Stacking-dependent magnetoelectronic properties in multilayer graphene

The generalized Peierls tight-binding model is developed to study multilayer graphenes. For an $N$-layer system, there are $N$ groups of conduction and valence Landau levels. Each group is clearly specified by the corresponding sublattice. The Landau-level spectra strongly depend on the stacking configuration. ABC-stacked graphenes exhibit two kinds of Landau-level anticrossings, the intergroup and intragroup Landau levels, as a function of the applied magnetic field. On the other hand, in contrast to its frequent wide-energy presence in ABC-stacked graphenes, the anticrossing only occurs occasionally in AB-stacked graphenes, and is absent in AA-stacked graphenes. Furthermore, all $4N$ Dirac-point related Landau levels are distributed over a limited energy range near the Fermi level. In AA- and AB-stacked graphenes, the total number of such levels is fixed, while their energies depend on the stacking configuration. These results reflect the main features of the zero-field band structures.

Figure 1

(a) The geometric structure of ABC-stacked graphene under a uniform magnetic field $\mathbf{B}=B_0\widehat{z}$, perpendicular to the graphene plane. The interlayer atomic interactions are illustrated in the right panel. At $B_0=0$, the low-energy band structure of (b) tetralayer graphene is plotted and (c) shows a zoomed-in view near the Fermi level.

Figure 2

The Landau levels corresponding to (a) tetralayer graphene under $B_0=25$ T. For each level, the odd-indexed envelop functions of sublattices $B_o^1,B_o^2,B_o^3$, and $B_o^4$ are shown in (b), (c), (d), and (e), respectively.

Figure 3

The Landau-level spectrum of ABC-stacked tetralayer graphene.

Figure 4

(a) Intragroup and intergroup Landau-level anticrossing patterns. The evolutions of subenvelope functions are demonstrated during the anticrossing processes for (b)–(i) self-group (the second group) and (j)–(q) intergroup (the second and the third groups) Landau levels.

Figure 5

The field-dependent energies of the four Dirac-point related Landau levels of ABC-stacked tetralayer graphene are shown in (a). In (b), energies are plotted for $B_0=25$ T based on their dependence on the number of stacked layers.

Figure 6

The Landau-level spectra of ABC-stacked (a) trilayer, (b) pentalayer, and (c) hexalayer graphenes.

Figure 7

The Landau-level spectrum of AA-stacked tetralayer graphene.

Figure 8

The Landau-level spectrum of AB-stacked tetralayer graphene.