Magnetic Confinement of Massless Dirac Fermions in Graphene

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.

Figure 1

Polar graphs depicting the transmission probability $T(\varphi )$ for a magnetic barrier of width $2d$ at various energies $ϵ$. The outermost semicircle corresponds to $T=1$, the center to $T=0$, with grid spacing $0.2$. Angles between $-\pi /2$ and $+\pi /2$ are shown; the angular grid spacing is $\pi /6$. (a) $T$ as function of barrier width for fixed energy, $ϵl_B=3.7$. For $d/l_B\ge 3.7$, the transmission is zero for all $\varphi$. (b) Same as function of $ϵ$ for $d/l_B=1.5$. The transmission vanishes for $ϵl_B\le 1.5$.

Figure 2

Low-energy eigenenergies (labeled by $m$) for a disklike magnetic quantum dot in graphene versus missing flux $\delta =R^2/2l_B^2$.