Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

Abstract

The physics of Dirac fermions in condensed-matter systems has received extraordinary attention following the discoveries of two new types of quantum Hall effect in single-layer and bilayer graphene [1][2][3] . The electronic structure of trilayer graphene (TLG) has been predicted to consist of both massless single-layer-graphene-like and massive bilayer-graphene-like Dirac subbands [4][5][6][7] , which should result in new types of mesoscopic and quantum Hall phenomena. However, the low mobility exhibited by TLG devices on conventional substrates has led to few experimental studies 8,9 . Here we investigate electronic transport in high-mobility (>100,000 cm Bernal-or ABA-stacked TLG (Fig. 1b) is an intriguing material to study Dirac physics and the quantum Hall effect (QHE) because of its unique band structure, which, in the simplest approximation, consists of massless single-layer-graphene (SLG)-like and massive bilayer graphene (BLG)-like subbands at low energy (Fig. 1c;. The energies of the Landau levels (LLs) for massless charge carriers depend on the square root of the magnetic field √ B (refs 1, 2,11-13), whereas for massive charge carriers they depend linearly on B (refs 3,11,12,14). Therefore, the LLs from these two different subbands in TLG should cross at some finite fields, resulting in accidental LL degeneracies at the crossing points. However, one of the main challenges so far to observe the QHE in TLG has been its low mobility on SiO 2 substrates 8,9 . To overcome this problem, we use hexagonal boron nitride (hBN) single crystals 15 as local substrates, which have been shown to reduce carrier scattering in graphene devices 16 (See Methods and Supplementary Information for fabrication). Substrate-supported devices also enable us to reach higher carrier density than suspended samples 17 , which is necessary for the observation of the LL crossings. Figure 1e,f shows the resistivity and conductivity of a TLG device at zero magnetic field. The resistivity at the Dirac peak exhibits a strong temperature dependence, which in SLG is a strong indication of high device quality 18,19 . In addition, we also observe a doublepeak structure at low temperatures (Fig. 1e). This double-peak structure is probably due to the band overlap that occurs in TLG when all SWMcC parameters are included in the tight-binding calculation of its band structure, as we show below. The field-effect mobility of this device reaches 110,000 cm 2 V −1 s −1 at 300 mK at densities as high as 6 × 10 11 cm −2 . This mobility value is two orders of magnitude higher than previously reported values for supported TLG (refs 8,9) and comparable to suspended samples 17,19 . The low disorder and high mobility enable us to probe LL crossings of Dirac fermions through the measurement of Shubnikov-de Haas oscillations (SdHOs). Figure 2a shows longitudinal resistivity ρ xx as a function of 1/B, for a carrier density n = −4.4 × 10 12 cm −2 . At low B (below ∼1 T), there are a number of oscillations characterized by broad minima separated by relatively n...

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