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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:

Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG), in which the real spin, orbital pseudospin and layer pseudospins of the lowest Landau level form spontaneous ordering. We observe intermediate quantum Hall plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only the in presence of an interlayer potential U⊥. In the phase space of U⊥ and filling factor ν, we observe an intriguing "hexagon" pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.Keywords: quantum Hall ferromagnetism, graphene, trilayer, rhombohedral stacking, Landau level crossing * Emails: kenosis101@gmail.com, yafisb@gmail.com; lau@physics.ucr.edu In the quantum Hall (QH) regime, when the energies of two or more Landau levels (LLs) are brought to alignment, the spinor language is often used to describe the different degrees of freedom, such as layer and orbital pseudospins, due to their close analogy to the spins in a twodimensional ferromagnet. When these LLs are less than completely full, competition between these degrees of freedom leads to formation of electronic states with spontaneous ordering of pseudospins, much like the spontaneous real spin alignment in a ferromagnet. For this reason, these symmetry-broken QH states are called QH ferromagnets, with real or pseudo-spin orderings that maybe easy-plane, i.e. akin to a XY Heisenberg magnet, or easy-axis, i.e. akin to an Ising ferromagnet. These QH ferromagnetic states provide a rich platform for investigation of the competition among different symmetries, as well as providing insight into the itinerant magnetism in standard magnets.The recent emergence of two-dimensional (2D) graphene provides new playground for multicomponent QH ferromagnetic states and the associated phase transitions 1-6 7-19 20-28 . With the advent of high mobility samples that may be either suspended 29,30 or supported on BN substrates 31,32 , and advanced device geometry such as dual-gates or split top gates [33][34][35] , few-layer graphene provides QH systems with unusual symmetries and unprecedented tunability.In particular, rhombohedral trilayer graphene is such a QH system with very flat bands near the charge neutrality point. Its LL energies are given bywhere N is an integer denoting the LL index, e the electron charge, v F~1 0 6 m/s the Fermi velocity of single layer graphene, γ 1~0 .3 eV the interlayer hopping energy, and h Planck's constant. The degeneracy between the N=0, 1 and 2 LLs, together with the spin and valley degrees of freedom, yield the 12-fold degeneracy of the lowest LL, and give rise to plateaus at filling factors ν=±6, ±10, ±14… Interactions and/or single particle effects lift this 12-fold degeneracy, leading to incompressible QH ferromagnetic states at intermediate fillings 36,37 , with ex...

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Conventionally, magnetism arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. It can also emerge in perfect lattices from nonmagnetic elements, such as that exemplified by the Stoner criterion. Here we report tunable magnetism in suspended rhombohedral-stacked few-layer graphene (r-FLG) devices with flat bands. At small doping levels (n ∼ 1011 cm–2), we observe prominent conductance hysteresis and giant magnetoconductance that exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by density and temperature and disappear at n > 1012 cm–2 or T > 5 K. These results are confirmed by first-principles calculations, which indicate the formation of a half-metallic state in doped r-FLG, in which the magnetization is tunable by electric field. Our combined experimental and theoretical work demonstrate that magnetism and spin polarization, arising from the strong electronic interactions in flat bands, emerge in a system composed entirely of carbon atoms.