Figure 1

Schematic electronic structure of few-layer graphene. The sites coupled by the strongest interlayer bonds characterized by the ${\gamma }_1$ hopping parameter are indicated by shading and have little weight in $N=0$ Landau levels.Reuse & Permissions

Figure 2

Upper panel: Filling factor dependence of the Hartree-Fock energies of occupied and unoccupied LLs for a balanced ABC trilayer at 20 T. Energies are in units of ${(\pi /2)}^{1/2}{e}^2/\varepsilon {\ell }_B$. Unoccupied LLs are sextets (blue), triplets (green), or singlets (cyan); occupied LLs are doublets (magenta) or singlets (red); LLs at $\nu =\pm 6$ are split only by the small Zeeman splitting. These energies include only exchange interactions within the $N=0$ level. Particle-hole symmetry within the $N=0$ space is recovered if exchange interactions with remote Landau levels are included; these interactions do not influence the energy spacings between Landau levels. Lower panel: Filling factor dependence of the polarizations of up spin (blue) and layer (red), and population differences between $n=2$ and $n=0$ (green) and $n=1$ (cyan) LL orbitals.Reuse & Permissions

Figure 3

(a) Filling factor dependence of the Hartree-Fock (HF) energies (eV) of occupied and unoccupied LLs for a balanced ABA trilayer at 10 T. Unoccupied LLs are quartets (green), doublets (blue), or singlets (cyan); occupied LLs are doublets (magenta) or singlets (red). (b)–(d) Field dependence of the HF energies (eV) of the lowest four LLs at $\nu =-5,-4$, and $-3$. Results are given for magnetic field $B$ equal to (b) 15 T, (c) 25 T, and (d) 35 T. Magenta and red denote the $n=0$ and 1 orbitals, respectively, of LL $|A_1+A_3\uparrow \rangle$; green and blue denote the $n=0$ and 1 orbitals, respectively, of LL $|B_2\uparrow \rangle$. The Zeeman splitting is small enough to ignore in this figure, and we assume that $\varepsilon =1$.Reuse & Permissions