Electronic Highways in Bilayer Graphene

Bilayer graphene with an interlayer potential difference has an energy gap and, when the potential difference varies spatially, topologically protected one-dimensional states localized along the difference's zero-lines. When disorder is absent, electronic travel directions along zero-line trajectories are fixed by valley Hall properties. Using the Landauer-B\"uttiker formula and the non-equilibrium Green's function technique we demonstrate numerically that collisions between electrons traveling in opposite directions, due to either disorder or changes in path direction, are strongly suppressed. We find that extremely long mean free paths of the order of hundreds of microns can be expected in relatively clean samples. This finding suggests the possibility of designing low power nanoscale electronic devices in which transport paths are controlled by gates which alter the inter-layer potential landscape.Comment: 8 pages, 5 figure

Microscopic theory of quantum anomalous Hall effect in graphene

We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in graphene due to a joint effect of Rashba spin-orbit coupling $\lambda_R$ and exchange field $M$. Based on a continuum model at valley $K$ or $K'$, we show that there exist two distinct physical origins of QAH effect at two different limits. For $M/\lambda_R\gg1$, the quantization of Hall conductance in the absence of Landau-level quantization can be regarded as a summation of the topological charges carried by Skyrmions from real spin textures and Merons from \emph{AB} sublattice pseudo-spin textures; while for $\lambda_R/M\gg1$, the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane's model, giving rise to a nonzero Chern number $\mathcal{C}=1$ at either $K$ or $K'$. In the presence of staggered \emph{AB} sublattice potential $U$, a topological phase transition occurs at $U=M$ from a QAH phase to a quantum valley-Hall phase. We further find that the band gap responses at $K$ and $K'$ are different when $\lambda_R$, $M$, and $U$ are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling $\lambda_{SO}$, and it transitions a trivial phase when $\lambda_{SO}>(\sqrt{M^2+\lambda^2_R}+M)/2$. Moreover, we use a tight-binding model to reproduce the ab-initio method obtained band structures through doping magnetic atoms on $3\times3$ and $4\times4$ supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene.Comment: 10pages, ten figure

Low field phase diagram of spin-Hall effect in the mesoscopic regime

When a mesoscopic two dimensional four-terminal Hall cross-bar with Rashba and/or Dresselhaus spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field $B$, both integer quantum Hall effect (IQHE) and mesoscopic spin-Hall effect (MSHE) may exist when disorder strength $W$ in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the $(B,W)$ plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance $G_{sH}$ and its fluctuations $rms(G_{SH})$ vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values $G_{SH}=1/2$ and $rms(G_{SH})=0$ on those odd numbered plateaus induced by Zeeman energy. For moderate disorder, the system crosses over into a regime where both $G_{sH}$ and $rms(G_{SH})$ are finite. A larger disorder drives the system into a chaotic regime where $G_{sH}=0$ while $rms(G_{SH})$ is finite. Finally at large disorder both $G_{sH}$ and $rms(G_{SH})$ vanish. We present the physics behind this ``phase diagram".Comment: 4 page, 3 figure

Two-Dimensional Topological Insulator State and Topological Phase Transition in Bilayer Graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling $\lambda_{\mathrm{R}}$, and transitions to a strong TI when $\lambda_{\mathrm{R}} > \sqrt{U^2+t_\bot^2}$, where $U$ and $t_\bot$ are respectively the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.Comment: 5 pages and 4 figure

Topological Zero-Line Modes in Folded Bilayer Graphene

We theoretically investigate a folded bilayer graphene structure as an experimentally realizable platform to produce the one-dimensional topological zero-line modes. We demonstrate that the folded bilayer graphene under an external gate potential enables tunable topologically conducting channels to be formed in the folded region, and that a perpendicular magnetic field can be used to enhance the conducting when external impurities are present. We also show experimentally that our proposed folded bilayer graphene structure can be fabricated in a controllable manner. Our proposed system greatly simplifies the technical difficulty in the original proposal by considering a planar bilayer graphene (i.e., precisely manipulating the alignment between vertical and lateral gates on bilayer graphene), laying out a new strategy in designing practical low-power electronics by utilizing the gate induced topological conducting channels