Quantum Hall to Charge-Density-Wave Phase Transitions inABC-Trilayer Graphene

Abstract

ABC-stacked trilayer graphene's chiral band structure results in three (n = 0, 1, 2) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction driven states of the 12-fold degenerate (including spin and valley) N = 0 Landau level. In particular, at many filling factors νT = ±5, ±4, ±2, ±1 a quantum phase transition from a quantum Hall liquid state to a triangular charge density wave occurs as a function of the single-particle induced LL orbital splitting ∆LL. Experimental signatures of this phase transition are also discussed.PACS numbers: 73.22.Gk,72.80.Vp Introduction-When a group of partially filled Landau levels (LLs) with internal flavor indices are nearly degenerate, electron-electron interactions can lead to spontaneous broken symmetries which induce quasiparticle gaps and hence interaction driven integer quantum Hall (IQH) effects [1]. In semiconducting two-dimensional electron systems (2DES) where Zeeman splitting is negligible and the LLs consist of narrowly spaced doublets, interactions lead to spontaneous electron spin polarization [2] accompanied by a large exchange enhanced spin gap. More recently interaction driven broken symmetry states at integer fillings have been observed in both graphene [3,4] and bilayer graphene [5,6] which in most cases exhibits a set of four-fold degenerate LLs. At many filling factors this four-fold degeneracy, which is due to the spin and valley degree of freedom, is spontaneously broken resulting in charge gaps and hence incompressible quantum Hall (QH) states. Bilayer graphene's chiral bands lead to an additional degeneracy doubling of the zero-energy LL associated with the n = 0 and n = 1 LL orbitals [7], leading to an eight-fold degenerate LL. This additional LL degeneracy also results in interaction driven QH effects due to an exchange induced gap between the LL pseudospins [5,8].At relevant energy scales few layer graphene with different stacking sequences, referred to as chiral 2DES (C2DES), exhibit electronic properties distinct from semiconducting 2DES [9]. The difference in the LL structure of C2DES is most evident in the zero-energy LL: for certain stacking sequences (such as AB, ABC, ABCB, etc.) multiple LL orbitals are degenerate [10]. The role of interactions on the ground state when multiple LL orbital degrees of freedom are degenerate remains relatively unexplored. In this Letter we show that, unlike bilayer graphene, at certain filling factors interaction induced QH states are unstable in ABC-stacked trilayer graphene's 12-fold degenerate zero-energy LL. This is due to the presence of a degenerate set of triplet (n = 0, 1, 2) LL orbitals. While the QH liquid state is stable for ν = −3, 3, 6 the nature of the ground states at ν = ±5, ±4, ±2, ±1 depends on the ratio of a single

Fine structure of the lowest Landau level in suspended trilayer graphene

“…[5][6][7][8] The subsequent filling factors are related to the lifting of the degeneracy of the lowest Landau level: first ν = 3 and at higher fields ν = 1, 2, and 5, a sequence which is in agreement with Hund's rules of ABC-TLG. 28,29 However, filling factor ν = 4 is also observed experimentally in this sequence whereas it is not predicted by Hund's rules for ABC-TLG. We attributed its appearance to a layer asymmetry caused by an external electric field of the back gate or local inhomogeneities.…”

Interacting electrons on trilayer honeycomb lattices

“…At temperatures below 5K, transport experiments found gap openings of about 2-3 meV [7][8][9] . For trilayer graphene the stacking order is crucial for the electronic properties [20][21][22][23][24][25][26][27][28][29] . In Ref.…”

Ferromagnetism in ABC-stacked trilayer graphene

“…23 It has been suggested that the differences in the quantum Hall effect between ABC and ABA stacking might be used to identify the stacking order of high-quality trilayer samples. 24,25 By using infrared absorption spectroscopy, it has been shown that the optical conductivity spectra for ABC-and ABA-stacked graphene differs considerably. 26 These optical properties have been calculated and reproduced in the framework of a tight-binding model.…”