Visualizing Atomic-Scale Negative Differential Resistance in Bilayer Graphene

We investigate the atomic-scale tunneling characteristics of bilayer graphene on silicon carbide using the scanning tunneling microscopy. The high-resolution tunneling spectroscopy reveals an unexpected negative differential resistance (NDR) at the Dirac energy, which spatially varies within the single unit cell of bilayer graphene. The origin of NDR is explained by two near-gap van Hove singularities emerging in the electronic spectrum of bilayer graphene under a transverse electric field, which are strongly localized on two sublattices in different layers. Furthermore, defects near the tunneling contact are found to strongly impact on NDR through the electron interference. Our result provides an atomic-level understanding of quantum tunneling in bilayer graphene, and constitutes a useful step towards graphene-based tunneling devices.

Figure 1

(a) Experimental configuration for the local tunneling spectroscopy, consisting of an STM tip and bilayer graphene on silicon carbide. (b) STM topographic image ($1.5\times 1.5{\mathrm{nm}}^2$) taken on bilayer graphene with sample bias of $-0.2\mathrm{V}$ and tunneling current of 300 pA. Inset shows the atomic structure overlaid with part of the STM image. Balls are carbon atoms, and solid (dashed) lines represent chemical bonds in the top (bottom) layer. (c) Point—$dI/dV$ spectrum and a corresponding $I\mathrm{\text{−}}V$ spectrum (inset) taken on the $B_T$ site. The red line overlaid is the result of model simulations. Red arrows highlight NDR. (d) $dI/dV$ spectra normalized by $I\mathrm{\text{−}}V$ at each initial setting current marked. Dotted lines in (c) and (d) indicate conductance zero.

Figure 2

(a) Point—$dI/dV$ spectra taken on three different atomic sites of bilayer graphene, and its spatial average offset for clarity. Dotted lines indicate conductance zero. (b), (c) $dI/dV$ maps taken with a $96\times 96$ grid at the bias voltage indicated by arrows in (a). The inset in (b) shows the simultaneously acquired topographic image overlaid with the atomic structure of bilayer graphene.

Figure 3

(a) Band structure of bilayer graphene with (solid lines) and without (dashed lines) the band gap. Red and blue colors in a low-energy band pair represent the atomic site, at which corresponding states are localized ($B_T\mathrm{\text{:}}\mathrm{red}$, $A_B\mathrm{\text{:}}\mathrm{blue}$). (b) Site-resolved density of states in biased bilayer graphene [26, 27]. (c) Energy-distribution curve at the $K$ point taken by ARPES. Data were taken at the Advanced Light Source, using a Scienta R4000 electron analyzer (VG-Scienta, Sweden) and a 95-eV photon. Energy and angular resolutions were 30 meV and 0.1°. Red and blue arrows indicate positions of two van Hove singularities. (d) Energy diagram for the tunnel junction of the tip and the sample. Red solid and dashed lines are, respectively, the sample density of states at $V_0$ for local maximum current ($I_{\max }$) and at $V_1$ for local minimum current ($I_{\min }$) after broadening by Gaussian. The gray line is the tip density of states, and the shaded region is the filled tip states below $E_F$.

Figure 4

(a) STM image ($10\times 10{\mathrm{nm}}^2$) with $-0.05\mathrm{V}$ and 300 pA, where a local defect (the yellow blob) is present at the corner. $dI/dV$ maps taken (b),(c) at two different regions about 16 nm away from defects and (d) at a region right next to a defect. The atomic structure of bilayer graphene is overlaid. (e),(f) Schematic illustration for two possible NDR patterns due to constructive or destructive interference of defect scatterings. (g) Normalized $dI/dV$ spectra taken on three different $B_T$ atoms marked in (b) and (d). Solid and dotted lines indicate $E_D$ and conductance zero, respectively.