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Register a new userLandau level diagram and the continuous rotational symmetry breaking in trilayer graphene
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The sequence of the zeroth Landau levels (LLs) between filling factors $ u$=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the non-uniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the non-uniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the continuous rotational to textit{C}$_3$ symmetry by the trigonal warping.
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The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding filling factors $ u=$0, 1, 2, & 3. Measurements of the activation energy gap in tilted magnetic fields suggest that the Landau level splitting at the newly formed $ u=$1, 2, & 3 filling factors are independent of spin, consistent with the formation of a quantum Hall ferromagnet. In addition, measurements taken at the $ u$ = 0 charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.
Magneto-transport experiments on ABC-stacked suspended trilayer graphene reveal a complete splitting of the twelve-fold degenerated lowest Landau level, and, in particular, the opening of an exchange-driven gap at the charge neutrality point. A quantitative analysis of distinctness of the quantum Hall plateaus as a function of field yields a hierarchy of the filling factors: u=6, 4, and 0 are the most pronounced, followed by u=3, and finally u=1, 2 and 5. Apart from the appearance of a u=4 state, which is probably caused by a layer asymmetry, this sequence is in agreement with Hunds rules for ABC-stacked trilayer graphene.
Layer stacking and crystal lattice symmetry play important roles in the band structure and the Landau levels of multilayer graphene. ABA-stacked trilayer graphene possesses mirror-symmetry-protected monolayer-like and bilayer-like band structures. Broken mirror symmetry by a perpendicular electric field therefore induces hybridization between these bands and various quantum Hall phases emerge. We experimentally explore the evolution of Landau levels in ABA-stacked trilayer graphene under electric field. We observe a variety of valley and orbital dependent Landau level evolutions. These evolutions are qualitatively well explained by considering the hybridization between multiple Landau levels possessing close Landau level indices and the hybridization between every third Landau level orbitals due to the trigonal warping effect. These observations are consistent with numerical calculations. The combination of experimental and numerical analysis thus reveals the entire picture of Landau level evolutions decomposed into the monolayer- and bilayer-like band contributions in ABA-stacked trilayer graphene.
We construct a continuum model of twisted trilayer graphene using {it ab initio} density-functional-theory calculations, and apply it to address twisted trilayer electronic structure. Our model accounts for moire variation in site energies, hopping between outside layers and within layers. We focus on the role of a mirror symmetry present in ABA graphene trilayers with a middle layer twist. The mirror symmetry is lost intentionally when a displacement field is applied between layers, and unintentionally when the top layer is shifted laterally relative to the bottom layer. We use two band structure characteristics that are directly relevant to transport measurements, the Drude weight and the weak-field Hall conductivity, and relate them via the Hall density to assess the influence of the accidental lateral stacking shifts currently present in all experimental devices on electronic properties, and comment on the role of the possible importance of accidental lateral stacking shifts for superconductivity in twisted trilayers.
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, we observe an intriguing hexagon pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.
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