Multicomponent Quantum Hall Ferromagnetism and Landau Level Crossing in Rhombohedral Trilayer Graphene

Abstract

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...

Competition between exchange-driven dimerization and magnetism in diamond (111)

“…As diamond(111) can be seen as formed from buckled graphene layers with rhombohedral (ABC) stacking (see Fig. 1), it is instructive to compare our magnetic state with the one recently detected in multilayer graphene with ABC stacking [3][4][5][6][7] . In ABC graphene multilayers the state is globally antiferromagnetic, but weakly ferrimagnetic on the outer layers, exactly as in the present case.…”

“…cell-relaxed 1.419(8) 1.419(7) 0.000(1) 0.006(7) HSE06 unrelaxed 1.475(5) 1.400(1) 0.026(2) 0.005(2) HSE06 ion-relaxed 1.438(7) 1.438(5) 0.000(1) 0.006 (3) eV 27 to the experimental gap of 1.47 eV, this leads to an experimental single particle gap of 1.57 − 1.87 eV. The PBE0 gap value with the magnetism is thus on the higher side of the experimental window.…”

“…In the case of 3d transition metal oxides or high T c superconductors, Mott insulating, magnetic, and superconducting states are stabilized via the strong localization of electrons in 3d orbitals. Recently, it has been shown that a new class of strongly correlated systems can be achieved in ultraflat edge-states or surface bands having small Fermi velocities but not necessarily 3d states, as it happens in twisted bilayer graphene 1,2 , or multilayer graphene with rhombohedral stacking [3][4][5][6][7] . All these works expand the range of materials hosting strong correlation effects and exotic states of matter and point to the need of understanding exchange and correlation effects in flat edge-states.…”

“…The weak, but not negligible, hopping integral in the direction parallel to the surface but perpendicular to the chains is responsible for the ≈ 0.5 eV energy dispersion of the band. Even if this surface state is not as flat as the one detected in twisted bilayer graphene 1,2 or in multilayer graphene with rhombohedral stacking [3][4][5][6][7] , it is substantially more extended in reciprocal space and it holds a larger number of electrons. For this reason diamond(111) should be prone to strong exchange and correlation effects.…”

Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene

“…The key role of interactions is also reflected in the hysteresis of R xx in the vicinity of the symmetry broken QHF states. Though QHF has been extensively studied in 2DES using semiconductors 2 29 there are only a few reports of studying QHF in graphene 30 31 32 33 . In our experiment, we vary filling factor by changing V bg at a fixed B ( Fig.…”