Characterization and Manipulation of Intervalley Scattering Induced by an Individual Monovacancy in Graphene

Intervalley scattering involves microscopic processes that electrons are scattered by atomic-scale defects on the nanoscale. Although central to our understanding of electronic properties of materials, direct characterization and manipulation of range and strength of the intervalley scattering induced by an individual atomic defect have so far been elusive. Using scanning tunneling microscope, we visualize and control intervalley scattering from an individual monovacancy in graphene. By directly imaging the affected range of monovacancy-induced intervalley scattering, we demonstrate that it is inversely proportional to the energy; i.e., it is proportional to the wavelength of massless Dirac fermions. A giant electron-hole asymmetry of the intervalley scattering is observed because the monovacancy is charged. By further charging the monovacancy, the bended electronic potential around the monovacancy softens the scattering potential, which, consequently, suppresses the intervalley scattering of the monovacancy.

Figure 1

(a), (b) Atomic resolution STM image and corresponding FFT image of a monovacancy in TBG. (c) FFT-filtered STM image along a specific direction of the intervalley scattering. (d) Typical STS spectra recorded on and off the monovacancy under 0 T. The $V_{\pi }$ state and $E_D$ are marked. (e) The evolution of STS spectra recorded across the monovacancy under 8 T. The monovacancy locates at 0 nm. The Landau level indices are marked.

Figure 2

(a) Atomic structure of TBG with $\theta \approx 6°$. A monovacancy is located at the $AB$-stacked region of TBG, as marked by the black circle. The red and blue spheres indicate C atoms of the topmost and underlying graphene layers, respectively. (b) Band structure of a monovacancy in TBG. (c) ${\mathrm{\Delta }}_{\rho }$ around the monovacancy with the isosurface value of $0.0015e/{\AA }^3$. Red and blue clouds indicate the electron accumulation and depletion, respectively.

Figure 3

(a), (b) STM images of a monovacancy in TBG acquired at $-0.2$ and $-0.5\mathrm{V}$ with $512\times 512\mathrm{pixels}$, respectively. The yellow dashed circles indicate the ranges of monovacancy-induced intervalley scattering. (c), (d) Line profiles of the red arrows in (a) and (b). The arrows indicate the locations of the carbon atoms in the topmost graphene layer. The alternate heights marked by black and light gray arrows for $x<d$ imply the existence of signal from the intervalley scattering, while the homogeneous heights marked by dark gray arrows for $x>d$ imply the negligible signal from the intervalley scattering. The $x=d$ is the length of the intervalley scattering, determined as the position when the difference of the apparent heights between two adjacent carbon atoms is less than 1 pm or the apparent heights no longer follow the rule of alternation. (e) A linear relation between ($E-E_D$) and $1/d$.

Figure 4

(a) The evolution of STS spectra recorded at the monovacancy as a function of $B$. The $V_{\pi }$ states, $E_D$, $E_F$, and the Landau level indices are labeled. (b) Schematic DOS at the monovacancy in TBG. The $V_{\pi }$ state is partially filled under 0 T, implying the monovacancy is charged. As increasing $B$, the $V_{\pi }$ state is gradually filled and finally fully filled under 8 T, implying the monovacancy is nearly neutral. (c) Schematic scattering of carriers induced by neutral and charged monovacancy. (d) $\mathrm{\Delta }{E}_{0\mathrm{LL}}$ and $Z$ as a function of $B$. (e) Line profiles along the directions of $G\text{−}\mathrm{\Gamma }\text{−}{G}^{\prime }$ and $K\text{−}\mathrm{\Gamma }\text{−}{K}^{\prime }$ in the FFT images at 0.5 V under 8 T. (f) $I_K/I_G$ versus $Z$. Inset: Schematic of intervalley scattering.