High-resolution tunneling spectroscopy of ABA-stacked trilayer graphene

ABA-stacked trilayer graphene (TLG), the simplest system consisting of both monolayerlike and bilayerlike Dirac fermions, is expected to exhibit many interesting broken-symmetry quantum Hall states and interaction-induced phenomena. However, difficulties in microscopically identifying the stacking order of the TLG and limited spectroscopic resolution have stymied experimental probes of these interesting states and phenomena in scanning tunneling microscopy (STM) studies. Here we studied the detailed features of the electronic structure in the ABA TLG by using high-resolution STM measurements. Landau-level (LL) crossings of the monolayerlike and bilayerlike Dirac fermions and effective-mass renormalization of the bilayerlike Dirac fermions were observed, indicating strong electron-electron interactions in the ABA TLG. Most unexpectedly, we observed unconventional splittings of the lowest LLs for both the monolayerlike and the bilayerlike Dirac fermions in high perpendicular magnetic fields. These splittings of the LLs, which are beyond the description of the tight-binding model, reveal unexplored broken-symmetry quantum Hall states in the ABA TLG induced by many-body effects.

Figure 1

Electronic band structure and Landau quantization in ABA TLG. (a) Schematic of ABA TLG with all the SWMcC hopping parameters. The $A$ and $B$ sites are denoted by blue and yellow balls, respectively. (b) Numerical calculation of a typical band structure of TLG within a full-parameter model. The red and blue lines represent the MLG-like Dirac fermions and BLG-like Dirac fermions, respectively. (c) Calculations of the $B$-dependent LLs. (d) The $100\times 100\mathrm{n}{\mathrm{m}}^2$ STM images of decoupled ABA TLG on Ni foil. Zoom in is the atomic-resolution topography. (e) The evolution of the series of Landau levels as a function of magnetic-field $B$ from 3 to 15 T as a variation of 0.2 T. Each panel of every $B$ consists of ten dI/dV spectra acquired at different spatial points along a line of 10 nm.

Figure 2

The strong electron-electron interactions of MLG-like Dirac fermions and BLG-like Dirac fermions through LL crossings. (a) dI/dV − V spectra of ABA TLG plotted against the reduced energy E/B from 11 to 15 T as a variation of 0.2 T. The aligned peaks (blue dashed lines) are labeled with sequential LL indices of BLG-like Dirac fermions and the nontrivial parabolic lines (red dashed lines) arising at the bias of LL crossings. (b) LL crossings of MLG-like $N=1$ LL and BLG-like $N=5$ LL of the holes, and the significant shifts near the crossing points are noted by arrows. (c) LL crossings of MLG-like $N=1$ LL and BLG-like $N=5$ LL of electrons in experiment.

Figure 3

The electron-electron interaction in a BLG-like band of ABA TLG. (a) and (b) The calculated $m^{*}$ versus $B$ for electrons and holes, respectively. The effective-mass $m^{*}{}^{\prime }\mathrm{s}$ of each LL are obtained from the gapped BLG-like LL sequences. (c) The relationship between $m^{*}$ and the energy of BLG-like Dirac fermions, the obvious electron-hole asymmetry, and the increasingly suppressed $m^{*}$ at lower carrier densities are clearly identified. The inset: schematic of the BLG-like band with and without taking into account e-e interactions. The outer parabolic bands are the single-particle spectra, and the inner parabolic bands illustrate the many-body spectrum predicted by the renormalization-group theory and observed in the current experiments.

Figure 4

The broken-symmetry quantum Hall states of ABA TLG. (a) A typical STS spectrum of ABA TLG recorded at 15 T. The zoom in is the differential conductance maps recorded at 15 T at the bias voltages of the $M$(0−) and $M$(0+) LLs, respectively. (b) The energy separations of the valleys in the MLG-like lowest LL with different perpendicular magnetic fields. (c) The $B$(0,1) LL evolution with magnetic fields. (d) $B$(0,1, −) LL and $B$(0,1,+) LL at 15 and 10 T, respectively, implying the symmetry-broken states at high magnetic fields. (e) The energy separations of each valley in the BLG-like LL with the limited range of the magnetic fields, yielding $g^{*}\left[B\left(0,1,-\right)\right]=14.5$ and $g^{*}\left[B\left(0,1,+\right)\right]=11.5$ for $B>12$ T. The blue dashed line shows the calculated result in Fig. 1.