Mode-Selective Cloaking and Ghost Quantum Wells in Bilayer Graphene Transport

Abstract

We study ballistic electron transport through electrostatic barriers in AB-stacked bilayer graphene within a full four-band framework. A mode-resolved analysis reveals how propagating and evanescent channels couple across electrostatic interfaces and how channel selectivity governs transport at normal incidence. We show that, even when decoupled channels remain inactive, perfect transmission can occur at discrete energies due to phase matching of a single internal mode within an individual barrier. This effect is interpreted as a ghost quantum well, namely an effective cavity formed by internal phase coherence inside the barrier, without true bound states and without restoring coupling to decoupled channels. For single- and double-barrier geometries, we derive compact analytical expressions for the transmission and identify the corresponding resonance conditions. Extending the analysis to multibarrier structures using a transfer-matrix approach, we demonstrate how perfect resonances driven by internal phase matching coexist with Fabry-Perot-like resonances arising from inter-barrier interference. Our results provide a unified, channel-resolved description of tunnelling suppression and resonance-assisted transport in bilayer graphene barrier systems.

Figures (3)

• Figure 1: Quantum transport in BG. Schematics of the electronic structure of AB-stacked BG in the presence of a single electrostatic barrier. The left and right $N$ regions are unperturbed, while the central $S$ region is subjected to a uniform on-site electrostatic potential $V_{0}$, producing a rigid shift of the energy bands. At normal incidence, transport occurs through two independent channels, $T^+_+$ and $T^-_-$, corresponding to non-scattering processes $k^{\pm}\rightarrow k^{\pm}$, as indicated by the dashed arrows in the figure. Below the bands in the S region we show the schematics of a two-terminal BG device with a single barrier.
• Figure 2: Transport modes. Band structure in the $N$ region (blue lines) with modes $k^{\pm}$, and in the $S$ region with modes $q_{1,2}^{\pm}$ (solid and dashed red lines) for $V_{0}=0.6\text{ eV}$ and $\gamma_1=0.4\text{ eV}$. For $k_{y}=0$, the colored regions ($\text{I} \text{ to } \text{V}$) denote distinct transport regimes characterized by different combinations of propagating and evanescent modes as a function of energy. Panel (b) shows a schematic representation of a wave propagating through a perfect resonant mode (dashed orange) in the ghost quantum well of region $\text{I}$. Transmission probabilities in panel (c) for the $T^{-}_{-}$ channel and in panel (d) for the $T^{+}_{+}$ channel are shown for $L=20\text{ nm}$ and $V_{0}=0.6\text{ eV}$. The color bars between plots correspond to the regions defined in panel (a), and the dashed orange lines in panel (d) indicate the perfect resonances. Orange insets in panel (d) illustrate the resonant states inside the barrier for incident energies in region I and different values of the barrier width $L$ and height $V_{0}$. Additional inset in (d) display an enlarged zoom of a region with nearly zero transmission (blue line).
• Figure 3: Multibarrier transport. Transmission probability in the $T^{+}_{+}$ channel for (a) a double-barrier structure (blue curve) and (b) a triple-barrier structure (green curve). Insets in panels (a) and (b) show schematics of the corresponding multibarrier geometries. Panels (c) and (d) display enlarged views of the transmission spectrum in selected energy windows of panel (a), corresponding to regions I (orange) and IV (green), respectively. Panels (e) and (f) show the transmission in additional representative regions of panel (b), highlighting the evolution of the resonance structure with the number of barriers. For comparison, the transmission through a single barrier is shown in red, while blue and green correspond to two and three barriers, respectively. Black arrows in the lower panels indicate the perfect resonances associated with internal phase matching within each barrier.