Landau Level Splittings, Phase Transitions, and Nonuniform Charge Distribution in Trilayer Graphene

Abstract

We report on magnetotransport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the 12-fold degeneracy of the zeroth Landau level. As a function of perpendicular electric field, our data exhibit a sequence of phase transitions between all integer quantum Hall states in the filling factor interval −8 < ν < 0. We develop a theoretical model and argue that, in contrast to monolayer and bilayer graphene, the observed Landau level splittings and quantum Hall phase transitions can be understood within a single-particle picture, but imply the presence of a charge density imbalance between the inner and outer layers of TLG, even at charge neutrality and zero transverse electric field. Our results indicate the importance of a previously unaccounted band structure parameter which, together with a more accurate estimate of the other tight-binding parameters, results in a significantly improved determination of the electronic and Landau level structure of TLG. DOI: 10.1103/PhysRevLett.117.066601 The electronic properties of ABA-stacked trilayer graphene (TLG) are being intensively investigated [1-6] due to its distinct band structure which consists of two overlapping monolayer-graphene-like (MLG-like) and bilayergraphene-like (BLG-like) bands [1,[7][8][9][10][11][12][13][14]. However, in contrast to MLG and BLG, which are gapless, both subbands in ABA-stacked TLG are gapped, with small masses of the order of a few meV.One of the most interesting characteristics of ABAstacked TLG compared to other graphene systems is the way in which its band structure is modified by a perpendicular electric field [2,12,[14][15][16][17][18]. Theory predicts that a weak electric field hybridizes the MLG-like and BLG-like bands, rather than inducing a band gap, as in BLG or ABC-stacked TLG [3,16,[19][20][21]. The hybridized bands are characterized by a strong trigonal warping. For very strong electric fields, a new set of Dirac points was theoretically predicted, with masses and velocities that are controlled by the electric field [18,22]. Thus biased TLG can potentially provide an opportunity to study chiral carriers with tunable anisotropic dispersion, different symmetry, and higher valley degeneracy (6 as opposed to two in MLG and BLG), not accessible in MLG and BLG.Here we report on transport studies of high-mobility TLG samples in the quantum Hall effect regime. We fabricated dual-gated TLG samples encapsulated in hexagonal boron nitride [23,24] crystals (hBN) [Figs. 1(a)-1(b)], which allowed us to independently control the carrier density n and perpendicular electric displacement field D. We use magnetotransport measurements to study how Landau levels (LLs) evolve under D. By inspecting the pattern of LL crossings resulting from the hybridization of the BLG-like and MLG-like bands as a function of n, D, and magnetic field B, we are able to refine the values of the TLG band structure parameters.Additional...

Nontrivial quantum oscillation geometric phase shift in a trivial band

“…Figure 1B shows that the MLG-like Dirac cone has a robust π Berry’s phase, which only reduces to zero in the vicinity of the MLG-like band edge. However, since the Dirac bandgap is very small, ~1 meV ( 38 , 39 ), it was not possible to resolve the Dirac bandgap and controllably tune the Fermi level through the gap in most of the previous studies ( 33 , 38 ). Since the LL broadening in our device is small, we can resolve the Dirac bandgap and study the phase of the BLG-like SdH oscillations as the Fermi level is tuned through the MLG-like bandgap.…”

“…Details of the tight binding calculation are provided in Materials and Methods and in section S2. The distinct dispersion of the LLs along with the corresponding Hall conductance enables easy identification of the MLG-like and the BLG-like LLs ( 34 , 38 , 39 , 41 ).…”

Landau Level Diagram and the Continuous Rotational Symmetry Breaking in Trilayer Graphene

“…The two variants, namely Bernal (ABA) [7][8][9][10][11][12][13][14][15][16][17][18] and rhombohedral (ABC) [19][20][21][22][23][24][25][26] stackings have been studied for their tunable symmetries. ABA-stacked TLG has a rich low energy bandstructure consisting of a monolayer graphene (MLG)-like linear and a bilayer graphene (BLG)-like quadratic bands 27,28 .…”

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

“…While one class of experiments were conducted on bilayer two-dimensional electron systems (2DES) realized in semiconductor heterostructures, the other class of experiments focussed on probing multiple interacting sub-bands in quantum well structures 2 . There is an increasing interest in the electronic properties of few-layer graphene 3 4 5 6 7 8 9 10 11 12 13 as it offers a platform to study electronic interactions because the dispersion of bands can be tuned with number and stacking of layers in combination with electric field. Bernal/ABA-stacked trilayer graphene (ABA-TLG) provides a natural platform to observe such multi-subband physics as the band structure gives rise to monolayer-like (ML) and bilayer-like (BL) bands.…”