Suppression of Quasiparticle Scattering Signals in Bilayer Graphene Due to Layer Polarization and Destructive Interference

We study chemically gated bilayer graphene using scanning tunneling microscopy and spectroscopy complemented by tight-binding calculations. Gating is achieved by intercalating Cs between bilayer graphene and Ir(111), thereby shifting the conduction band minima below the chemical potential. Scattering between electronic states (both intraband and interband) is detected via quasiparticle interference. However, not all expected processes are visible in our experiment. We uncover two general effects causing this suppression: first, intercalation leads to an asymmetrical distribution of the states within the two layers, which significantly reduces the scanning tunneling spectroscopy signal of standing waves mainly present in the lower layer; second, forward scattering processes, connecting points on the constant energy contours with parallel velocities, do not produce pronounced standing waves due to destructive interference. We present a theory to describe the interference signal for a general $n$-band material.

Figure 1

Dispersion of chemically gated BLG along $\mathrm{\Gamma }KM$ using a tight-binding approach with the hopping parameters and the interlayer potential $U=0.4\mathrm{eV}$ as explained in the text. The conduction (CB1, CB2) and valence bands (VB1, VB2) are symmetric with respect to the Dirac energy $E_D$. The color code indicates the weight of the eigenstates. Red (blue) states have a weight of 1 (0) in the upper layer. At the chemical potential (thick dashed line at 0.9 eV), the weights are approximately 0.8 and 0.2, respectively. The dashed Dirac cones show the dispersion of the two monolayers when they would not be coupled by interlayer hopping. The lower layer is more strongly $n$ doped than the upper layer. The four arrows represent the principal scattering vectors responsible for QPI (depicted here at different energies for clarity).

Figure 2

QPI in strongly doped MLG and BLG: (a) STM image of Cs intercalated MLG/Ir(111) ($I=0.1\mathrm{nA}$, $U=0.01\mathrm{V}$, image size $40\times 40{\mathrm{nm}}^2$). (b) Corresponding STS map at $E=-0.01\mathrm{eV}$. (c) FT image revealing electronic (triangles and hexagons) and structural (spots) features. For discussion, see text. (d) Sketch of the scattering processes causing the standing wave pattern in MLG. The expected FT has one feature at $\mathrm{\Gamma }$ and $K$, respectively. (e) STM image of Cs intercalated $\mathrm{BLG}/\mathrm{Ir}(111)$ ($I=0.1\mathrm{nA}$, $U=-0.09\mathrm{V}$, image size $30\times 30{\mathrm{nm}}^2$). The antiphase boundaries of the underlying Cs superstructure are visible, together with the honeycomb lattice of graphene. (f) STS map of BLG recorded at $E=-0.01\mathrm{eV}$. (g) FT image, revealing features at $\mathrm{\Gamma }$ (magnified in the inset) and $K$. (h) Sketch of the principal scattering processes. The expected FT has four features at $\mathrm{\Gamma }$ and $K$, respectively.

Figure 3

QPI analysis of $\mathrm{BLG}/(2\times 2)\mathrm{Cs}/\mathrm{Ir}(111)$: (a) FT of a STS image. (b) Averaged isotropic line scan around the $\mathrm{\Gamma }$ point of the FT. (c) Second derivative of the line scan, $d^{2}i/d{k}^2$. (d) (Left) Energy resolved $d^{2}i/d{k}^2$, superimposed with the band structure of BLG in the $K\mathrm{\Gamma }$ direction (red) in the form $E(2k)$ and the second derivative of the JDOS intensity in the background. The energy interval is 0.02 eV. The yellow dot represents $q_{22,\uparrow \downarrow }$ determined from intervalley scattering; see Fig. 4. We mark the positions of the expected scattering wave vectors. The apparent splitting of $q_{12,\uparrow \uparrow }$ and $q_{12,\uparrow \downarrow }$, as well as the smaller wave vector of CB1 compared to its JDOS feature, is due to warping effects. Features of the band structure that are visible in STS spectra (right) are highlighted with dashed lines.

Figure 4

$T$-matrix simulations of BLG near the chemical potential: (a) Calculated QPI pattern for an on-site potential of 1 eV on sublattice $A1$ and $E-E_D=(0.9+i0.04)\mathrm{eV}$. The top is the QPI pattern present in the upper layer, while the bottom pattern is the total QPI intensity. (b) Line scan along $\mathrm{\Gamma }K$ for the total QPI intensity, as well as the intensity present in the upper layer only. Both are normalized to one and obtained by averaging over 2000 different local impurities. At the $K$ point, the inner feature (red arrow) is clearly favored, while the outer feature is strongly suppressed (black arrow). (c) Experimental line scan along $\mathrm{\Gamma }K$ ($E=0.03\mathrm{eV}$), together with a four-component fit using Eq. (S18) in the Supplemental Material [22].