Umklapp-Enhanced Interlayer Valley Drag in Moiré Bilayers

Abstract

Van der Waals materials may be combined to form moiré patterns that are effectively crystal lattices. These systems are unique in that their in-plane unit cell sizes may be orders of magnitude larger than interlayer separations, leading to unique behaviors emerging from interlayer interactions. In this work, we investigate interlayer valley drag in lattice-matched moiré bilayers, demonstrating a remarkable enhancement due to umklapp scattering. In contrast to drag phenomena in more conventional two-dimensional systems, interlayer valley drag appears at first order in the interlayer interaction, and remains non-vanishing in the low temperature limit even at this low order in the interlayer coupling. We propose an experimental geometry, feasible with current state-of-the-art fabrication techniques, to detect and characterize this effect in moiré bilayer systems.

Figures (2)

• Figure 1: Band-structure and valley drag condutivity: (a) Left: Band structure of aligned graphene/hBN heterostructure near the K and $\mathrm{K'}$ valleys of graphene, plotted along high-symmetry paths in the moiré Brillouin zone. For the K valley, the path connects $\mathbf{k}_1 = (1/2,\sqrt{3}/2)$, $\mathbf{k}_2 = (0,0)$, and $\mathbf{k}_3 = (1,0)$ and for the $\mathrm{K'}$ valley, the path connects $\mathbf{k}_1 = (-1/2,\sqrt{3}/2)$, $\mathbf{k}_2 = (-1,0)$, and $\mathbf{k}_3 = (0,0)$, in units of $k_\epsilon$. Right: Density of states corresponding to these bands. (b) Valley drag conductivity $\sigma_{21,xx}^v$ as a function of the chemical potentials $\mu_1$ and $\mu_2$ of the top and bottom layers, respectively, computed for a system size $N = 60 \times 60$ at temperature $k_B T = 1\,\mathrm{meV}$. (c) Temperature dependence of $\sigma_{21,xx}^v$. (d) Dependence of $\sigma_{21,xx}^v$ on the interlayer separation $d$. We have used $\hbar \delta = 1$ meV.
• Figure 2: Proposed experiment: A current injected in the top (red) layer generates a transverse valley current via the valley Hall effect (VHE). The diffusing valley current drags a valley current in the bottom (blue) layer and induces a nonlocal voltage at a distance $L$ via the inverse valley Hall effect (IVHE). The layers have width $W$ and are separated by an hBN spacer of thickness $d$.