In rhombohedral-stacked few-layer graphene, the very flat energy bands near the charge neutrality point are unstable to electronic interactions, giving rise to states with spontaneous broken symmetries. Using transport measurements on suspended rhombohedral-stacked tetralayer graphene, we observe an insulating ground state with a large interaction-induced gap up to 80 meV. This gapped state can be enhanced by a perpendicular magnetic field, and suppressed by an interlayer potential, carrier density, or a critical temperature of ~ 40 K.Since 2004, graphene has rapidly become an extra-ordinary 2D electron system for low dimensional physics, as it hosts massless Dirac fermions exhibiting an unconventional quantum Hall effect with a with a Berry's phase of π[1,2]. More recently, the few-layer "cousins" of monolayer graphene (MLG) have also attracted significant attention, as they constitute highly unusual, fascinating 2D platforms [3][4][5][6]. Like MLG, they are atomically thin membranes with chiral charge carriers; however, they differ from MLG in band structure, crystal symmetries, and strength of electronic interactions, all of which have profound effects on their electronic properties[7-10].Few-layer graphene (FLG) has two natural stable allotropes which can be distinguished by Raman spectroscopy [11,12]. ABA or Bernal stacking is the most stable and abundant form found in 85% of natural graphite. ABC or rhombohedral stacking, which occurs in ~14% of bulk graphite, obeys inversion symmetry, and its dispersion can be approximated as simply E~k M , where k is the wave vector and M the number of layers [13]. Thus, rhombohedral-stacked FLG (r-FLG) is highly unusual in the very flat bands near the charge neutrality, which host large and even diverging (for M>2) density of states and extremely large electronic interactions. The interaction parameter, r s , also known as the Wigner-Seitz radius, is the ratio of the average electron Coulomb interaction energy to the Fermi energy, given by r s ∝ n −(M −1)/2 , where n is charge density and M is the power of the dispersion relation. For MLG, M=1, r s = e 2 / ε r !v F~2 .2 in suspended MLG, independent of density. Here, e is the electron charge, ε r is the background dielectric constant, ~1 for suspended graphene, ħ is reduced Planck's constant and v F ~ 10 6 m/s is the Fermi velocity. For bilayer graphene (BLG) and rhombohedral-stacked trilayer (r-TLG) and tetralayer (r-4LG) graphene, r s ∝ !!/! , n -1 , and !!/! , respectively. Close to the charge neutrality point, r s increases by 1-2 orders of magnitude when an extra layer is added. Indeed, interaction-induced gaps of ~ 2 meV in suspended BLG [14][15][16][17], and ~42 meV in suspended r-TLG [18,19] have been observed (see Table 1). Among theoretical proposals [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], the experimental observations are most consistent with a layer antiferromagnetic state (LAF) with broken time reversal symmetry. *
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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