Miniband Generation by Surface Acoustic Waves

Abstract

We introduce a new class of tunable periodic structures, formed by launching two obliquely propagating surface acoustic waves on a piezoelectric substrate that supports a two-dimensional quantum material. The resulting acoustoelectric superlattice exhibits two salient features. First, its periodicity is widely tunable, spanning a length scale intermediate between moiré superlattices and optical lattices, enabling the formation of narrow, topologically nontrivial energy bands. Second, unlike moiré systems, where the superlattice amplitude is set by intrinsic interlayer tunneling and lattice relaxation, the amplitude of the acoustoelectric potential is externally tunable via the surface acoustic wave power. Using massive monolayer graphene as an example, we demonstrate that varying the frequencies and power of the surface acoustic waves enables in-situ control over the band structure of the 2D material, generating flat bands and nontrivial valley Chern numbers, featuring a highly localized Berry curvature.

Figures (4)

• Figure 1: (A) Schematic of the device. A 2D material is placed on a piezoelectric substrate, separated by a spacer layer. Two SAWs propagating through the substrate, generate a superlattice potential in the 2D material. (B) The SAW wavevectors $\bm{q}_1$ and $\bm{q}_2$ define a mBZ which tiles a K-lattice within the original BZ. (C) The valence and conduction bands of the 2D material split into a set of minibands defined over the mBZ.
• Figure 2: Evolution of the minibands (A–D) and corresponding Berry curvature of the top valence miniband (F–I) at the K valley as the SAW wavelength is varied for $m = 20$ meV and $P = 1$ W/m. Minibands are labeled by their valley Chern numbers. At small wavelengths, the conduction and valence minibands near charge neutrality ($E = 0$) have zero Chern number. As $\lambda$ increases, a band inversion first occurs at the Dirac point $\Gamma$, followed by a second inversion at the $M$ point. (E) Direct gaps between top valence and bottom conduction minibands at $\Gamma$ and the band edge show a maximum value of $\sim 5$ meV at $\lambda \approx 66$ nm. (J) Even at this wavelength, where the gap is maximal, the Berry curvature (BC) remains highly localized in momentum space.
• Figure 3: Support of $C_v$, the valley Chern number of the top valence miniband, in the $m$-$\lambda$ plane for $P=1$ W/m. Inset: direct and indirect gaps between the top valence miniband and bottom conduction miniband along the dotted line. A topological valley Hall response appears for $63~\textrm{nm} \lesssim \lambda \lesssim 68~\textrm{nm}$, where the indirect gap is positive.
• Figure 4: (A) Bandwidth of the highest valence miniband as a function of $\lambda$ for selected $(m,P)$ values (B) Average energy of top valence minibands as a function of $\lambda$ for $P=0.1$ W/m and $m=40$ meV; the curve width reflects the bandwidth. (C) Atomic-like spectra at $\lambda = 180$ nm, $m=40$ meV, and $P = 0.1$ W/m. (D) Dispersive minibands with non-zero $C_v$ at $\lambda=158$ nm, $m=20$ meV and $P=0.2$ W/m.