Signatures of van Hove Singularities Probed by the Supercurrent in a Graphene-hBN Superlattice

The band structure of graphene can be strongly modified if its lattice is aligned with the one of a boron nitride substrate. A moiré superlattice forms, which manifests itself by the appearance of new Dirac points, accompanied by van Hove singularities. In this work, we present supercurrent measurements in a Josephson junction made from such a graphene superlattice in the long and diffusive transport regime, where the critical current depends on the Thouless energy. We can then estimate the specific density of states of the graphene superlattice from the combined measurement of the critical current and the normal state resistance. The result matches with theoretical predictions and highlights the strong increase of the density of states at the van Hove singularities. By measuring the magnetic field dependence of the critical current, we find the presence of edge currents at these singularities. We explain it by the reduction of the Fermi velocity associated with the van Hove singularity, which suppresses the supercurrent in the bulk while the electrons at the edges remain less localized, resulting in an edge supercurrent. We attribute these different behaviors of the edges to defects or chemical doping.

Figure 1

(a) Top: Schematic side view of the device. Bottom: False-colored SEM image. The graphene (brown) is encapsulated between hBN (green) and contacted with MoRe (blue). The white scale bar corresponds to $5\mu \mathrm{m}$. (b) Normal state resistance (red line) and critical current (blue line) as a function of gate voltage $V_g$ for junction $D$. (c) Differential resistance as a function of $V_g$ and dc current bias $I$ for junction $D$. Right: Line cut at $V_g=-26\mathrm{V}$.

Figure 2

Density of state estimated from measured $R_N$ and $I_c$ [Eq. (1)] (in red, blue, yellow, and green, respectively, for $B$, $C$, $D$, and $E$) compared to a calculation for $\theta =0.7°$ (black line), as a function of the charge carrier density. The moiré superlattice parameters (defined in Ref. [52]) used to produce the theoretical DOS are $U_0^{+}=8.5\mathrm{meV}$, $U_1^{+}=-8.5\mathrm{meV}$, and $U_3^{+}=-14.7\mathrm{meV}$. The gray shaded areas correspond to regions where the critical current was too small to be measured.

Figure 3

(a) Differential resistance as a function of the current bias and magnetic field at $n_1=-1.4\times {10}^{12}{\mathrm{cm}}^{-2}$ (blue star) and $n_2=-2.7\times {10}^{12}{\mathrm{cm}}^{-2}$ (red star). White dashed line, expected Fraunhofer pattern for a homogeneous current density. (b) Normalized critical current as a function of magnetic field $B$ and carrier density $n$ measured in junction $D$, superimposed with the calculated DOS in green. (c) Calculated current density as a function of $n$ and position along the contacts. (d) Line cuts of (c) at $n_1$ and $n_2$. The black dashed lines indicate the junction edges.

Figure 4

DOS as a function of charge carrier density $n$ in junction $D$, estimated from the bulk current (blue line; see inset) and the total current (yellow line). Inset: Current distribution at the VHS at a negative charge carrier density.