There is an increasing interest in the electronic properties of few-layer graphene as it offers an incredibly rich and tunable system -- the dispersion of bands can be tuned with number and stacking of layers in combination with an electric field. Bernal (ABA) stacked trilayer graphene (TLG) is the simplest system that hosts both Dirac-like massless linear bands and massive quadratic bands. Interplay between multiple bands and different competing symmetries give rise to a variety of quantum phenomena. Here, we will talk about our recent studies on very high mobility (~500,000 cm^{2}V^{-1}s^{-1}) ABA-trilayer graphene samples in quantum Hall regime.

First, we study the effect of the trigonal warping which despite being small in magnitude, has important effects on the low energy physics of few-layer graphene. In presence of a magnetic field, it leads to a selection rule for the coupling between different Landau levels. In particular, we observe anti-crossings between some LLs, which result from the breaking of the continuous rotational symmetry to C_{3} symmetry by the trigonal warping. Our experiment provides smoking-gun evidence for the trigonal warping of the low energy bands. [1]

Second, we study the consequence of the non-uniform charge distribution in the ABA-stacked TLG. It is theoretically predicted that the charge distribution on the three layers of the ABA-stacked TLG can be non-uniform and this has an important effect on the substructure of the lowest Landau level. In particular, the sequence of the zeroth Landau levels between filling factors -6 to 6 in ABA-stacked trilayer graphene depends sensitively on this non-uniform charge distribution. Using the sensitivity of quantum Hall data on the electric field and magnetic field, we quantitatively estimate the non-uniformity of the electric field and determine the sequence of the zeroth LLs. [1]

Third, we will discuss about the existence of a new quantum oscillation phase shift in multiband systems. In particular, we observe that Shubnikov-de Haas (SdH) oscillation of the quadratic band in ABA-trilayer graphene is shifted by a phase that sharply departs from the expected 2π Berry's phase and is inherited from the non-trivial Berry's phase of the linear band. Our analysis reveals that this happens due to the simultaneous filling of both the bands -- required by the uniform Fermi energy. Moreover, we measure a continuous gate tuning of the extracted phase from π to – π across the weakly gapped linear Dirac band. Given that many topological materials contain multiple bands, our work indicates how additional bands, which are thought to obscure the analysis, can actually be exploited to tease out the effect of often subtle quantum mechanical geometric phases. [2]

[1] Biswajit Datta, et al. Physical Review Letters 121, 056801 (2018)

[2] Biswajit Datta et al. arXiv:1902.04264 (2019).