Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene

Twisted bilayer graphene (tBLG) forms a quasicrystal whose structural and electronic properties depend on the angle of rotation between its layers. Here, we present a scanning tunneling microscopy study of gate-tunable tBLG devices supported by atomically smooth and chemically inert hexagonal boron nitride (BN). The high quality of these tBLG devices allows identification of coexisting moiré patterns and moiré super-superlattices produced by graphene-graphene and graphene-BN interlayer interactions. Furthermore, we examine additional tBLG spectroscopic features in the local density of states beyond the first van Hove singularity. Our experimental data are explained by a theory of moiré bands that incorporates ab initio calculations and confirms the strongly nonperturbative character of tBLG interlayer coupling in the small twist-angle regime.

Figure 1

STM topographic images of tBLG/BN. (a) Gated tBLG/BN field effect transistor. The tip bias $(-V_s)$, back-gate voltage $\left(V_g\right)$, and grounding scheme are shown. (b)–(d) STM topographic images show coexisting graphene-graphene and graphene-BN moiré patterns. Tunneling parameters: (b) $V_s=-0.2\mathrm{V},I=0.30\mathrm{nA},V_g=0\mathrm{V}$; (c) $V_s=-0.3\mathrm{V},I=0.30\mathrm{nA},V_g=+30\mathrm{V}$; (d) $V_s=-3.0\mathrm{V},I=0.02\mathrm{nA},V_g=0\mathrm{V}$.

Figure 2

STM topographic images of tBLG/BN for different graphene-graphene twist angles. (a)–(c) STM topographic images of tBLG show both the top-layer atomic lattices and the graphene-graphene moiré patterns for decreasing twist angle ${\theta }_{g-g}$. No graphene-BN moiré patterns are visible in these images since ${\theta }_{g-BN}>{15}^{\circ }$. Tunneling parameters: (a) $V_s=-0.5\mathrm{V},I=0.1\mathrm{nA},V_g=0\mathrm{V}$; (b) $V_s=-0.5\mathrm{V},I=0.2\mathrm{nA},V_g=+30\mathrm{V}$; (c) $V_s=-0.1\mathrm{V},I=0.1\mathrm{nA},V_g=-60\mathrm{V}$.

Figure 3

STM $dI/dV$ spectra of tBLG for different graphene-graphene moiré wavelengths. The $dI/dV$ spectra reveal three features (the VHS peak labeled by a black arrow, first dip labeled by a red arrow, and second dip labeled by a green arrow) that disperse with graphene-graphene moiré wavelength ${\lambda }_{g-g}$. Curves have been shifted vertically for clarity. Initial tunneling parameters: $V_s=1\mathrm{V},0.2\mathrm{nA}\le I\le 0.4\mathrm{nA}$, ac modulation $6\mathrm{mV}\le V_{\mathrm{rms}}\le 8\mathrm{mV}$.

Figure 4

Calculated tBLG electronic structure. (a) Dependence of theoretical tBLG spectroscopic features on moiré wavelength ${\lambda }_{g-g}$ (dashed lines) compared to experiment (symbols). Experimental error bars are approximately the size of the symbols. (b) Schematic plot of the repeated-zone momentum space structure of tBLG. The Wigner-Seitz cell (green line) of the moiré reciprocal lattice and the Dirac points of the two graphene layers (red and black circles) are shown. A–D mark high symmetry points in the moiré Brillouin zone. (c) Calculated moiré-induced band structure of tBLG for ${\lambda }_{g-g}=7.6\mathrm{nm}$ plotted along $k$ space lines connecting points A-B-C-D-A in (b). Gray, red, and green highlights locate the energies of the VHS peak, the first dip, and the second dip, respectively. (d) Theoretical DOS of tBLG for ${\lambda }_{g-g}=7.6\mathrm{nm}$ calculated by integrating the band structure over the moiré Brillouin zone and then Gaussian broadening with a 15 meV width (the broadening represents the effects of temperature, finite quasiparticle lifetime, and ac wiggle voltage). The semitransparent highlighting bars are located at the same energies as in (c) and match the three spectroscopic features observed in the experiment.