Atomic resolution imaging of the two-component Dirac-Landau levels in a gapped graphene monolayer

The wave function of Dirac fermions is a two-component spinor. In graphene, a one-atom-thick film showing two-dimensional Dirac-like electronic excitations, the two-component representation, reflects the amplitude of the electron wave function on the $A$ and $B$ sublattices. This unique property provides unprecedented opportunities to image the two components of Dirac fermions spatially. Here, we report atomic resolution imaging of two-component Dirac-Landau levels in gapped graphene monolayers by scanning tunneling microscopy and spectroscopy. A gap of about 20 meV, driven by inversion symmetry breaking by the substrate potential, is observed in the graphene sheets on both SiC and graphite substrates. Such a gap splits the $n=0$ Landau level (LL) into two levels, $0_{+}$ and $0_{-}$. We demonstrate that the amplitude of the wave function of the $0_{+}$ LL is mainly on the $A$ sites and that of the $0_{-}$ LL is mainly on the $B$ sites of graphene, characterizing the internal structure of the spinor of the $n=0$ LL. This provides direct evidence of the two-component nature of Dirac fermions.

Figure 1

Electronic band structure and Landau quantization in a gapped graphene monolayer. (a) Schematic diagram of a graphene monolayer with a staggered sublattice potential breaking the inversion symmetry. The $A$ and $B$ sites are denoted by blue and red balls, respectively. (b) Energy spectrum of a graphene monolayer with broken inversion symmetry. (c) Schematic Landau levels and DOS of a gapped graphene monolayer in the quantum Hall regime. Peaks in the DOS correspond to the Landau Levels $n_{\lambda }$ ($\lambda =+,-$ denote the $K^{\prime }$ and $K$ valleys).

Figure 2

STM images and STS spectra of gapped graphene sheets. (a) and (d) show STM images of graphene on a SiC $\left(000\overline{1}\right)$ terrace and on highly oriented pyrolytic graphite (HOPG), respectively. The periodic protuberances in (a) are attributed to the moiré pattern arising from a stacking misorientation between adjacent graphene layers. (b) and (e) show zoom-in atomic-resolution topographies obtained in the black frame in (a) and (d), respectively. The honeycomb structures of graphene are overlaid onto the STM images. The STM images show a triangular lattice, indicating the broken sublattice symmetry. Here, we define the bright spots as the $A$-site atoms and the dark spots as the $B$-site atoms. (c) and (f) show $\mathit{dI}/\mathit{dV}$ spectra obtained at different positions, as marked in different colors in (b) and (e), respectively. The black arrows in both panels denote the position of the charge neutrality point of the topmost graphene sheets in zero magnetic field. In the magnetic field of 8 T, the spectra exhibit Landau quantization of Dirac fermions, as expected in a gapped graphene monolayer. LL indices are marked. For the graphene on both substrates, the $n=0$ LL splits into two peaks and the intensity of the two peaks depends sensitively on the recorded positions.

Figure 3

Conductance maps of the gapped graphene monolayer on SiC at different energies. (a) The conductance map recorded at the bias voltage of the $0_{+}$ LL ($V_{\mathrm{sample}}=65.5\mathrm{mV}$). (b) The conductance map recorded at the bias voltage of the $0_{-}$ LL ($V_{\mathrm{sample}}=45\mathrm{mV}$). (c) The conductance map recorded at the bias voltage of the +1 LL ($V_{\mathrm{sample}}=108\mathrm{mV}$). (d) The conductance map recorded at the bias voltage of the −1 LL ($V_{\mathrm{sample}}=-22\mathrm{mV}$). The honeycomb structure of graphene and the atomic resolution STM image are overlaid onto the maps. The amplitude of the $0_{+}$ and +1 LLs on the $A$ sites is much stronger than that on the $B$ sites, whereas the amplitude of the $0_{-}$ and −1 LLs on the $B$ sites is much stronger than that on the $A$ sites.

Figure 4

Internal structures of different LLs. (a) The conductance map recorded at the bias voltage of the +3 LL for the graphene on the SiC substrate ($V_{\mathrm{sample}}=170\mathrm{mV}$). (b) Vertical line cuts of the conductance maps of the $0_{+}, 0_{-}$, −1, +1, and +3 LLs along the $A$ and $B$ atoms. The curves are offset vertically for clarity, and the zero-line for these curves is denoted by dashed lines. (c) The theoretical local DOS (LDOS) showing amplitudes of these LLs on the $A$ and $B$ atoms. The amplitudes of the two components are calculated according to Eq. (2), and we use Gaussian peaks to reflect the linewidth of the DOS at the $A$ and $B$ atoms.