state properties, and response to external fields. These spontaneous quantum Hall (SQH) states at zero field smoothly evolve into quantum Hall ferromagnet states at finite field. Various phase transitions occur by tuning carrier densities, temperature, and external fields. Recently, SQH states have started to be observed and explored in transport and Hall experiments on suspended devices with dual gates.   

Interaction-Driven Insulating States in Bilayer Graphene

Bilayer graphene (BLG) at the charge neutrality point (CNP) is unstable to electronic interactions, and expected to host a ground state with spontaneously broken symmetries. Here I will present our transport spectroscopy measurements on singly- and dual-gated suspended BLG devices, which have field effect mobility values up to 250,000 and 100,000 cm$^2$/Vs, respectively. We observe an insulating state at CNP with a gap $\sim $2 meV, which can be closed by elevated temperature, finite doping or a perpendicular electric field of either polarity. For magnetic field B$>$1T, the gap increases linearly with B. Our work contributes towards understanding the rich interaction-driven physics in BLG.   

Electronic structure of multilayer graphene

The single-particle low-energy Hamiltonian of bilayer graphene describes chiral quasiparticles with a dominantly parabolic dispersion exhibiting Berry phase 2$\pi$. This chiral Hamiltonian produces a doubly-degenerate zero-energy Landau level incorporating two different orbital states with the same energy. Taking into account spin and valley degeneracies, the zero-energy Landau level in a bilayer is eightfold degenerate, as compared to the fourfold degeneracy of other bilayer states and the fourfold degeneracy of all levels in a monolayer. Such levels can be split by interlayer asymmetry, due to the presence of an external gate or doping, or by interaction effects. This talk will describe the electronic behavior of multilayer graphene, focusing on three, four and five layers. The goal will be to identify features that are distinct from those observed in monolayers and bilayers, and to highlight effects - such as level splitting and crossing - that can be explained either within the single-particle picture or that require an understanding of electronic interactions. For example, the low-energy Hamiltonian of ABA-stacked multilayer graphene may be partially diagonalized into an approximate block-diagonal form, with each diagonal block contributing parabolic bands except for an additional block describing Dirac-like bands with a linear dispersion in a multilayer with an odd number of layers. By taking into account the symmetry of the crystal structure, it is possible to fully include the band parameters and to analyze their effect on the block-diagonal Hamiltonian. Next-nearest-layer couplings are shown to be particularly important in determining the low-energy spectrum and the phase diagram of the quantum Hall conductivity by causing energy shifts, level anti-crossings, and valley splitting of the low-lying Landau levels. \\[4pt] This work was done in collaboration with Mikito Koshino of the Department of Physics, Tohoku University, Sendai 980-8578, Japan.