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Many physical phenomena can be understood by single-particle physics; that is, treating particles as non-interacting entities. When this fails, many-body interactions lead to spontaneous symmetry breaking and phenomena such as fundamental particles' mass generation, superconductivity and magnetism. Competition between single-particle and many-body physics leads to rich phase diagrams. Here we show that rhombohedral-stacked trilayer graphene offers an exciting platform for studying such interplay, in which we observe a giant intrinsic gap B42 meV that can be partially suppressed by an interlayer potential, a parallel magnetic field or a critical temperature B36 K. Among the proposed correlated phases with spatial uniformity, our results are most consistent with a layer antiferromagnetic state with broken time reversal symmetry. These results reflect the interplay between externally induced and spontaneous symmetry breaking whose relative strengths are tunable by external fields, and provide insight into other low-dimensional systems.

ABA-stacked trilayer graphene is a unique 2D electron system with mirror reflection symmetry and unconventional quantum Hall effect. We present low-temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν = -8, -2, 2, 6, and 10, which is in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau level (LL). Under an out-of-plane electric field E(perpendicular), we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E(perpendicular) selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.

The quantum Hall effect, in which a two-dimensional sample's Hall conductivities become quantized, is a remarkable transport anomaly commonly observed at strong magnetic fields. However, it may also appear at zero magnetic field if time-reversal symmetry is broken. Charge-neutral bilayer graphene is unstable to a variety of competing and closely related broken symmetry states, some of which have non-zero quantized Hall conductivities. Here we explore those states by stabilizing them with external fields. Transport spectroscopy measurements reveal two distinct states that have two quantum units of Hall conductivity, stabilized by large magnetic and electric fields, respectively. The majority spins of both phases form a quantum anomalous Hall state, and the minority spins constitute a Kekulé state with spontaneous valley coherence for phase I and a quantum valley Hall state for phase II. Our results shed light on the rich set of competing ordered states in bilayer graphene.

These authors contribute equally to this work.Keywords: graphene, suspended structure, strain engineering, conductance change, NEMS Abstract：We develop two types of graphene devices based on nanoelectromechanical systems (NEMS), that allows transport measurement in the presence of in situ strain modulation. Different mobility and conductance responses to strain were observed for single layer and bilayer samples. These types of devices can be extended to other 2D membranes such as MoS2, providing transport, optical or other measurements with in situ strain.TOC figure: