Energy-Dependent Chirality Effects in Quasifree-Standing Graphene

We present direct experimental evidence of broken chirality in graphene by analyzing electron scattering processes at energies ranging from the linear (Dirac-like) to the strongly trigonally warped region. Furthermore, we are able to measure the energy of the van Hove singularity at the $M$ point of the conduction band. Our data show a very good agreement with theoretical calculations for free-standing graphene. We identify a new intravalley scattering channel activated in case of a strongly trigonally warped constant energy contour, which is not suppressed by chirality. Finally, we compare our experimental findings with $T$-matrix simulations with and without the presence of a pseudomagnetic field and suggest that higher order electron hopping effects are a key factor in breaking the chirality near to the van Hove singularity.

Figure 1

Scattering patterns in strongly doped graphene. (a) Inverted LEED pattern of $\mathrm{gr}/\mathrm{Cs}/\mathrm{Ir}(111)$ at $E=143.5\mathrm{eV}$, the intercalated Cs forms a ${(2\times 2)}_{\mathrm{gr}}$ superstructure. The sketch below shows a schematic cross section of the sample. (b) STM image and (c) simultaneously recorded STS map of the two different standing wave patterns at $U=-50\mathrm{mV}$, $I=500\mathrm{pA}$. (d) Fourier transformation of image (c) reveals triangular and hexagonal scattering patterns. The dashed hexagon indicates the first Brillouin zone. The right side shows a magnification of the framed areas.

Figure 2

Scattering processes in strongly doped graphene, (a) sketch of the first Brillouin zone with trigonally warped CEC (black), and (b) schematic drawing of the scattering patterns for the CEC shown in (a). The intervalley scattering between $K$ and $K^{\prime }$ leads to triangular features around the $K$ and $K^{\prime }$ points (magenta). The intravalley scattering (green) leads to hexagonal features around the $\mathrm{\Gamma }$ points. The vectors $\mathit{q}$ and ${\mathit{q}}^{\prime }$ are exemplarily marked scattering vectors.

Figure 3

Energy dependence of scattering patterns. (a) Experimentally observed scattering patterns. Their size decreases with decreasing bias voltage. A gap opening in the intervalley feature is observed simultaneously with the vanishing of the central intravalley feature near the Dirac point. Imaging parameter: $I=80\mathrm{pA}$ for $U\ge -150\mathrm{mV}$, and $I=500\mathrm{pA}$ for $U\le -350\mathrm{mV}$. Simulation of the scattering patterns for (b) free-standing graphene and (c) free-standing graphene in the presence of a global pseudomagnetic field. The sketch on the right side indicates the position of the scattering patterns in reciprocal space.

Figure 4

Dispersion (left side) and normalized $dI/dV$ spectrum (right side) of graphene. The dispersion (left) contains data points extracted from the two types of scattering patterns (magenta and green), complemented by one data point (black) from the $dI/dV$ measurement. The data are compared with TB theory (dashed gray lines) with 1NN and 3NN hopping (see labels) as well as with an ab initio calculation for free-standing graphene (full gray line) [22] and a DFT calculation specifically for our experimental system (orange lines). For the $dI/dV$ spectrum, tip was stabilized at $U_{\mathrm{stab}}=1\mathrm{V}$, $I_{\mathrm{stab}}=170\mathrm{pA}$.