High-Magnetic-Field Tunneling Spectra of $ABC$-Stacked Trilayer Graphene on Graphite

$ABC$-stacked trilayer graphene (TLG) was predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat bands near the charge neutrality point. Here, using high-magnetic-field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality $ABC$-stacked TLG on graphite. We observe an approximately linear magnetic-field scaling of valley splitting and spin splitting in the $ABC$-stacked TLG. Our experiment indicates that the spin splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the spin splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the $ABC$-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlated effects could emerge in the $ABC$-stacked TLG in the presence of high magnetic fields.

Figure 1

(a) STM image ($V_b=100\mathrm{mV}$, $I=100\mathrm{pA}$) of a decoupled $ABC$ TLG on graphite. It shows a step edge in the right region of the image. Up inset: the atomic-resolution image ($V_b=50\mathrm{mV}$, $I=300\mathrm{pA}$) of the $ABC$ TLG surface showing the triangular contrasting. Bottom inset: height profile across the step along the solid line. The step height $\sim 0.35\mathrm{nm}$ corresponding to one-layer spacing. (b) and (c) Typical $dI/dV$ spectra for $ABC$ TLG and gaped $AB$ bilayer recorded at the left and right region of the step in (a) at 0 T, respectively. Insets show the corresponding band structures of the $ABC$ TLG and gaped $AB$ bilayer. (d) LL spectra of the $ABC$ TLG recorded from 0 to 15 T in 1 T increments. Curves are shifted vertically for clarity. (e) LL energies extracted from 5–8 T in (d) plotted versus momentum $k_n$ as deduced from $k_n=\sqrt{2enB/\hslash }$. The solid and dashed lines are cubic and tight-binding (TB) fits to the data, respectively. The inset shows the ${[n(n-1)(n-2)B^3]}^{1/2}$ dependence of LL energies. (f) LL fan diagram under low fields. The red dots are data obtained from (d) and the blue curves are fits with Eq. (1).

Figure 2

(a) $dI/dV$ spectra focusing on the Fermi level region for the indicated magnetic fields. The $n=(0,1,2)$ and $n=3$ levels are all split in high fields (12 T as an example). ${\mathrm{LL}}_{(0,1,2)}$ splits into four peaks with the larger gap between ${\mathrm{LL}}_{(0,1,2,+)}$ and ${\mathrm{LL}}_{(0,1,2,-)}$ (marked by dashed lines in the top panel) corresponding to the valley splitting. The green line indicates the position of the Fermi level. (b) Valley splitting as a function of magnetic field for partially filled ${\mathrm{LL}}_{(0,1,2)}$. The line is a linear fit to the data. (c) Magnetic field dependence of energy positions of ${\mathrm{LL}}_{(0,1,2,+)}$, ${\mathrm{LL}}_{(0,1,2,-)}$ and the CNP, showing different filling states of the ${\mathrm{LL}}_{(0,1,2,+)}$ and ${\mathrm{LL}}_{(0,1,2,-)}$.

Figure 3

Spin splitting of VB (a) and CB (b) LLs as a function of magnetic field. Lines are linear fits to the data. For the ${\mathrm{LL}}_{(0,1,2,+)}$, the linear fit is only applied to the full filling data. (c) $g$ factor for different LLs. (d) Schematic of the spin ($\uparrow \downarrow$) and valley ($+-$) splittings for the $n=(0,1,2)$ and 3 LLs in our $ABC$ TLG. The sequence of symmetry-breaking (under an interlayer potential) is as follows: for the $n=(0,1,2)$ LL, valley (layer) degeneracy is first lifted, then spin degeneracy; for $n=3$ LLs, spin degeneracy is first lifted.

Figure 4

Energy dependence of LL peak (unsplit) width, as deduced by Gaussian fit function, for $n>4$ index at hole side. The dashed lines are linear fits to the lower ($\le 10\mathrm{T}$) and higher ($\ge 12\mathrm{T}$) fields with nearly the same slope ($\hslash /{\gamma }^{\prime }$), showing the linear energy scaling and the field-induced increase of the peak width.