Figure 1

(Color online) Transmission through a single square barrier of height $V=100\text{meV}$ and width 10 nm. The potential difference $\delta =\left(V_1-V_2\right)/2\hslash v_F$ is zero in panel (a) and $\Delta =100\text{meV}$ in panel (b) inside the barrier/well region.Reuse & Permissions

Figure 2

(Color online) Transmission through a double barrier. The square barriers are 100 meV high and 10 nm wide; the distance between them is $L=10\text{nm}$. In panel (a) the potential difference between the layers is zero; in panel (b) it is 100 meV inside the barrier/well regions.Reuse & Permissions

Figure 3

(Color online) Transmission through a 100-nm-wide barrier as a function of the angle of incidence for constant energy $E=17\text{meV}$. Panel (a) results from the $4\times 4$ Hamiltonian of Eq. (1) and panel (b) from the $2\times 2$ one of Eq. (3). The solid red and dashed green curves are for a single barrier with height 50 and 100 meV, respectively.Reuse & Permissions

Figure 4

(Color online) (a) Conductance as a function of energy. The very thick blue, thick red, and thin black solid curves are for 2, 5, and 10 barriers, respectively, of width 10 nm, height 50 meV, and interbarrier distance of 5 nm. They result from the $4\times 4$ Hamiltonian, Eq. (1), while the dashed curves result from the $2\times 2$ one, Eq. (3). (b) Contour plot of the transmission versus energy and angle of incidence. (c) The main conductance feature of panel (a), for $N=2$, versus energy for different well widths. The solid curves are for the $4\times 4$ Hamiltonian and the dashed ones for the $2\times 2$ one.Reuse & Permissions

Figure 5

(Color online) Schematics of two experimental setups for realizing the three SL potentials we investigated. In panel (a) the layer potentials $V_1$ and $V_2$ are kept the same: the experimental setup shown can be used. The setup in panel (b) can establish a bias $\Delta =V_1-V_2$. In both experimental setups the layer potentials are controlled by the applied top $V_{tg}$ and back $V_{bg}$ gates.Reuse & Permissions

Figure 6

(Color online) Dispersion relation and DOS for three types of SLs. (1) The barriers are 50 meV high and the wells $-50\text{meV}$ deep. (2) The barriers are biased by $\Delta =50\text{meV}$, and the wells are unbiased, i.e., $\Delta =0\text{meV}$. (3) The barriers are biased by $\Delta =50\text{meV}$ and the wells by $\Delta =25\text{meV}$. Left column: energy vs $k_x$ and $k_y$ for $a=b=10\text{nm}$ and $t_{\perp }=390\text{meV}$. Lines of constant energy, belonging to the lower miniband, are projected onto the $\left(k_x,k_y\right)$ plane. Middle column: slices of the corresponding dispersion relation, (a) for constant $k_x=0$ (solid magenta curves) and $k_x=\pi /l$ (dashed green curves), and (b) for constant $k_y=0$ (solid red curves) and $k_y=0.2/\text{nm}$ (dashed blue curves). Only half the Brillouin zone is shown. Right column: DOS for the corresponding SL. For the unbiased SL (1) we also show the DOS (red area) for a SL with the same parameters on a single-layer graphene. The dashed (dashed-dotted) curves show the bilayer (single-layer) DOS in the absence of the SL potential.Reuse & Permissions