Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference

Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of $\pm 2\pi$. This nontrivial topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties. Here we show that the quantum interference due to intervalley scattering induced by single-atom vacancies or impurities provides insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct valleys with opposite chirality undergo a rotation of pseudospin that results in the Friedel oscillation with wavefront dislocations. The number of dislocations reflects the information about pseudospin texture and hence can be used to measure the Berry phase. As demonstrated both experimentally and theoretically, the Friedel oscillation, depending on the single-atom vacancy or impurity at different sublattices, can exhibit $N=4$, 2, or 0 additional wavefronts, characterizing the $2\pi$ Berry phase of the bilayer graphene. Our results provide a comprehensive study of the intervalley quantum interference in bilayer graphene and can be extended to multilayer graphene, shedding light on the pseudospin physics.

Figure 1

(a)–(c) The topography STM images of the individual single-atom vacancy (a), (c) and impurity (b) in the decoupled BLG. The single-atom vacancies or impurities (black circles) locate at the center of the tripod shapes. (d)–(f) Atomic structures of BLG overlying onto the enlarged STM images. (g)–(i) Atomic structures of the BLG with the single-atom vacancy or impurity at the $B^{\prime }$, $B$, and $A$ sublattices, respectively. The locations of the vacancy or impurity are marked by the dotted circles. (j)–(l) FFT of panels (a)–(c). The outer and inner hexangular spots, linking by the yellow and green lines, correspond to the reciprocal lattice of graphene and the intervalley scattering, respectively. (m)–(o) FFT-filtered images of panels (a)–(c) along the direction of intervalley scattering marked by white circles in panels (j)–(l), which exhibit $N=4$, 2, and 0 additional wavefronts (blue dashed lines), respectively.

Figure 2

(a)–(c) Simulated charge density in the top layer of the BLG with a single-atom vacancy at the $B^{\prime }$, $B$, and $A$ sublattices, respectively. The single-atom vacancy (black circles) is at the center of the tripod-shaped charge density (black dotted outlines). Here the charge density is calculated at the energy of 30 meV and is represented by the spots whose size is proportional to the charge density. The FFT of the charge density is shown as insets. (d)–(f) Charge density oscillations due to the intervalley quantum interference are obtained from the filtered FFT enclosed by white circles in (a)–(c), respectively. For the single-atom vacancy located at the three distinct sublattices in (a)–(c), there are $N=4$, 2, and 0 additional wavefronts marked by blue dashed lines.

Figure 3

(a) Low-energy band structures around the Brillouin zone corners of the BLG. (b) Pseudospin textures along the Fermi surfaces in the BLG. (c) Schematic intravalley scattering in the BLG. (d) Schematic intervalley scattering in the BLG. The pseudospin rotates by $4{\theta }_q$ in the intervalley scattering. (e) The real space representation of the intervalley backward scattering in panel (d). The red and blue arrows denote the pseudospins of reflected and incident quasiparticles from the $K_{+}$ and $K_{-}$ valleys, respectively. (f)–(h) Charge density oscillations due to the intervalley scattering are calculated from the low-energy continuum model and projected onto the top layer of the BLG. For the single-atom vacancy or impurity at the $B^{\prime }$, $B$, and $A$ sublattices, the charge density oscillations at the energy of 30 meV exhibit $N=4$, 2, and 0 additional wavefronts, as marked by blue dashed lines.