Negative Differential Resistance in van der Waals Heterostructures Due to Moiré-Induced Spectral Reconstruction

Formation of moiré superlattices is common in van der Waals heterostructures as a result of the mismatch between lattice constants and misalignment of crystallographic directions of the constituent two-dimensional crystals. Here we discuss theoretically electron transport in a van der Waals tunneling transistor in which one or both of the electrodes are made of two crystals forming a moiré superlattice at their interface. As a proof of concept, we investigate structures containing either an aligned graphene/hexagonal boron nitride heterostructure or twisted-bilayer graphene and show that negative differential resistance is possible in such transistors and that this arises as a consequence of the superlattice-induced changes in the electronic density of states and without the need for momentum-conserving tunneling present in high-quality exfoliated devices. We extend this concept to a device with electrodes consisting of aligned graphene on $\alpha {\text{-In}}_2{\mathrm{Te}}_2$ and demonstrate negative-differential-resistance peak-to-valley ratios of approximately $10$.

Figure 1

(a) The tunneling device with a source made of an aligned graphene/hBN heterostructure. Also shown are the distances $d$ and $d_g$, as well as contacts for voltages $V_b$ and $V_g$. (b) The conical bands and DOS of unperturbed monolayer graphene (top) and corresponding graphene minibands and DOS of an aligned graphene/hBN heterostructure (bottom). In the miniband spectrum, the black lines indicate the boundaries of a rhombic superlattice Brillouin zone. The Van Hove singularity in the DOS of the heterostructure is highlighted in red.

Figure 2

(a) Calculated tunneling current for a device from Fig. 1 as a function of voltages $V_g$ and $V_b$. (b) Tunneling current as a function of $V_b$ for constant $V_g$ from 0 V (orange) to 50 V (black) in steps of 10 V. The cuts in ($V_g,V_b$) space corresponding to current curves in (b) are shown with dashed lines in (a). (c) Diagrams showing alignment of source DOS and drain DOS as well as the positions of chemical potentials ${\mu }_s$ and ${\mu }_d+\mathrm{\Delta }$ for points in ($V_g,V_b$) space corresponding to tunneling currents marked as (I), (II), (III), and (IV) in (b).

Figure 3

(a) Low-energy band structure and DOS for tBLG with a misalignment angle of $2^{\circ }$. Note that both the position and the height of the Van Hove singularity change with misalignment angle. The black line indicates the superlattice Brillouin-zone edge. (b) Tunneling current from tBLG to graphene across a hBN barrier as a function of gate and bias voltages $V_g$ and $V_b$. (c) Tunneling current as a function of $V_b$ for constant $V_g$ from 0 V (orange) to 40 V (green) in steps of 10 V. The cuts in $(V_b,V_g)$ space corresponding to the current curves in (c) are shown with dashed lines in (b).

Figure 4

(a) Low-energy band structure of graphene on aligned $\alpha {\text{-In}}_2{\mathrm{Te}}_2$. The outline of the superlattice Brillouin zone is shown in red for clarity. (b) Corresponding DOS. (c) Tunneling current between two graphene-on-aligned-$\alpha {\text{-In}}_2{\mathrm{Te}}_2$ electrodes across a hBN barrier as a function of gate and bias voltages $V_g$ and $V_b$. (d) Absolute tunneling current as a function of $V_b$ for constant $V_g$ from 0 V (orange) to 15 V (green) in steps of 5 V. The cuts in $(V_b,V_g)$ space corresponding to the current curves in (d) are shown with dashed lines in (c). The current lines in (d) are scaled to highlight NDR features. (e) Same as (d) except for negative gate and bias voltages with steps of $-5\mathrm{V}$ from 0 V (orange) to $-15\mathrm{V}$ (yellow).