Experimental observation of surface states and Landau levels bending in bilayer graphene

We report on microscopic measurements of the low-energy electronic structures both at the zigzag and armchair edges of bilayer graphene using scanning tunneling microscopy and spectroscopy (STM and STS). We have found that, both in the absence and in the presence of a magnetic field, an almost zero-energy peak in the density of states was localized at the zigzag edges, as expected for the surface states at the zigzag edges of bilayer graphene. In the quantum Hall regime, we have clearly observed Landau levels bending away from the charge neutrality point near both the zigzag and armchair edges. Such a result is direct evidence for the evolution of Landau levels into quantum Hall edge states in graphene bilayers. Our experiment indicates that it is possible to explore rich quantum Hall physics in graphene systems using STM and STS.

Figure 1

(a) $100\mathrm{nm}\times 100\mathrm{nm}$ STM topographic image of a bilayer graphene region on a graphite surface ($V_b=0.2\mathrm{V}, I=0.2\mathrm{nA}$). Inset (upper): Atomic resolution image of the graphene bilayer showing the triangular contrasting, which reflects only one of the two sublattices of the topmost graphene due to the inversion symmetry breaking in Bernal ($AB$-stacked) bilayers. Inset (lower): Height profile along the black line shows the height difference of two steps $\sim \left(0.70\pm 0.01\right)\mathrm{nm}$, which is slightly larger than the equilibrium spacing of the bilayer step ($\sim 0.67\mathrm{nm}$). (b) Tunneling spectra of the graphene bilayers recorded away from the edges under various magnetic fields. LL peak indices are labeled ($+/-$ are valley indices) and the data are offset in the $Y$ axis for clarity. (c) The LL peak energies extracted from (b) plotted vs the magnetic fields $B$. The solid curves are the fitting of the data with Eq. (1).

Figure 2

Atomic resolution images of (a) a zigzag bilayer edge and (b) an armchair bilayer edge. The insets are the the fast Fourier transforms (FFTs) of the STM images. The outer hexangular spots and inner bright spots correspond to the reciprocal lattice of the graphene lattice and the interference of the scattering, respectively. (c) Schematic of the Bernal bilayer graphene with the zigzag and armchair edges. The green dots, representing a set of sublattices imaged in STM topography, can be used to determine the type of graphene edge. Energy spectrum of (d) an unbiased and (e) biased bilayer graphene with zigzag edges. The green curves correspond to the quasilocalized surface states of the two zigzag edges. (f) Energy spectrum of an unbiased (solid curves) and biased (dotted curves) bilayer graphene ribbon with armchair edges.

Figure 3

(a) Spatially resolved STS spectra recorded along the line drawn in (b) around the zigzag edge of bilayer graphene under 0 T. The DOS peaks marked by green arrows correspond to the quasilocalized surface states of the zigzag edge in graphene bilayer. The blue and red dashed lines label the positions of the VBE and the CBE in the bulk graphene bilayer. (c) The decay of the DOS peak height of the surface state obtained in (a). The blue and gray curves correspond to the expected decaying behavior of the surface states in graphene bilayer and monolayer, respectively.

Figure 4

(a) and (c) show the spatial variation of the LL spectra measured at 7 T around the zigzag and armchair edges of bilayer graphene, respectively. The dashed lines indicate the energy positions of the $\mathrm{L}{\mathrm{L}}_{(0,1,-)}$ and $\mathrm{L}{\mathrm{L}}_{(0,1,+)}$ in the bulk of bilayer graphene. The blue and red arrows mark the spatial evolution of the $\mathrm{L}{\mathrm{L}}_{(0,1,-)}$ and $\mathrm{L}{\mathrm{L}}_{(0,1,+)}$ peaks. (b) and (d) show LL spectra maps at 7 T recorded around the zigzag and armchair edges, respectively. In (a) and (b), the peaks marked by green arrows correspond to the quasilocalized surface states of the zigzag edge. (e) Evolution of the peak positions and heights at 7 T with distance from the armchair edge on the conduction-band side. The inset shows LL peak heights extracted from (e) as a function of the distance from the edge. (f) LL bending as a function of distance around the armchair edge measured at 8 T. It shows an explicit shift of the energy positions for the $\mathrm{L}{\mathrm{L}}_{(0,1,+)}, \mathrm{L}{\mathrm{L}}_2$, and $\mathrm{L}{\mathrm{L}}_3$ toward high energy when approaching the edge. The insets show calculated probability densities for the wave functions of the $\mathrm{L}{\mathrm{L}}_{(0,1,+)}, \mathrm{L}{\mathrm{L}}_2$, and $\mathrm{L}{\mathrm{L}}_3$ at 8 T. (g) Shift lengths of the $\mathrm{L}{\mathrm{L}}_{(0,1,+)}$ and $\mathrm{L}{\mathrm{L}}_2$ bending from the bilayer edges taken at different magnetic fields. The solid dots (open dots) correspond to the data of armchair edges (zigzag edges). The dashed lines are the average values of $\sim 1.4l_B$ and $\sim 2.0l_B$ for the $\mathrm{L}{\mathrm{L}}_{(0,1,+)}$ and $\mathrm{L}{\mathrm{L}}_2$, respectively.