Tuning Anti-Klein to Klein Tunneling in Bilayer Graphene

We show that in gapped bilayer graphene, quasiparticle tunneling and the corresponding Berry phase can be controlled such that they exhibit features of single-layer graphene such as Klein tunneling. The Berry phase is detected by a high-quality Fabry-Pérot interferometer based on bilayer graphene. By raising the Fermi energy of the charge carriers, we find that the Berry phase can be continuously tuned from $2\pi$ down to $0.68\pi$ in gapped bilayer graphene, in contrast to the constant Berry phase of $2\pi$ in pristine bilayer graphene. Particularly, we observe a Berry phase of $\pi$, the standard value for single-layer graphene. As the Berry phase decreases, the corresponding transmission probability of charge carriers at normal incidence clearly demonstrates a transition from anti-Klein tunneling to nearly perfect Klein tunneling.

Figure 1

Sketches of band structure and pseudospin orientation for (a) pristine and (b) gapped BLG. Pseudospin vectors at different Fermi levels (contours) are projected as small cones on a plane between the conduction (yellow) and valence (blue) bands. (c) and (d) show the corresponding Berry phase as the solid angle traced out by the pseudospin (arrows) on the Bloch sphere for (a) and (b), respectively. The red (green) color in (a)–(d) refers to high (low) Fermi energy ($E_F$). (e) Anti-Klein tunneling for pristine BLG. $k$ or $q$ is the wave vector for electrons or holes, and $\mathit{\sigma }$ denotes the pseudospin. (f) Klein tunneling is possible in gapped BLG.

Figure 2

(a) Sketch and (b) AFM image of the devices. Scale bar in (b) is $1\mu \mathrm{m}$. (c) Experimental and (d) simulation results of conductance $G$ varying with $V_{\mathrm{tg}}$ and $V_{\mathrm{bg}}$ at 4.2 K and zero magnetic field for device PNJ-A. (e) The initial charge-carrier density $n(x)$ across device PNJ-A when $V_{\mathrm{bg}}$ and $V_{\mathrm{tg}}$ are both zero. (f) Transconductance $dG/d{V}_{\mathrm{tg}}$ in the $p\overline{p}pn$ and $p\overline{p}pp$ regions of (c).

Figure 3

(a) Fabry-Pérot interference measurements and (b) simulations at $V_{\mathrm{bg}}=20\mathrm{V}$ under low magnetic fields for device PNJ-B (conductance measurements at zero magnetic field are shown in the Supplemental Material [37]). The regions labeled by $\mathbf{c}$ to $\mathbf{h}$ in (a) and (b) are highlighted in the corresponding panels (c)–(h). (i) Berry phases for regions $B$ and $T$ are shown as blue and red curves, respectively. The corresponding transmission probability at normal incidence is calculated with phase-coherent (grey curve) and phase-incoherent (black curve) methods.

Figure 4

Fabry-Pérot interferences at zero magnetic field are shown both (a) experimentally and (b) theoretically, zoomed in on the white rectangle of Figs. 2 and 2, respectively. (c) Calculation of the Berry phase in region $T$ as a function of $V_{\mathrm{tg}}$ and $V_{\mathrm{bg}}$. The dash-dotted line shows the position of ${\mathrm{\Phi }}_{\text{Berry}}^{(T)}=\pi$. The green dots mark the phase-shift positions that appear in (a) and define the dotted line. The displacement field axis ($D$) and the charge-carrier density axis in region $T$ ($n_T$) are shown in yellow.