Spatially resolving unconventional interface Landau quantization in a graphene monolayer-bilayer planar junction

Hybrid quantum Hall (QH) junctions have been extensively studied by transport measurements due to their exciting physics and device applications. Here we report on spatially resolving electronic properties of such a junction on the nanoscale. We present a subnanometer-resolved scanning tunneling microscopy (STM) and scanning tunneling spectroscopy study of a monolayer-bilayer graphene planar junction in the QH regime. The atomically well-defined interface of such a junction allows us to spatially resolve the interface electronic properties. Around the interface, we detect Landau quantization of massless Dirac fermions as expected in the graphene monolayer for filled states of the junction, whereas unexpectedly, only Landau quantization of massive Dirac fermions as expected in the graphene bilayer is observed for empty states. The observed unconventional interface Landau quantization arises from the fact that the quantum conductance across the interface is solely determined by the minimum filling factors (number of edge modes) in the graphene monolayer and bilayer regions of the junction. Our finding opens the way to spatially explore the QH effect of different graphene hybrid structures only using a STM.

Figure 1

STM image and STS of a graphene monolayer-bilayer planar junction. (a) A typical atomic-resolution STM image of a graphene monolayer-bilayer planar junction on a Rh foil ($V_{\mathrm{sample}}=-880\mathrm{mV}$ and $I=0.35\mathrm{nA}$). The inset shows an enlarged image in the blue frame. The hexagonal structures of graphene are overlaid onto the STM image. In the rippled region (monolayer region), we can observe a honeycomb lattice, whereas, in the relatively flat area (bilayer region), only a triangular lattice can be observed. (b) Tunneling spectra, i.e., $dI/dV-V$ curves, taken at the red solid circle marked in panel (a). They show LLs of massless Dirac fermions in the graphene monolayer. For clarity, the curves are offset on the $Y$ axis, and LL indices are marked. (c) STS spectra recorded at the blue circle marked in panel (a). The spectra show LLs of massive Dirac fermions, and the LL indices are marked. The $\mathrm{L}{\mathrm{L}}_{\left(0,+\right)(1,+)}$ and $\mathrm{L}{\mathrm{L}}_{(0,-)(1,-)}$ projected on the top and the bottom graphene layers, respectively, and an energy gap between $\mathrm{L}{\mathrm{L}}_{(0,+)(1,+)}$ and $\mathrm{L}{\mathrm{L}}_{(0,-)(1,-)}$ is measured to be about 80 meV. (d) LL peak energies recorded in the rippled region show square-root dependence on both the LL index and the magnetic field, i.e., $\mathrm{sgn}\left(n\right){\left(\left|n\right|B\right)}^{1/2}$ as expected for massless Dirac fermions in the graphene monolayer. The red solid line is the linear fit of the data with the slope yielding a Fermi velocity of $v_F=\left(1.208\pm 0.016\right)\times {10}^6\mathrm{m}/\mathrm{s}$ for electrons and $v_F=\left(0.992\pm 0.014\right)\times {10}^6\mathrm{m}/\mathrm{s}$ for holes. The inset: the schematic LL structure of the graphene monolayer in the quantum Hall regime. (e) LL peak energies of the Bernal bilayer plotted against $n(n-1)B$ [2]. The purple lines are fits of the data with Eq. (2), yielding the effective mass of $\left(0.0110\pm 0.0005\right)m_e$ for both electrons and holes. The inset is the schematic LLs of the Bernal bilayer in the quantum Hall regime with a finite band gap. The charge neutrality points $N_c$ of both the monolayer and the bilayer regions are determined as $(73\pm 5)$ and $\left(112\pm 5\right)\mathrm{meV}$, respectively.

Figure 2

Unconventional Landau quantization around the interface of the junction. STS spectra obtained at different positions [as marked in Fig. 1] around the interface in magnetic fields of (a) $B=0\mathrm{T}$, (b) 3 T, (c) 4 T, and (d) 5 T, respectively. The blue shadow in (a) indicates an opening gap about 80 meV in the bilayer region of the junction. LL indices of massless and massive Dirac fermions are marked with red and blue numbers, respectively.

Figure 3

(a) LL peak energies of holes (LL energies below the $N_c$ of the junction) recorded at positions 4–6 show a linear dependence on $\mathrm{sgn}\left(n\right){\left(\left|n\right|B\right)}^{1/2}$, which corresponds to the Landau quantization of massless Dirac fermions in the graphene monolayer. The Fermi velocity of the holes is determined as $v_F=\left(1.22\pm 0.01\right)\times {10}^6\mathrm{m}/\mathrm{s}$. (b) LL peak energies of electrons (LL energies above the $N_c$ of the junction) recorded at positions 4–6 plotted against $n(n-1)B$ [2], which corresponds to the Landau quantization of massive Dirac fermions in the graphene bilayer. The effective mass of electrons yielded from the fit curve is $\left(0.0110\pm 0.0005\right)m_e$. The insets of (a) and (b) show schematics of low-energy dispersion with quantized LLs in the graphene monolayer and bilayer, respectively. Only the LLs plotted on solid curves are observed in the STS spectra at positions 4–6.

Figure 4

(a) Schematic showing the link between the tunneling spectrum and the LLs is a graphene monolayer. Left panel: tunneling spectrum taken in the monolayer region (the rippled region) of the junction under the magnetic field of 5 T. The spectrum shows pronounced peaks of discrete LLs. Right panel: schematic of LLs in monolayer graphene in the quantum Hall regime showing their upward and downward bendings at the sample edges. The green line indicating the Fermi energy lies in the gap between $N=0$ and $N=-1$ levels. Ballistic channels form when the Fermi energy intersects with the filled LLs at the edge. The dotted lines are guides to the eyes. (b) The Hall conductivity in the monolayer-bilayer planar junction. We show the expected Hall conductivity as a function of $ng{e}^2/h$ for the graphene monolayer and for the Bernal bilayer, where $n$ is an integer, $g$ is the system degeneracy, and $e^2/h$ is conductance quantum. The Hall conductivity of the monolayer-bilayer planar junction is also plotted according to Eq. (3). The corresponding sequences of LLs are shown in red and blue for massless Dirac fermions and massive Dirac fermions, respectively. Obviously, only LLs of massless (massive) Dirac fermions can be observed for holes (electrons). (c) Schematic of the two different channels for the current transferring from the rippled graphene sheet to the Rh substrate as illustrated by red and blue dashed curves. The resistance for the process that the current passes through the interface of the junction through the topmost graphene sheet is defined as $R_{\mathrm{G}}\left(L\right)$ [or $R_{\mathrm{G}}\left(L^{\prime }\right)$]. The resistance for the process that the current transfers from graphene to the Rh foil is defined as $R_{\text{G-Rh}}$. $R_{\text{G-G}}$ represents the resistance for the process that the current tunnels from the topmost graphene sheet to the underlying layer.